combinedgroupquestions-exam1

56
Chapter 2 In order to project the future of the business, a restaurant owner collect opinions from their customers by sending surveys in the restaurant, the survey mainly concerns about customers's satisfaction over the restaurant's food.Identify the Ws and name the variables Answer:what---customer's satisfaction over the restaurant's food Who---The restaurant's customer Where---in the restaurant When---recently Why---in order to project the future of the business Variable---customer's satisfaction over the restaurant 's food Chapter 3 The students union is considering holding a party to welcome the new student, they put an ad poster asking people to give their opinion on the activities during the party, what kind of sampling strategy is involved and what biases might result? Answer:Volunteer response,those individuals who see the

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Page 1: CombinedGroupQuestions-exam1

Chapter 2In order to project the future of the business a restaurant owner collect opinions from their customers by sending surveys in the restaurant the survey mainly concerns about customerss satisfaction over the restaurants foodIdentify the Ws and name the variablesAnswerwhat---customers satisfaction over the restaurants foodWho---The restaurants customerWhere---in the restaurantWhen---recentlyWhy---in order to project the future of the businessVariable---customers satisfaction over the restaurant s food

Chapter 3The students union is considering holding a party to welcome the new student they put an ad poster asking people to give their opinion on the activities during the party what kind of sampling strategy is involved and what biases might resultAnswerVolunteer responsethose individuals who see the ad and feel strongly about the issue will respond the opinions may not be representative of the rest of the public

Chapter 4Below are the dates from a primary school on how do students spend their moneyThe way student spend their money Percent1food and drink 602toy 153stationery 104other entertainment 15(1) Is that reasonable to conclude that toy and other entertainment were the cause of

30 of the students expenditure(2) Answerbecause the categories do not overlap(3) Create an appropriate display for these data(4) Answer either be a bar chart or pie chart

Chapter 5This histogram displays heights of black cherry trees Give a short summary of this distribution(Shape Centre Spread)

Answer Shape-the distribution is approximately symmetric with a single peak making it unimodal Centre-the centre of the distribution is close to the single peak The bin values can be added up as follows 3+3+8+10+5+2=31 The median occurs to the 15th data point Fourteen data points are contained in the first three bins The 15 th

data point is therefore contained in the 4th bin Spread- the spread is determined from the range of data high minus low 90-60=30

Chapter 6Please consider whether the following statements are true of false1 If an event is unlikely to occur its probability could be negative2 The probability of the set of all possible outcomes must be 13 For event A and B the formula P(A and B)=P(A)P(B) is always correctAnswer FTF

Chapter 7Please compute the correlation coefficientSuppose the data pairs are X 2 14 5 20 9Y 7 4 9 12 13

Answer r=0206Chapter 7

1Casio produced 1 million electronic watches in April 2012 Checked 1000 electronic watches by random sampling without repetition the Casio drew out the data that the failure rate was 2 If we assumed the pass rate would be 9973 Please calculate the range of variables of failure rate

pminustup≪P≪ p+tu p

068≪P≪332

Chapter8

2A school randomly samples 10 male students within the all male students Their average height is 170CM standard deviation is 12CM What is the percentage that the male students average height will be sure between the 1605CM---1795CM

t=Δx

minusiquest

Δ yminusiquestiquest

iquest

minus iquestxminusiquest tux

minusiquestiquestiquest iquest =1605 (iquest170iquest iquestxminusiquestiquest

Or + tuxminusiquest

xminusiquest iquest iquest=1795 t=2503

F(t)=9876

Chapter9

3A automobile manufacturer wants to analysis the correlation between the quantity of shipment and the quantity of automobile ownership They have investigated a region

Year Quantity of Shipment (x)

(million tons per kilometers )

Quantity of Automobile (y)

(Thousand )

2000 410 27

2001 450 31

2002 560 35

2003 600 40

2004 640 52

2005 680 55

2006 750 58

2007 850 60

2008 980 65

2009 1100 73

Please calculate the correlation coefficient

(r=0956)

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 What is the difference between contingency tables and cross tabulation2 What is the difference between interval and ordinal

3 In book page 97 Table 54 how to get the number of (MidPt- Mean)2 4 What is the table percentages5 How to calculate the percentile Is there any difference between sample and population6 Which of the following correlation properties is right (In assignment) a Correlation is always between -2 and 2 b Correlation treats X and Y unsymmetrical c Correlation measures whether the two variables are linear association d Correlation has no units7 What is the type of the data The number of students in a statistics course The letter grades received by students in a computer science class

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Whats statistics

Chapter 2

Customers satisfaction (eg very satisfactor

ysatisfactorydissatisfactoryvery dissatisfactory)belongs to()A

Nominal B Ordinal C Interval D Ratio

Chapter 3 What is the different between stratified sampling and cluster sampling

Chapter 4Talk about the difference between bar chart and histogram

Chapter 5Give the answers of mean median mode range variance and standard deviation (35 40 45 30 35 45 50 35 40 35)

Chapter 7 what are the features of correlation-r

Chapter 8 What are right belowa if events A and B are mutually exclusive P(A+B)=P(A)+P(B)

b P(A+B+C)=P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC)c P(AB)=P(B) P(A|B) (P(A)gt0 P(B)gt0)d P(A|B)= P(AB)P(B) (P(A)gt0 P(B)gt0)

Chapter 9 Suppose the heights of employees in one company is normally distributed with a mean of 171cm and a standard deviation of 5cm what is the probability of employees height less than 176cm

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1 Generally what are statistics used for

Chapter 2 The classification of student hobby in university of Windsor (sport music computer and other) is an example of A a categorical random variable B a discrete random variable C a continuous random variable D a parameter

Chapter 3The administration of a large university is interested in learning about the types of wellness programs that would interest its employees To do this they plan to survey a sample of their employees Suppose that there are five categories of employees (administration faculty professional staff clerical and maintenance) and the university decides to randomly select ten individuals from each category This sampling plan is calledA Systematic SamplingB Simple Random SamplingC Stratified SamplingD Cluster SamplingE Convenience Sampling

Chapter 4 What is pie chart

Chapter 5 Table 5-1 shows us the annual temperature in China from 2005 to 2010 Annual Temperature in China 2005 2006 2007 2008 2009 2010 Tempera 82 75 104 97 88 100

ture (degrees Celsius)

1) What are the Mean Median and Mode for these data 2) Would you use the mean or the median to summarize the center of this distribution Why

Chapter 6 Event A and B are independent P (A) = 09 and P (B) =05 what is P(AcapB) A 09

B 045C 05 D 03 E None of above

Chapter 7 Which of the following correlation properties is right A correlation is always between -2 and 2 B correlation treats x and y unsymmetrically C correlation measures whether the two variables are linear association D correlation has no units

Chapter 9Assume that the number of students entering library comply with Poisson Probability Distribution The probability of none students at the average one hour entering library is 001 please compute the probability of at least two students at the average one hour entering librarySolutionKnown F(X)=u^x e^(-u)x When X=0 F(X)=001So F(X)=e^-u=001 u= 2ln10The probability of at least two students 1-P(X=0)-P(X=1) =1-001(1+2ln10)=0944

Chapter 10 The sampling of the population X as follows 21 54 32 98 35 So the sample mean________ the sample variance_________

Solution 48 22716

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1 What are the three steps of doing statistics

Ans The three main steps involved in the statistics process are1 Plan Clearly defining and understanding the objective prior to starting

will save a lot of work and time You must know the direction where you

are heading

2 Do Calculations are required in this step and the making of graphical

displays is also important

3 Report According to this step you need to explain others what you

have understood from the results

Q 2 What are the scales of measurement Which scale is always numeric What is the difference between ratio and intervalAns The four scales of measurement are Nominal Ordinal Interval and RatioInterval and ratio data are always numericThe difference is that in ratio data zero means zero which makes it possible for us to divide the data whereas in interval data zero does not mean zero and it does not start from 0

Q 3 A survey was conducted amongst the students living in University residence 80 students were selected to respond on an online questionnaire about the quality of food at market place 60 students responded to the questionnaire with their response

a Is the sampling frame correct If NOT Why b What number of students account as subjects and respondents

Ans (a) The sample technique is not correct because it is open to those who have access to the internet Anyone who doesnt have access to the internet cannot participate Also the students selected were not randomly selected from the population therefore they may not represent the population

(b) Students who responded to the survey are the respondents while the subject are students selected by the surveyor

Q 4 Construct a Bar chart using the following information

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 2: CombinedGroupQuestions-exam1

Answer Shape-the distribution is approximately symmetric with a single peak making it unimodal Centre-the centre of the distribution is close to the single peak The bin values can be added up as follows 3+3+8+10+5+2=31 The median occurs to the 15th data point Fourteen data points are contained in the first three bins The 15 th

data point is therefore contained in the 4th bin Spread- the spread is determined from the range of data high minus low 90-60=30

Chapter 6Please consider whether the following statements are true of false1 If an event is unlikely to occur its probability could be negative2 The probability of the set of all possible outcomes must be 13 For event A and B the formula P(A and B)=P(A)P(B) is always correctAnswer FTF

Chapter 7Please compute the correlation coefficientSuppose the data pairs are X 2 14 5 20 9Y 7 4 9 12 13

Answer r=0206Chapter 7

1Casio produced 1 million electronic watches in April 2012 Checked 1000 electronic watches by random sampling without repetition the Casio drew out the data that the failure rate was 2 If we assumed the pass rate would be 9973 Please calculate the range of variables of failure rate

pminustup≪P≪ p+tu p

068≪P≪332

Chapter8

2A school randomly samples 10 male students within the all male students Their average height is 170CM standard deviation is 12CM What is the percentage that the male students average height will be sure between the 1605CM---1795CM

t=Δx

minusiquest

Δ yminusiquestiquest

iquest

minus iquestxminusiquest tux

minusiquestiquestiquest iquest =1605 (iquest170iquest iquestxminusiquestiquest

Or + tuxminusiquest

xminusiquest iquest iquest=1795 t=2503

F(t)=9876

Chapter9

3A automobile manufacturer wants to analysis the correlation between the quantity of shipment and the quantity of automobile ownership They have investigated a region

Year Quantity of Shipment (x)

(million tons per kilometers )

Quantity of Automobile (y)

(Thousand )

2000 410 27

2001 450 31

2002 560 35

2003 600 40

2004 640 52

2005 680 55

2006 750 58

2007 850 60

2008 980 65

2009 1100 73

Please calculate the correlation coefficient

(r=0956)

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 What is the difference between contingency tables and cross tabulation2 What is the difference between interval and ordinal

3 In book page 97 Table 54 how to get the number of (MidPt- Mean)2 4 What is the table percentages5 How to calculate the percentile Is there any difference between sample and population6 Which of the following correlation properties is right (In assignment) a Correlation is always between -2 and 2 b Correlation treats X and Y unsymmetrical c Correlation measures whether the two variables are linear association d Correlation has no units7 What is the type of the data The number of students in a statistics course The letter grades received by students in a computer science class

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Whats statistics

Chapter 2

Customers satisfaction (eg very satisfactor

ysatisfactorydissatisfactoryvery dissatisfactory)belongs to()A

Nominal B Ordinal C Interval D Ratio

Chapter 3 What is the different between stratified sampling and cluster sampling

Chapter 4Talk about the difference between bar chart and histogram

Chapter 5Give the answers of mean median mode range variance and standard deviation (35 40 45 30 35 45 50 35 40 35)

Chapter 7 what are the features of correlation-r

Chapter 8 What are right belowa if events A and B are mutually exclusive P(A+B)=P(A)+P(B)

b P(A+B+C)=P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC)c P(AB)=P(B) P(A|B) (P(A)gt0 P(B)gt0)d P(A|B)= P(AB)P(B) (P(A)gt0 P(B)gt0)

Chapter 9 Suppose the heights of employees in one company is normally distributed with a mean of 171cm and a standard deviation of 5cm what is the probability of employees height less than 176cm

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1 Generally what are statistics used for

Chapter 2 The classification of student hobby in university of Windsor (sport music computer and other) is an example of A a categorical random variable B a discrete random variable C a continuous random variable D a parameter

Chapter 3The administration of a large university is interested in learning about the types of wellness programs that would interest its employees To do this they plan to survey a sample of their employees Suppose that there are five categories of employees (administration faculty professional staff clerical and maintenance) and the university decides to randomly select ten individuals from each category This sampling plan is calledA Systematic SamplingB Simple Random SamplingC Stratified SamplingD Cluster SamplingE Convenience Sampling

Chapter 4 What is pie chart

Chapter 5 Table 5-1 shows us the annual temperature in China from 2005 to 2010 Annual Temperature in China 2005 2006 2007 2008 2009 2010 Tempera 82 75 104 97 88 100

ture (degrees Celsius)

1) What are the Mean Median and Mode for these data 2) Would you use the mean or the median to summarize the center of this distribution Why

Chapter 6 Event A and B are independent P (A) = 09 and P (B) =05 what is P(AcapB) A 09

B 045C 05 D 03 E None of above

Chapter 7 Which of the following correlation properties is right A correlation is always between -2 and 2 B correlation treats x and y unsymmetrically C correlation measures whether the two variables are linear association D correlation has no units

Chapter 9Assume that the number of students entering library comply with Poisson Probability Distribution The probability of none students at the average one hour entering library is 001 please compute the probability of at least two students at the average one hour entering librarySolutionKnown F(X)=u^x e^(-u)x When X=0 F(X)=001So F(X)=e^-u=001 u= 2ln10The probability of at least two students 1-P(X=0)-P(X=1) =1-001(1+2ln10)=0944

Chapter 10 The sampling of the population X as follows 21 54 32 98 35 So the sample mean________ the sample variance_________

Solution 48 22716

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1 What are the three steps of doing statistics

Ans The three main steps involved in the statistics process are1 Plan Clearly defining and understanding the objective prior to starting

will save a lot of work and time You must know the direction where you

are heading

2 Do Calculations are required in this step and the making of graphical

displays is also important

3 Report According to this step you need to explain others what you

have understood from the results

Q 2 What are the scales of measurement Which scale is always numeric What is the difference between ratio and intervalAns The four scales of measurement are Nominal Ordinal Interval and RatioInterval and ratio data are always numericThe difference is that in ratio data zero means zero which makes it possible for us to divide the data whereas in interval data zero does not mean zero and it does not start from 0

Q 3 A survey was conducted amongst the students living in University residence 80 students were selected to respond on an online questionnaire about the quality of food at market place 60 students responded to the questionnaire with their response

a Is the sampling frame correct If NOT Why b What number of students account as subjects and respondents

Ans (a) The sample technique is not correct because it is open to those who have access to the internet Anyone who doesnt have access to the internet cannot participate Also the students selected were not randomly selected from the population therefore they may not represent the population

(b) Students who responded to the survey are the respondents while the subject are students selected by the surveyor

Q 4 Construct a Bar chart using the following information

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 3: CombinedGroupQuestions-exam1

Chapter8

2A school randomly samples 10 male students within the all male students Their average height is 170CM standard deviation is 12CM What is the percentage that the male students average height will be sure between the 1605CM---1795CM

t=Δx

minusiquest

Δ yminusiquestiquest

iquest

minus iquestxminusiquest tux

minusiquestiquestiquest iquest =1605 (iquest170iquest iquestxminusiquestiquest

Or + tuxminusiquest

xminusiquest iquest iquest=1795 t=2503

F(t)=9876

Chapter9

3A automobile manufacturer wants to analysis the correlation between the quantity of shipment and the quantity of automobile ownership They have investigated a region

Year Quantity of Shipment (x)

(million tons per kilometers )

Quantity of Automobile (y)

(Thousand )

2000 410 27

2001 450 31

2002 560 35

2003 600 40

2004 640 52

2005 680 55

2006 750 58

2007 850 60

2008 980 65

2009 1100 73

Please calculate the correlation coefficient

(r=0956)

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 What is the difference between contingency tables and cross tabulation2 What is the difference between interval and ordinal

3 In book page 97 Table 54 how to get the number of (MidPt- Mean)2 4 What is the table percentages5 How to calculate the percentile Is there any difference between sample and population6 Which of the following correlation properties is right (In assignment) a Correlation is always between -2 and 2 b Correlation treats X and Y unsymmetrical c Correlation measures whether the two variables are linear association d Correlation has no units7 What is the type of the data The number of students in a statistics course The letter grades received by students in a computer science class

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Whats statistics

Chapter 2

Customers satisfaction (eg very satisfactor

ysatisfactorydissatisfactoryvery dissatisfactory)belongs to()A

Nominal B Ordinal C Interval D Ratio

Chapter 3 What is the different between stratified sampling and cluster sampling

Chapter 4Talk about the difference between bar chart and histogram

Chapter 5Give the answers of mean median mode range variance and standard deviation (35 40 45 30 35 45 50 35 40 35)

Chapter 7 what are the features of correlation-r

Chapter 8 What are right belowa if events A and B are mutually exclusive P(A+B)=P(A)+P(B)

b P(A+B+C)=P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC)c P(AB)=P(B) P(A|B) (P(A)gt0 P(B)gt0)d P(A|B)= P(AB)P(B) (P(A)gt0 P(B)gt0)

Chapter 9 Suppose the heights of employees in one company is normally distributed with a mean of 171cm and a standard deviation of 5cm what is the probability of employees height less than 176cm

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1 Generally what are statistics used for

Chapter 2 The classification of student hobby in university of Windsor (sport music computer and other) is an example of A a categorical random variable B a discrete random variable C a continuous random variable D a parameter

Chapter 3The administration of a large university is interested in learning about the types of wellness programs that would interest its employees To do this they plan to survey a sample of their employees Suppose that there are five categories of employees (administration faculty professional staff clerical and maintenance) and the university decides to randomly select ten individuals from each category This sampling plan is calledA Systematic SamplingB Simple Random SamplingC Stratified SamplingD Cluster SamplingE Convenience Sampling

Chapter 4 What is pie chart

Chapter 5 Table 5-1 shows us the annual temperature in China from 2005 to 2010 Annual Temperature in China 2005 2006 2007 2008 2009 2010 Tempera 82 75 104 97 88 100

ture (degrees Celsius)

1) What are the Mean Median and Mode for these data 2) Would you use the mean or the median to summarize the center of this distribution Why

Chapter 6 Event A and B are independent P (A) = 09 and P (B) =05 what is P(AcapB) A 09

B 045C 05 D 03 E None of above

Chapter 7 Which of the following correlation properties is right A correlation is always between -2 and 2 B correlation treats x and y unsymmetrically C correlation measures whether the two variables are linear association D correlation has no units

Chapter 9Assume that the number of students entering library comply with Poisson Probability Distribution The probability of none students at the average one hour entering library is 001 please compute the probability of at least two students at the average one hour entering librarySolutionKnown F(X)=u^x e^(-u)x When X=0 F(X)=001So F(X)=e^-u=001 u= 2ln10The probability of at least two students 1-P(X=0)-P(X=1) =1-001(1+2ln10)=0944

Chapter 10 The sampling of the population X as follows 21 54 32 98 35 So the sample mean________ the sample variance_________

Solution 48 22716

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1 What are the three steps of doing statistics

Ans The three main steps involved in the statistics process are1 Plan Clearly defining and understanding the objective prior to starting

will save a lot of work and time You must know the direction where you

are heading

2 Do Calculations are required in this step and the making of graphical

displays is also important

3 Report According to this step you need to explain others what you

have understood from the results

Q 2 What are the scales of measurement Which scale is always numeric What is the difference between ratio and intervalAns The four scales of measurement are Nominal Ordinal Interval and RatioInterval and ratio data are always numericThe difference is that in ratio data zero means zero which makes it possible for us to divide the data whereas in interval data zero does not mean zero and it does not start from 0

Q 3 A survey was conducted amongst the students living in University residence 80 students were selected to respond on an online questionnaire about the quality of food at market place 60 students responded to the questionnaire with their response

a Is the sampling frame correct If NOT Why b What number of students account as subjects and respondents

Ans (a) The sample technique is not correct because it is open to those who have access to the internet Anyone who doesnt have access to the internet cannot participate Also the students selected were not randomly selected from the population therefore they may not represent the population

(b) Students who responded to the survey are the respondents while the subject are students selected by the surveyor

Q 4 Construct a Bar chart using the following information

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 4: CombinedGroupQuestions-exam1

3 In book page 97 Table 54 how to get the number of (MidPt- Mean)2 4 What is the table percentages5 How to calculate the percentile Is there any difference between sample and population6 Which of the following correlation properties is right (In assignment) a Correlation is always between -2 and 2 b Correlation treats X and Y unsymmetrical c Correlation measures whether the two variables are linear association d Correlation has no units7 What is the type of the data The number of students in a statistics course The letter grades received by students in a computer science class

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Whats statistics

Chapter 2

Customers satisfaction (eg very satisfactor

ysatisfactorydissatisfactoryvery dissatisfactory)belongs to()A

Nominal B Ordinal C Interval D Ratio

Chapter 3 What is the different between stratified sampling and cluster sampling

Chapter 4Talk about the difference between bar chart and histogram

Chapter 5Give the answers of mean median mode range variance and standard deviation (35 40 45 30 35 45 50 35 40 35)

Chapter 7 what are the features of correlation-r

Chapter 8 What are right belowa if events A and B are mutually exclusive P(A+B)=P(A)+P(B)

b P(A+B+C)=P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC)c P(AB)=P(B) P(A|B) (P(A)gt0 P(B)gt0)d P(A|B)= P(AB)P(B) (P(A)gt0 P(B)gt0)

Chapter 9 Suppose the heights of employees in one company is normally distributed with a mean of 171cm and a standard deviation of 5cm what is the probability of employees height less than 176cm

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1 Generally what are statistics used for

Chapter 2 The classification of student hobby in university of Windsor (sport music computer and other) is an example of A a categorical random variable B a discrete random variable C a continuous random variable D a parameter

Chapter 3The administration of a large university is interested in learning about the types of wellness programs that would interest its employees To do this they plan to survey a sample of their employees Suppose that there are five categories of employees (administration faculty professional staff clerical and maintenance) and the university decides to randomly select ten individuals from each category This sampling plan is calledA Systematic SamplingB Simple Random SamplingC Stratified SamplingD Cluster SamplingE Convenience Sampling

Chapter 4 What is pie chart

Chapter 5 Table 5-1 shows us the annual temperature in China from 2005 to 2010 Annual Temperature in China 2005 2006 2007 2008 2009 2010 Tempera 82 75 104 97 88 100

ture (degrees Celsius)

1) What are the Mean Median and Mode for these data 2) Would you use the mean or the median to summarize the center of this distribution Why

Chapter 6 Event A and B are independent P (A) = 09 and P (B) =05 what is P(AcapB) A 09

B 045C 05 D 03 E None of above

Chapter 7 Which of the following correlation properties is right A correlation is always between -2 and 2 B correlation treats x and y unsymmetrically C correlation measures whether the two variables are linear association D correlation has no units

Chapter 9Assume that the number of students entering library comply with Poisson Probability Distribution The probability of none students at the average one hour entering library is 001 please compute the probability of at least two students at the average one hour entering librarySolutionKnown F(X)=u^x e^(-u)x When X=0 F(X)=001So F(X)=e^-u=001 u= 2ln10The probability of at least two students 1-P(X=0)-P(X=1) =1-001(1+2ln10)=0944

Chapter 10 The sampling of the population X as follows 21 54 32 98 35 So the sample mean________ the sample variance_________

Solution 48 22716

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1 What are the three steps of doing statistics

Ans The three main steps involved in the statistics process are1 Plan Clearly defining and understanding the objective prior to starting

will save a lot of work and time You must know the direction where you

are heading

2 Do Calculations are required in this step and the making of graphical

displays is also important

3 Report According to this step you need to explain others what you

have understood from the results

Q 2 What are the scales of measurement Which scale is always numeric What is the difference between ratio and intervalAns The four scales of measurement are Nominal Ordinal Interval and RatioInterval and ratio data are always numericThe difference is that in ratio data zero means zero which makes it possible for us to divide the data whereas in interval data zero does not mean zero and it does not start from 0

Q 3 A survey was conducted amongst the students living in University residence 80 students were selected to respond on an online questionnaire about the quality of food at market place 60 students responded to the questionnaire with their response

a Is the sampling frame correct If NOT Why b What number of students account as subjects and respondents

Ans (a) The sample technique is not correct because it is open to those who have access to the internet Anyone who doesnt have access to the internet cannot participate Also the students selected were not randomly selected from the population therefore they may not represent the population

(b) Students who responded to the survey are the respondents while the subject are students selected by the surveyor

Q 4 Construct a Bar chart using the following information

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 5: CombinedGroupQuestions-exam1

b P(A+B+C)=P(A)+P(B)+P(C)-P(AB)-P(AC)-P(BC)+P(ABC)c P(AB)=P(B) P(A|B) (P(A)gt0 P(B)gt0)d P(A|B)= P(AB)P(B) (P(A)gt0 P(B)gt0)

Chapter 9 Suppose the heights of employees in one company is normally distributed with a mean of 171cm and a standard deviation of 5cm what is the probability of employees height less than 176cm

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1 Generally what are statistics used for

Chapter 2 The classification of student hobby in university of Windsor (sport music computer and other) is an example of A a categorical random variable B a discrete random variable C a continuous random variable D a parameter

Chapter 3The administration of a large university is interested in learning about the types of wellness programs that would interest its employees To do this they plan to survey a sample of their employees Suppose that there are five categories of employees (administration faculty professional staff clerical and maintenance) and the university decides to randomly select ten individuals from each category This sampling plan is calledA Systematic SamplingB Simple Random SamplingC Stratified SamplingD Cluster SamplingE Convenience Sampling

Chapter 4 What is pie chart

Chapter 5 Table 5-1 shows us the annual temperature in China from 2005 to 2010 Annual Temperature in China 2005 2006 2007 2008 2009 2010 Tempera 82 75 104 97 88 100

ture (degrees Celsius)

1) What are the Mean Median and Mode for these data 2) Would you use the mean or the median to summarize the center of this distribution Why

Chapter 6 Event A and B are independent P (A) = 09 and P (B) =05 what is P(AcapB) A 09

B 045C 05 D 03 E None of above

Chapter 7 Which of the following correlation properties is right A correlation is always between -2 and 2 B correlation treats x and y unsymmetrically C correlation measures whether the two variables are linear association D correlation has no units

Chapter 9Assume that the number of students entering library comply with Poisson Probability Distribution The probability of none students at the average one hour entering library is 001 please compute the probability of at least two students at the average one hour entering librarySolutionKnown F(X)=u^x e^(-u)x When X=0 F(X)=001So F(X)=e^-u=001 u= 2ln10The probability of at least two students 1-P(X=0)-P(X=1) =1-001(1+2ln10)=0944

Chapter 10 The sampling of the population X as follows 21 54 32 98 35 So the sample mean________ the sample variance_________

Solution 48 22716

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1 What are the three steps of doing statistics

Ans The three main steps involved in the statistics process are1 Plan Clearly defining and understanding the objective prior to starting

will save a lot of work and time You must know the direction where you

are heading

2 Do Calculations are required in this step and the making of graphical

displays is also important

3 Report According to this step you need to explain others what you

have understood from the results

Q 2 What are the scales of measurement Which scale is always numeric What is the difference between ratio and intervalAns The four scales of measurement are Nominal Ordinal Interval and RatioInterval and ratio data are always numericThe difference is that in ratio data zero means zero which makes it possible for us to divide the data whereas in interval data zero does not mean zero and it does not start from 0

Q 3 A survey was conducted amongst the students living in University residence 80 students were selected to respond on an online questionnaire about the quality of food at market place 60 students responded to the questionnaire with their response

a Is the sampling frame correct If NOT Why b What number of students account as subjects and respondents

Ans (a) The sample technique is not correct because it is open to those who have access to the internet Anyone who doesnt have access to the internet cannot participate Also the students selected were not randomly selected from the population therefore they may not represent the population

(b) Students who responded to the survey are the respondents while the subject are students selected by the surveyor

Q 4 Construct a Bar chart using the following information

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 6: CombinedGroupQuestions-exam1

ture (degrees Celsius)

1) What are the Mean Median and Mode for these data 2) Would you use the mean or the median to summarize the center of this distribution Why

Chapter 6 Event A and B are independent P (A) = 09 and P (B) =05 what is P(AcapB) A 09

B 045C 05 D 03 E None of above

Chapter 7 Which of the following correlation properties is right A correlation is always between -2 and 2 B correlation treats x and y unsymmetrically C correlation measures whether the two variables are linear association D correlation has no units

Chapter 9Assume that the number of students entering library comply with Poisson Probability Distribution The probability of none students at the average one hour entering library is 001 please compute the probability of at least two students at the average one hour entering librarySolutionKnown F(X)=u^x e^(-u)x When X=0 F(X)=001So F(X)=e^-u=001 u= 2ln10The probability of at least two students 1-P(X=0)-P(X=1) =1-001(1+2ln10)=0944

Chapter 10 The sampling of the population X as follows 21 54 32 98 35 So the sample mean________ the sample variance_________

Solution 48 22716

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1 What are the three steps of doing statistics

Ans The three main steps involved in the statistics process are1 Plan Clearly defining and understanding the objective prior to starting

will save a lot of work and time You must know the direction where you

are heading

2 Do Calculations are required in this step and the making of graphical

displays is also important

3 Report According to this step you need to explain others what you

have understood from the results

Q 2 What are the scales of measurement Which scale is always numeric What is the difference between ratio and intervalAns The four scales of measurement are Nominal Ordinal Interval and RatioInterval and ratio data are always numericThe difference is that in ratio data zero means zero which makes it possible for us to divide the data whereas in interval data zero does not mean zero and it does not start from 0

Q 3 A survey was conducted amongst the students living in University residence 80 students were selected to respond on an online questionnaire about the quality of food at market place 60 students responded to the questionnaire with their response

a Is the sampling frame correct If NOT Why b What number of students account as subjects and respondents

Ans (a) The sample technique is not correct because it is open to those who have access to the internet Anyone who doesnt have access to the internet cannot participate Also the students selected were not randomly selected from the population therefore they may not represent the population

(b) Students who responded to the survey are the respondents while the subject are students selected by the surveyor

Q 4 Construct a Bar chart using the following information

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 7: CombinedGroupQuestions-exam1

Solution 48 22716

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1 What are the three steps of doing statistics

Ans The three main steps involved in the statistics process are1 Plan Clearly defining and understanding the objective prior to starting

will save a lot of work and time You must know the direction where you

are heading

2 Do Calculations are required in this step and the making of graphical

displays is also important

3 Report According to this step you need to explain others what you

have understood from the results

Q 2 What are the scales of measurement Which scale is always numeric What is the difference between ratio and intervalAns The four scales of measurement are Nominal Ordinal Interval and RatioInterval and ratio data are always numericThe difference is that in ratio data zero means zero which makes it possible for us to divide the data whereas in interval data zero does not mean zero and it does not start from 0

Q 3 A survey was conducted amongst the students living in University residence 80 students were selected to respond on an online questionnaire about the quality of food at market place 60 students responded to the questionnaire with their response

a Is the sampling frame correct If NOT Why b What number of students account as subjects and respondents

Ans (a) The sample technique is not correct because it is open to those who have access to the internet Anyone who doesnt have access to the internet cannot participate Also the students selected were not randomly selected from the population therefore they may not represent the population

(b) Students who responded to the survey are the respondents while the subject are students selected by the surveyor

Q 4 Construct a Bar chart using the following information

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 8: CombinedGroupQuestions-exam1

40 of MOM students opted for Financial Accounting 20 Logistics 15 English 10 HRM and 7 statistics and 8 others Ans

Subjects Percentage ()

Financial Accounting 40

Logistics 20

English 15

HRM 10

Statistics 7

Others 8

Financial Accounting

Logistics English HRM Statistics Others0

5

10

15

20

25

30

35

40

45

Subjects

Subjects

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 9: CombinedGroupQuestions-exam1

Q 5 Define the skewness of Barchart

a b c d e f g h i j k l m n o p q r s t0

10

20

30

40

50

60

70

a Symmetric

b Left skewed

c Right skewed

d None of the above

Ans Left Skewed

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 10: CombinedGroupQuestions-exam1

Q 6 Define the shaded area

a P(A)

+P(B)

+P(C)

b P(AcapC)

c P(A)

+P(B)-P(AcapBcapC)

d P(AcapB)

Ans P(AcapB)

Q 7 A researcher was assuming that the students who are good in statistics are also good in Logistics So he randomly selected 25 Midterm marks of MOM students for both statistics and Logistics and compared the results The data is given below

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 11: CombinedGroupQuestions-exam1

(Total marks 100)Statistics Logistics (Cont)

Statistics(Cont)

Logistics95 88 66 5690 94 32 3484 90 76 7982 85 34 4370 75 56 4572 68 76 8780 78 98 7965 70 55 6481 91 67 7675 88 76 6723 34 46 4488 98 12 7787 98

a) Make a scatter-plot for these data

b) Describe the direction form and strength of the plot

c) Find the correlation

Ans (a)

0 20 40 60 80 100 1200

20

40

60

80

100

120

Logistics

Logistics

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 12: CombinedGroupQuestions-exam1

(b) The pattern is running from lower left to upper left therefore it is positive

(c)

r = sum((95-674)(88-

723)+(90-674)(94-723)+(helliphelliphelliphelliphelliphelliphelliphellip

radic((95-674)+(90-674)hellip)sup2 x ((88-723)+(94-723)

helliphelliphelliphellip)sup2

r = 803348 1065358

r = 0754

Q 8 A linear models made to predict the monthly sales of t-shirts fronm the average price($unit) charged by sample of stores is Sales = 1136574 - 174815 price

a) What is the explanatory variable b) What is the response variable c) What does the slope mean in this context

Ans (a) Price is helping to predict the sales hence PRICE is the explanatory variable

in this context

(b) The sale of t-shirt is being predicted hence SALES is the response variable

(c) The slope is negative in the given linear model Hence for every extra dollar increase there will decrease in sales by 174815

Q 9 Last year in Windsor 40 road accident were reported If the number

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 13: CombinedGroupQuestions-exam1

of road accident for the last 12 months is independent and the mean has not changed what is the probability of having a month in Windsor with each of the following

a) No Accident

b) Exactly 1 Accident

Ans (a) (40 accidents12 months) = 23 accidentsmonthP(No Accident) = P(X=0) = eˉsup2middotsup3sup3 x 23ordm = 0095

0

(b) P(1 Accidents) = P(X=1) = eˉsup2middotsup3sup3 x 23sup1 = 0223 1

Q 10 In a class of 70 students the mean marks are 350 and standard deviation of 100 What is the standard error (SE) for the mean of this sample of students

Ans s=100 n= 70

SE = 100 radic70

SE = 1195

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1 A company started and managed by business students is selling campus calendars The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted (should they advertise in the alumni magazine and the local newspaper) the following table shows the results of the market survey

Buying likelihood

unlike Moderately likely Very likely total

students 197 388 320 905

Facultystuff 103 137 98 338

alumni 20 18 18 56

town Residents 13 58 45 116

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 14: CombinedGroupQuestions-exam1

total 333 601 481 1415

a) What percent of all these respondents are alumnib) What percent of these respondents are very likely to buy the calendarc) What percent of the respondents who are very likely to buy the calendar are alumnid) Of the alumni what percent are very likely to buy the calendare) What is the marginal distribution of the campus constituentsf) What is the conditional distribution of the campus constituents among those very likely yo

buy the calendarg) Does this study present any evidence that this company should focus on selling to certain

campus constituents

2 Canadian weekly earningsCanadian average weekly earnings classified by province and territory are given in the table for 2007a) Calculate the mean earnings for the year 2007b) Calculate the standard deviation for the year 2007c) Calculate the coefficient of variation for 2007d) Calculate the z-scores for Ontario and Nunavut and interpret their meaning

Provincial average weekly earnings in 2007

Newfoundland and Labrador 71465

Prince Edward island 62890

Nova scotia 67338

New Brunswick 70793

Quebec 72529

Ontario 80346

Manitoba 70193

Saskatchewan 72403

Alberta 83552

British Columbia 76101

Yukon 88247

Northwest territories 100463

Nunavut 94868

3 Telemarketers continue to attempt to reach consumers by calling land-line phone numbers According to estimates from a national 2003 survey based on face to face interviews in 16677 households approximately 582 of US adults have both a land line in their residence and a cell phone 28 have only cell phone service but no land line and 16 have no telephone service at all

a Polling agencies wonrsquot call cell phone numbers because customers object to paying for such calls What proportion of US households can be reached by a landline call

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 15: CombinedGroupQuestions-exam1

b Are having a cell phone and having a landline independent Explain

4 The share prices of Toronto Dominion Bank and Royal Bank of Canada on the Toronto Stock Exchange for 10 days in 2008 are given in the table In order to investigate the relationship between these stocks for investment purposes draw a scatterplot and calculate the correlation coefficient between them showing the intermediate steps in your calculation TD Bank RBC11212008 413 364811202008 4357 356511192008 4993 411911182008 5218 435411172008 5175 433611142008 5357 44511132008 5458 462511122008 5295 439111112008 5586 464511102008 5681 4738

5 A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale The market price for apples(per kilogram) each day is a random variable with a mean of 05 dollars and a standard deviation of 02 dollars Similarly for a kilogram of potatoes the mean price is 03 dollars and the standard deviation is 01 dollars It also costs him two dollars to bring all the apples and potatoes to the market The market is busy all the eager shoppers so we can assume that hersquoll be able to sell all of each type of produce at that dayrsquos price

a Define your random variables and use them to express the farmerrsquos net income

b Find the mean of the net income

c Find the standard deviation of the net income

d Do you need to make any assumptions in calculating the mean How about the standard deviation

6 In 2008 the income per capita measured in US dollars was $31639 in Canada and $40807 in Norway Let us assume that income per capita is Normally distribution with a standard deviation equal to 31 of the mean for each country You select a random sample of six people in Norway and six people in Canada

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 16: CombinedGroupQuestions-exam1

a What is the probability that the mean income of your Canadian sample is above $40807b What is the probability that the mean income of your Norwegian sample is above $31639c What would be the effect of not assuming that the income per capita is Normally distributed

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1Statistic is a way of reasoning along with a collection of tools andmethods designed to help s understand the world

Chapter 2A few of the variables for which data were collected in the RBC FinancialGroup study include age gender income and number of hours spentshopping online per month Which of variable s is categoricalA) Number of hours spent shopping onlineB) AgeC) GenderD) IncomeE) NoneAnswer C) Gender

Chapter 3Suppose that there are five categories of employees ( Director RegionalManager Assistant Internship and Co-OP) and the company decides torandomly select ten individuals from each categoryThis sampling plan iscalled Stratified Sampling

Chapter 4This table indicates different genders of the graduate students in two MasterProgramsFull-time Part-time TotalMen 50 20 70Women 60 30 90

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 17: CombinedGroupQuestions-exam1

Total 110 50 160Question What percent of part-time masters are womenAnswer 3050=6=60

Chapter 5University of Windsor MoM Faculty received 50 applications from prospectivestudents The application form contains information of candidate that theirGMAT scoreHowever the necessary data on candidates have not yet been entered indatabase The program director estimate the value of the populationparameters of interest based on sample statistics10 candidates selected will be usedGMAT score of 10 candidates 600 620 630 648 600688 700 647 684 710Question Please use the point estimation knowledge to calculate the meanscores and standard deviation of the candidatesAnswerMean scores ΣXi=6527

x 1049273ΣXi10

104927365271010492736527Standard deviation

S=radicΣ1049273Xi- x )2

9=radic2704+106929+51529+2209+277729+124609+223729+3249+97969+328329 9=radic148668191049273radic16518791049273406

Chapter 6A random survey of autos parked in the student and staff lots at Universityof Windsor classified the brands by country of origin as seen in tableQuestion What is the probability that the students are Asian

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 18: CombinedGroupQuestions-exam1

Student Staff TotalAmerican 30 10 40Canadian 90 50 140Asian 50 20 70Total 170 80 250Answer50170=29=29

Chapter 7Three correlation conditions is Quantitative Variables ConditionLinearity Condition and Outlier Condition

Chapter 8The regression equation is y=b0+b1x

Chapter 9In Devonshire Mall customers buy a lottery ticker for $1 and choose threenumbers each form zero to nineThey also must select the play type whichdetermines what combinations are winners In one type of play they win ifthey match the three numbers in any order but the payout is greater if theorder is exact For the case where all three of the numbers selected aredifferent the probability and payouts areProbability PayoutExact 1 in 10000 $2800Any Order 5 in 10000 $500Question Fine the amount a player can expect to winAnswer1100002800+510000500=028+025=053

Chapter 10The Central Limit Theorem( CLT) states that the sampling distribution modelof the sample mean( and proportion) is approximately Normal for large nregardless of the distribution of the population as long as the observationsare independent

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 19: CombinedGroupQuestions-exam1

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Q 1) What is Statistics List some of the practical applications of it in the business

world that you can think of

Statistics is the discipline of understanding the world around us through the collection of

data organizing it presenting it in an understandable way and interpreting results from it

Statistics plays a significant role in business It is used to estimate demand for a new product

how much of it to produce predicting sales of existing and future products determining

which current products are doing well gathering feedback from customers through surveys

and in development of future products and services

Q 2) What is the data measured over time which has an equally spaced time interval

Ans Time Series Data

Q 3) The Odette School of Business offers Master of Management (MOM) course in

various specializations In this course the boys to girlsrsquo ratio is 4060 And the sample

gender ratio was the same as that of the populationrsquos Out of the 50 MOM course

students the supervisor of TIM Hortonrsquos randomly selected 40 students

A) What is the population

B) What is the number of boys and girls in the sample

C) What kind of sampling technique is it

D) Is there any wrong with the sampling Explain

Ansa) the population is 50

b) Since the sample gender ratio was the same as the population among the 40

students

the number of boys are = 40 times 04 = 16

the number of girls are = 40 times 6 = 24

c) Stratified sampling technique since the surveyor sliced the population into

homogeneous groups and then used random sampling

d) There is nothing wrong with the sampling since the surveyor guaranteed that the

proportions of men and women within the sample match the proportions in the

population So this sample will represent the entire population properly

Q 4) Recently a survey was conducted to find out the opinion of Canadians of the fact

that Europe would be most preferred holiday destination The respondents replied as

below

55 - Agree Completely

30 - Agree Somewhat

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 20: CombinedGroupQuestions-exam1

10 - Neither agree nor disagree

2-Disagree Completely

15 - Disagree Somewhat

05 - Donrsquot know

Represent the above categorical data using the best possible data chart and explain

why is this an appropriate display for these data

Ans

For the above data the best possible chart is a Pie Chart and it is a below

5500003000

1000200150 050

Opinions in percentagesAgree CompletelyAgree SomewhatNeither agree nor disagreeDisagree CompletelyDisagree SomewhatDonrsquot know

Pie chart is appropriate for this case since we have the data broken into several categories

and it does a better job of comparing portions of the whole

Q5) Calculate mean median and mode of the following data 8 4 57897810885

Ans Mean = 8+4+5+7+8+9+7+8+10+8+8+5

12 = 725

Median let the data items arrange in ascending order 45 5 7788 8 8 8 9 10

Median is the average of middle two values (8+8)2 = 8

Mode 8 occurred most frequently in the data set So Mode is 8

Q 6) If a box contains 8 yellow marbles 4 green marbles and 5 black marbles what is

the probability of selecting a green marble from the box

Ans Here Probability = number of favorableoutcomestotalnumber of possible outcomes

= 4

8+4+5 = 02352 = 2352

Q 7) What is the range of correlation of co-efficient

a 0 to 1

b -1 to 1

c -1 to 0

d 1 to 2

Ans B

Q 8) wind mobile wanted to examine whether the purchase of their service is related

to their customerrsquos monthly income or not The linear regression is

Purchase = 255 + 005 Income

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 21: CombinedGroupQuestions-exam1

a) What is the explanatory variable

b) What is the response variable

c) What does the slope mean in this context

d) What do you predict the purchase to be if the average income was $2000

e) If the total purchase turned out to be $130 for an income of $2000 what would

the residual be

Ans a) Income is the explanatory variable

b) Purchase is the response variable

c) The slope for this equation is 005 which means that for every extra dollar increase

in the customer monthly income purchase of wind service increase by $ 005

d) Purchase = 255 + (005 times 2000) = $ 1255

e)Residual = Data ndash Predicted = 130-1255 = $45

Q 9) Sample Prices of different Branded handsets are given Calculate standard

deviation and variance

Handset Price ($ X)

1 Brand a 35

2 Brand b 40

3 Brand c 20

4 Brand d 20

5 Brand e 15

6 Brand f 50

7 Brand g 30

8 Brand h 20

9 Brand i 35

10 Brand j 45

Ans

The formula of Variance

The mean value of price is = (35+40+20+20+15+50+30+20+35+45)10 = 31

X X - (X - ) 2

35 4 16

40 9 81

20 -11 121

20 -11 121

15 -16 256

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 22: CombinedGroupQuestions-exam1

50 19 361

30 -1 1

20 -11 121

35 4 16

45 14 196

Total 1290

S2 = 129010-1 = 14333

So the variance is 14333

Standard Deviation = radic14333 = 1197

So on an average the price of different branded handset differs by $1197 from each other

Q 10 At the Thomsonrsquos packaging plant when a truckload of watermelons arrives a

random sample of 180 is selected and scrutinized for any damage caused or rotten

watermelons Whole of the truckload will be rejected if more than 7 of the sample

fails to be fresh watermelons Given that 15 of the watermelons on the truck do not

meet the standard requirements What is probability that the shipment will be

accepted in anyway

Ans

Randomization condition

A random sample of 180 melons is taken from each vehicle

10 condition 180 is less than 10 of all watermelons

SuccessFailure Condition np =27 and nq = 153 are both greater than 10

Therefore the sampling distribution model for pˆ is Normal with

p= 015 q=085 n= 180 and according to the formulae we have

= radic(015lowast085)180 = 0026615

According to the Normal model the probability that less than 7 of the melons in the

sample are unsatisfactory is approximately 00734

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 23: CombinedGroupQuestions-exam1

= (007 ndash 015) 00266 = - 3008

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

1Data value no matter what kind are useless without their( )

2Jim got 89 in OB exam while Frank got 76 Jim scored 13 points more than Frank This measurement is ARatio B Nominal COrdinal DInterval

3Canada Airline is going to survey a random sample of 250 passengers on the flight from Shanghai to Toronto on April 1stIf the clerk on charge choose 10 people in business class15 in first class20 in economic class randomlyWhat kind of sampling is this describe aboveAStratified Sampling BCluster Sampling CSystematic Samples

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 24: CombinedGroupQuestions-exam1

DMultistage Sampling

4____ give a quick impression of how a whole group is partitioned into smaller groups AFrequency Tables BBar Charts CPie Charts DContingency Tables

5There is a group of sample data as=20212223242526 What is the Z-score of this group

6If the probability of Marina to pass the exam is 043while the probability of David is 026compute the probability of both Marina and David pass the exam

7Correlation is always between ( ) and ( ) A -10 B-11 C01 D -1212

8 Cars go through the crossing at the average rate of 10 cars per minute in

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 25: CombinedGroupQuestions-exam1

rush hours what is the probability of 7 cars go through the crossing in 30 seconds in rush hours

9 The mean of a random sample has a sampling distribution whose shape can be approximated by a normal model The larger the sample the better the approximation will be This is ( )

ltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgtltgt

Chapter 1

1) Categorical data include ____ DataA Numerical Nominal IntervalB Numerical Nominal OrdinalC Non-numerical Nominal RatioD Non-numerical Interval Ratio

Solution B

Chapter 2

2) Which of the following is based on cross-sectional data ____A Annual costB Yearly student enrollmentC Canadian employers work for full timeD The sale revenue of different departments in Devonshire Mall in January 2013

Solution D

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 26: CombinedGroupQuestions-exam1

3) What are two conditions when selecting a random sample from an infinite population

Solution 1 Each of the sampled elements is independent2 Each of the sampled elements follows the same probability

distribution as the elements in the population

Chapter 3

4) By placing the appropriate letter (A-G) beside the symbol match each symbol with its description1 P___ A Sample mean2 N___ B Sample proportion3 σ___ C Population size4 x___ D Sample size5 S ___ E Population mean6 n ___ F Sample standard deviation7 μ___ G Population standard deviation

Solution BCGAFDE

Chapter 4

5) A new restaurant did a survey about the degree of satisfaction among 400 customers the following data shows the result

Degree of

Satisfaction

age

DissatisfiedSlightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 400

Percentage of each degree

a) Complete the table and compute the percentage of each degree of satisfactionb) Which chart is an appropriate display of these data (pie chart bar chart ext)

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 27: CombinedGroupQuestions-exam1

Why or why not

Solutiona)

Degree of

Satisfaction

ageDissatisfie

d

Slightly satisfied

Moderately satisfied

Extremely satisfied Total

Under 20 15 23 45 17 100

20-40 10 48 17 25 100

40-60 18 27 34 21 100

Over 60 35 37 17 11 100

Total 78 135 113 74 400

Percentage of each degree 195 3375 2825 185 100

b)

19

3429

18

Degree of satisfactionDissatisfied Slightly satisfied Moderately satisfied Extremely satisfied

Pie chart shows the whole group of cases as a circle They slice the circle into pieces whose size is proportional to the fraction of the whole in each category The pie reflects the each degree of satisfaction clearly and is an appropriate display of these data

Chapter 5

6) A marketing director wants to determine whether the new advertising campaign how to attracting younger customers She has selected two samples of customers The first sample is selected from the customer database before the new advertising campaign The data indicates the age in years of the customers at the time the policy went into effect The second sample is taken from the customers who were

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 28: CombinedGroupQuestions-exam1

added after the new advertising campaign

Before

33 44 52 34 25 34 38 45 60 42

30 40 29 55 36 62 58 64 56 48

After

23 31 40 28 26 34 40 28 25 29

35 24 42 32 30 36 28 39 44 27

sum x=885 sum x2=41905

sum y=641 sum y2=21311

a) Calculate the mean median and mode for the customer age in the two samples b) Why would the insurance company like to attract younger customers

Solutiona)Order the data sets from min to maxBeforei 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 25 29 30 33 34 34 36 38 40 42 44 45 48 52 55 56 58 60 62 64

Mean x=88520=4425n=20 take the average of the two middle pointsMedian = (42+44)2=43Mode=34

Afteri 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20x i 23 24 25 26 27 28 28 28 29 30 31 32 34 35 36 39 40 40 42 44

Mean x=64120=3205n=20 take the average of the two middle pointsMedian=(30+31)2=305Mode=28

b) Maybe younger people have a lower probability to make a claim on their life insurance (Here any reasonable explanation would be acceptable)

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 29: CombinedGroupQuestions-exam1

Chapter 6

7) Rolling a dieA What is the probability occurring 1 pointB What is the probability occurring more than 4 points (including 4)C If rolling two dies and adding the two results together what is the probability

occurring 4 points

Solution a) 16b) 16+16+16=12c) (1616)+(1616)+(1616)=112

Chapter 7

8) The following statements descried the correlation which are correct

1 Correlation is always between -1 and +12 The correlation of x with y is not the same as the correlation of y with x3 Correlations always have clear units4 Correlation measures the strength of the linear association between the two variables5 Correlations is not affected by changes in the center of scale of either variable

A 1 2 3 B 3 4 5 C 1 4 5 D 2 3 4

Solution C

Chapter 9

9) Assume the probability of a student failing courses is 01 choosing 3 students at random What is the probability of two of them failing the course

Solution

Let P=01 n=3 x=2

f(x)=n

x (nminusx )px (1minusp)(nminusx)=

3 2 (3minus2 )

times012times09(3minus2)=300109=0027

Chapter 10

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704

Page 30: CombinedGroupQuestions-exam1

10) The border patrol on the Canadian side of the Ambassador Bridge claims that the time it spends questioning the occupants of cars that cross this border point has a normal distribution with a mean of 175 minutes with a standard deviation of 034 minutes If this claim is true

What is the probability that the occupants of a randomly observed car will be questioned for more than 250 minutes

What is the probability that the occupants of a randomly observed car will be

questioned for less than 200 minutes

Solution P(xgt25) = P(zgt(25-175)034)=P(zgt221)=05-04864=00136

P(xlt2) = P(zlt(2-175)034)=P(zlt074)=05+02704=07704