statistics 1040, sections 007 009, quiz 1 (20 points)symanzik/teaching/2008_stat1040/... · 2008....

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Statistics 1040 Sections 007 amp 009 Quiz 1 (20 Points)

Friday August 31 2007

Your Name

Question 1 Controlled ExperimentsjObservational StudiesI (14 Points)

(hypothetica~ Does regularly taking vitamin C help protect people against flu

A ---- was conducted to answer this question The were 500 volunteering college students assigned to two groups of 250 students The students in the took regularly a tablet of vitamin C whereas those in the took an identically looking and tasting pill called _ Neither participating students nor personell administrating drugs to them knew who was

taking which pill in other words it was a ----- _ experiment After a couple of months the numbers of flu cases in both groups were compared

Fill the gaps in the paragraph above using the most appropriate words from the following list

placebo doublfr-blind haphazardly treatnaent group observational study randonaly singlfr-blindmiddot vaccine

confounding factor objects control group controlled experinaent subjects poliomiddot

Please turn over

1

middot Question 2 Controlled ExperimentsObservational Studies II (6 Points)

In 1990 four passengers were killed by crashes on commuter airlines compared to 39 killed on scheduled carriers (like United TWA and so forth) True or false Circle your answer and explain the data show that if you have to fly it is safer to do so on a commuter airline

2

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Friday September 7 2007

Your Name

Question 1 Histograms (14 Points)

The following table is for the gestational age of 1210 babies

Gestational Age 230-250 250-270 270-290 290310 310-330

Number 47

206 731 199 27

Draw a histogram for these data on the graph paper provided Make sure to label the axes

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Please turn over

1

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Question 2 Observational Studies Controlled Experiments (6 Points)

For each of the following studies determine whether the study in question was a randomshyized controlled experiment or an observational study (circle the correct answer)

bull Twenty male employees and twenty female employees participate in research deshysigned to compare attitudes towards the Social Security System of men and women Each individual responds to a series of questions on a survey Mean scores are computed for men and for women

randomized controlled experiment observational study

bull A researcher wants to learn whether regularly taking zinc supplements may reduce the risk of getting a cold Volunteers in this study chose to (or chose not to) take a zinc supplement


bull A researcher wants to learn about whether computer simulations help students betshyter understand statistical concepts She puts the names of 20 volunteers into a box and randomly draws the names of 10 people who will use computer simulations to learn statistical concepts The other 10 study participants will use a conventional approach without computer simulations to learn the same concepts


2


Friday September 142007

Your Name ------------ shy

Question 1 The Average and the SDI (10 Points)

Here is a list of numbers

07 1698 32 54 08 77 63 22 41 81 65 37 06 69 99 88 31 57 91

1 Without doing any arithmetic guess whether the average is around (i) 1 (ii) 5 or (iii) 10 Circle your answer and explain

2 Without doing any arithmetic guess whether the SD is around (i) 1 (ii) 3 or (iii) 6 Circle your answer and explain

Question 2 The Average and the SD II (10 Points)

A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg The women had an average weight of about 55kg and an SD of about 9 kg (Note that 1 kg = 221b)

1 Just roughly what percentage of the men weighted between 57 kg and 75 kg Answer Fill in your answer and exp~ain

2 If you took the men and women together would the SD of their weights be (i) smaller than 9 kg (ii) just about 9 kg or (iii) bigger than 9 kg Circle your answer and explain

1



Your Name _------------- shy

Question 1 Normal Approximation for Data(20 Points)

The Graduate Record Examination (GRE) is a test taken by college students who intend to pursue a graduate degree in the United States For around 428000 examinees who took the General GRE Test in 2001-02 the mean for the verbal ability portion of the exam was around 470 and the standard deviation was around 125 We can assume that the histogram follows a normal curve Show your work

bull (7 Points) The percentage of examinees who scored less than 420 on the GRE test is roughly

bull (7 Points) The percentage of examinees who scored between 370 and 645 is about

bull (6 Points) In order to be among the top 4 a student must have obtained a minimum GRE score of about --- shy

) Please turn over

1

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A NORMAL TABLE

z Area z Area z Area

000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863

025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944

050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961

I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978

075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988

~ bull~-- 090 6319 240 9836 390 99990 j

0~95 6579 245 9857 395 99992 I

100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949

110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot

I 120 7699 270 9931 420 999913f

I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983

) ~gt 135 8230 285 9956 435 1999986

440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1



Your Name ------------- shy

Questionmiddot 1 Measurement Error (8 Points)

You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values

3596 inches 3601 inches 3603 inches

If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take

(a) 01 inches or so (b) 03 inches or so (c) 06inches or so

Circle your answer and explain

Question 2 Correlation (6 Points)

A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20

The correlation coefficient between the number of right answers andthe number of wrong answers is

(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20

(h) cant tell without the data


Please turn over

1


For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows

average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020

True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation

Formulas

sum of all numbers avg = ----------shy

how many numbers )

SD = Javerage of [(deviations from avg) 2]

2


Friday October 12 2007

Your Name -----~-----

Question 1 Regression (20 Points)

A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows

Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053

Show your work

1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories

2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup

Please turn over

1

3 (5 Points) Find the rms error for predicting mg sodium from calories

4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup

Formulas

rms error =Jl- r 2 x SDy

SD slope = r x --y intercept = avgy - slope x avgxSDx

)

2

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- - ~~~~~~_-


Monday October 22 2007

Your Name

Question 1 ChanceProbability I (6 Points)

A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer

1 There is a 1 chance in 52 for the first card to be the ace of clubs True False

2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False

3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False

~lt~J Question 2 ChanceProbability II (3 Points)

A coin is tossed six times Two possible sequences of results are

(i) H T T H T H (ii) H H H H H H

(The coin must land on H or T in the order given H = heads T = tails)

Which of the following is correct

Circle your answer

1 Sequence (i) is more likely

2 Sequence (ii) is more likely

3 Both sequences are equally likely

Please turn over

1

~ - -- _ -- -

Question 3 ChanceProbability III (3 Points)

Two cards will be dealt off the top of a well-shuffled deck You have a choice

(i) To win $1 if at least one of the two cards is a queen

(ii) To win $1 if the first card is a queen

Circle your answer

1 Option (i) is better for winning

2 Option (ii) is better for winning

3 Both options are equally good for winning

Question 4 ChanceProbability IV (4 Points)

One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences

If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances

Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances

Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances

Question 5 ChanceProbability V (4 Points)

A coin is tossed 10 times Circle your answer

1 The chance of getting 10 heads in a row is 11024 True False

2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False

2

Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)


Your Name ~---------

Question 1 Law of Averages I (2 Points)

A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations

1 The number of ls will be 6000 exactly

2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000

3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000

Question 2 Law of Averages II (8 Points)

Circle your answer for each of the following four parts You dont have to provide any explanations

1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time

Which is better 60 rolls or 600 rolls

2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15


3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20


4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot


1

Question 3 The Expected Value and Standard Error (10 Points)

One hundred draws are made at random with replacement from the box

1 (1 Point) If the sum of the draws is 321 what is their average

2 (1 Point) If the average of the draws is 378 what is the sum

3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work

Formulas

sum of all numbers in box box average =

how many numbers in box

box SD = Javerage of (deviations from box average)2]

EVsum = number of draws x box average

SEsum = vnumber of draws X box SD-)

2

Tablesmiddot

A NORMALTABLB

z iN- 1~ Ar~a

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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944

1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91

075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull

O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt

100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il

11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll

fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611

3

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~- ~~ - - - bull - -- -- - shy


Friday November 2 2007

Your Name

Question 1 Normal Approximation for Probability Histograms I (12 Points)

A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes

Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer

Please turn over

1

Question 2 Normal Approximation for Probability Histograms II (8 Points)

A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately

1 The expected value for the number of heads is 50

True False

2 The expected value for the number of heads is 50 give or take 5 or so

True False

3 The number of heads will be 50

True False

4 The number of heads will be around 50 give or take 2 or so

True False

Formulas


how many numbers In box

box SD = Javerage of [(deviations from box average)2]


SEsum = Jnumber of draws x box SD

Shortcut formulas for a box that contains only two different numbers

(smaller x how many) + (bigger x how many) average =

how many tickets in the box

fraction fractionSD = (bigger - smaller) x

bigger x

smaller

Shortcut formulas for a box that contains only [Q] s and ITJ s

number of ITJ s average =

how many tIckets In the box

fraction fraction SD = of [] s x of [Q] s

2

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3

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)


Frida~ November 16 2007

Your Name

Question 1 The Accuracy of Percentages (20 Points)

The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb

1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible

2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible

Please turn over

1

Formulas



box SD = Javerage of [(deviations from box ~erage)2]


SEsum = vnumber of draws x box SD

SEsumSE =EVavg = box average av 9 number of draws



how many tickets In the box

fraction fractionSD = (bigger - smaller) x x

bigger smaller

Shortcut formulas for a box that contains only [Q] s and IT] s

number of IT] s average =


fraction fraction SD

of IT] s x of [Q] s

EV = of[J s in the box

SEsumSEor = x 100 o number of draws

2

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Wednesday November 282007

Your Name

Question 1 The Accuracy of Averages (20 Points)

One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate

Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why

1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025

Yes No or Need more information Circle your answer and explain

2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools


Please turn over

1

3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500


4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students


5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve


2

Formulas

sum of all numbers in boxbox average = ----------shy







(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox

fraction x fractionSD = (bigger - smaller) x

bigger smaller

Shortcut formulas for a box that contains only [Q] s and [I] s

number of ill s average = h k h b ow many tIc ets III t e ox


of II] s x of] s

EV = of [I] s in the box

SE = SEsum x 100 number of draws

3

- ~- -- ~~-~--


Wednesday December 5 2007

Your Name ---------- shy

Question 1 Tests of Significance I (20 Points)

A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set

41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48

A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve

Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)

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In 1990 four passengers were killed by crashes on commuter airlines compared to 39 killed on scheduled carriers (like United TWA and so forth) True or false Circle your answer and explain the data show that if you have to fly it is safer to do so on a commuter airline

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Number 47

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I I I


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A NORMAL TABLE



025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944

050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961

I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978

075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988

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0~95 6579 245 9857 395 99992 I

100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949

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I 120 7699 270 9931 420 999913f

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A NORMAL TABLE



025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944

050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961

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075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988

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I 120 7699 270 9931 420 999913f

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Tablesmiddot )

A NORMAL TABLE



025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944

050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961

I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978

075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988

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0~95 6579 245 9857 395 99992 I

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I 120 7699 270 9931 420 999913f

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) ~gt 135 8230 285 9956 435 1999986














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A NORMALTABLB

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A NORMAL TABLE



025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944

050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961

I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978

075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988

~ bull~-- 090 6319 240 9836 390 99990 j

0~95 6579 245 9857 395 99992 I

100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949

110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot

I 120 7699 270 9931 420 999913f

I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983

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2

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A NORMALTABLB

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3

- ~- -- ~~-~--






41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48




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2

Formulas










bigger smaller




of II] s x of] s



3

- ~- -- ~~-~--






41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48




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bigger smaller




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S

183

4 2L

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20

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193

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278

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252

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83

SO

lirtC

Ada

ptcd

fro

in P

O 11

2 o(

Sir

R A

Fi

shcr

SIQtiIN~QI

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km

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1

71

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l

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2

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2

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25

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1

71

~06

2

79

~

~~

shy

statistics 1040, sections 007 009, quiz 1 (20 points)symanzik/teaching/2008_stat1040/... · 2008....

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