Assignment #1 – On material from Lecture #3

1) Construct a categorical frequency distribution for the men’s favorite color data in the Class Data Base. Consider anything that contains the word ‘blue’ to be blue and ‘orange’ to be orange. Each other color is a separate class. Don’t make a category for men with no favorite color. Include the name of the class, the tallies, the frequencies, and the relative frequencies to the nearest percent.

2) Construct a grouped frequency distribution table for the men’s age data in the Class Data Base. Let the lower limit of the first class be 17 and the class width be 4 years. Include in your table the class limits, class boundaries, tallies, frequencies, and relative frequencies as decimals rounded to the nearest hundredth.

3) Make a Pareto chart for the men’s favorite color data from Problem #1. Label each axis. Must be on graph paper.

4) Make a pie chart for the men’s favorite color data from Problem #1.

5) Make a histogram for the men’s age data from Problem #2. Include a label for each axis. Must be on graph paper.

6) Using only the men in the Class Data Base, make a scatter plot with shoe size as the x-variable and height as the y-variable. Label each axis. Must be on graph paper.

7) Looking at questions titled Native and Grad (local native, local high school graduate) on the survey, there are four possible outcomes for each person: YY, YN, NY, NN. Figure out a way to represent these categories, and have your representation include how many students are in each of the four categories. (Many different ways to do this.)

For use in Assignment #1:

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Assignment #2 – On material from Lectures #4 and #5

1) This small spreadsheet gives data for the five people in the Class Data Base who wear size 8.5 shoes:

Shoe Size Age Height in Inches

Number of Pets

8.5 18 67 08.5 32 67 08.5 18 65 08.5 20 68 18.5 30 68 3

For each variable (shoe size, age, height, and number of pets) find the

a) Modeb) Medianc) Meand) Midrangee) Rangef) Variance (to the nearest tenth)g) Standard Deviation (to the nearest tenth)h) Coefficient of Variation (to the nearest whole percent)

Use the table method in finding the variance, and include the tables in your homework paper.

2) Using the notation in Lecture #4, the following table describes the variables in the Class Data Base for shoe size, age, and number of pets:

Shoe Size Age Number of Pets

Men: nM=36 xM=10.528 xM=22.44 4 xM=1.528

Women: nF=41 xF=7.707 xF=24.927 xF=2.829

Use the weighted mean formula to find the mean shoe size, age, and number of pets for the entire sample, to the nearest thousandth.

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Assignment #3 – On material from Lecture #8

Number of PetsNo Pets 1 or 2 Pets 3 or 4 Pets At Least 5 Pets

SexMale 8 20 6 2

Female 12 16 8 5

Use the contingency table to answer these questions. Give answers as unreduced fractions. If one person is selected randomly from the survey group, find the probability that the person

1) Is female

2) Has one or two pets

3) Has no pets

4) Has fewer than five pets

5) Is female and has one or two pets

6) Is female or has one or two pets

7) Has at least one pet

8) Is male given that the person has no pets

9) Has no pets given that the person is male

10) Is male and has three or four pets

11) Is male or has three or four pets

12) Is female and has fewer than five pets

13) Is female or has fewer than five pets

14) Is female given that the person has one or two pets.

15) Has one or two pets, given that the person is female.

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DIE #21 2 3 4 5 6

11,1 1,2 1,3 1,4 1,5 1,622,1 2,2 2,3 2,4 2,5 2,6

DIE #1 33,1 3,2 3,3 3,4 3,5 3,644,1 4,2 4,3 4,4 4,5 4,655,1 5,2 5,3 5,4 5,5 5,666,1 6,2 6,3 6,4 6,5 6,6

These questions deal with the rolling of two fair dice. Give answers as unreduced fractions.

Find the probability that

16) their sum is 5

17) their sum is not 5

18) their sum is an even number

19) they are both even numbers

20) one is even and one is odd

21) die #1 has a smaller number than die #2

22) their product is a perfect square

23) their sum is at least 9

24) their sum is at most 8

25) the first is 2 and the second is 5

26) the first is 2 or the second is 5

27) the first is even and the second is odd

28) the first is even or the second is odd

29) the absolute value of their difference is 3

30) their product exceeds 12

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Assignment #4 – On material from Lecture #9

1. A garage sale offers 12 different novels, 7 different CDs, and 5 different DVDs. You want to buy one of each. How many different ways can this be done?

2. How many different ways can 9 children line up?

3. At a carnival, you may pick 4 rides to go on and the order in which to ride them. You don’t want to repeat any of the rides. There are 11 rides altogether. How many ways can you pick the rides?

4. How many different ways (orders) can you visit 6 tourist attractions during your vacation?

5. You want to study for 4 of your 6 courses tonight, and it matters to you which you study first, second, etc. How many different study schedules can you choose from?

6. How many ways can a diner select 3 appetizers and 2 vegetables if there are 7 appetizers and 5 vegetables on the menu?

7. How many ways can 6 sopranos and 7 altos be selected from 12 sopranos and 15 altos?

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8. A baseball team has 7 pitchers: 4 are left-handed (lefties), and 3 are right-handed (righties). Three of them are injured. Find these probabilities, and give them as decimals rounded to the nearest thousandth:

a. All three injured ones are lefties

b. All three injured ones are righties

c. 2 are righties and 1 is a lefty

d. 1 is a righty and 2 are lefties

9. A large litter consists of 10 kittens, 3 of which are striped. If 4 are selected, find the probability of getting

a. No striped ones

b. 1 striped one

c. 3 striped ones

Express your answers as decimals rounded to the nearest thousandth.

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Assignment #5 – On material from Lecture #10

1) A couple plans to have three children. The sex of each child is independent of the sex of the other children, and boys and girls are equally likely to be born.

a) Using M for a boy and F for a girl, list all possible birth-order sequences for the three children.

b) Let x be the random variable denoting how many boys are in the family.i) Make a probability table for the random variable xii) Find the mean of the probability distribution of x. Show your workiii) Find the standard deviation for the probability distribution of x to

the nearest tenth. Show your work.c) How many boys would you expect in 60 such families?

2) Do the same things and answer the same questions as in #1, only this time the couple plans to have five children.

3) Jon eats anywhere from one to five candy bars per day, a decision he makes in a random way. One-tenth of the days he eats one candy bar. One-fifth of the days he eats two candy bars. Two-fifths of the days he eats three candy bars, and one-tenth of the days he eats four candy bars. a) What fraction of the days does he eat five candy bars?b) Let the random variable x be the number of candy bars Jon eats during a day.

i) Make a probability table for the random variable xii) Find the mean for the probability distribution of x. Show your

workiii) Find the standard deviation for the probability distribution of x to

the nearest tenth. Show your work.iv) What is the probability that on any given day Jon will eat a number

of candy bars that is within one standard deviation of the mean? Show your work.

v) What is the expected value of the probability distribution of x?c) How many candy bars would Jon average in 8 days?d) How many candy bars can Jon expect to eat in 5 weeks? e) How many candy bars can Jon expect to eat in a year?

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Assignment #6 – On material from Lectures #13 and #14

Pretend that the Class Data Base is a random sample of Mendocino College students. Round answers in Problems 1-3 to the nearest hundredth.1) Find

a) a 99% confidence intervalb) a 95% confidence interval, andc) a 90% confidence intervalfor the average height of Mendocino College students.

2) Repeat #1 for the average age of Mendocino College students

3) Repeat #1 for the average number of pets owned by Mendocino College students.

In Problems 4-6, use s to the nearest thousandth.4) Find the minimum sample size needed to be 90% confident of estimating the average height of Mendocino College students accurately within a quarter of an inch?

5) Find the minimum sample size needed to be 95% confident of estimating the mean age of Mendocino College students accurately within 6 months?

6) Find the minimum sample size needed to be 99% confident of estimating the average number of pets owned by Mendocino College students accurately within 0.4 pets?

Round answers in Problems 7 and 8 to the nearest thousandth.7) Find

a) a 99% confidence interval,b) a 95% confidence interval, andc) a 90% confidence intervalfor the true proportion of Mendocino College students who are natives of Mendocino or Lake County.

8) Repeat #7 for the true proportion of Mendocino College students who wear shoes that are at least size 10.

9) Find the minimum sample size needed for estimating, at the 90% confidence level, a proportion with an accuracy of ± 4% .

10) Find the minimum sample size needed for estimating, at the 95% confidence level, a proportion within 0.02.

11)Find the minimum sample size needed for estimating, at the 99% confidence level, a proportion within 3%.

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Assignment #7 – On material from Lecture #16

STEPS IN TESTING CLAIMSA) State the hypotheses and identify the claim.B) Perform the test using the sample data or statistics, and make a diagram showing the distribution, the parameter and the statistic. Shade and label the p-value, which should be rounded to the nearest thousandth. C) Decide whether or not to reject the null hypothesis.D) Summarize the results.

1) It has been reported that the average annual amount that college seniors spend on cell phones is $1200. The student senate at a large university claims that their seniors spend much less than this, so it conducts a study of 75 randomly selected seniors and finds that the average spent is $1167, with a sample standard deviation of $106. Test the senate’s claim using the 1% significance level.

2) Ten years ago, the average acreage of farms in a certain geographic region was 48 acres. A recent study included 25 farms with sample mean 52.5 acres per farm and sample standard deviation 18.9 acres. Test the claim, at the 10% significance level, that the average has changed.

3) The average yield of wine grapes in a certain valley in Northern California is 3000 pounds per acre. A new method of viticulture has been developed and is tested on 50 individual vineyards. The mean yield under the new system is 3128 pounds of grapes per acre with a standard deviation of 574 pounds. At the 5% significance level, test the claim that the average yield has increased.

4) A special cable is said to have a breaking strength of 750 pounds. A researcher selects a sample of 20 cables and finds that the average breaking strength is 735.8 pounds, with a standard deviation of 19.6 pounds. Test the claim that the average breaking strength is 750 pounds at the 1% significance level.

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Assignment #8 – On Material from Lecture #17

STEPS IN TESTING CLAIMSA) State the hypotheses and identify the claim.B) State the values of x and n. Perform the test using the sample data or statistics, and make a diagram showing the distribution, the parameter and the statistic. Shade and label the p-value, which should be rounded to the nearest thousandth. C) Decide whether or not to reject the null hypothesis.D) Summarize the results.

Test these claims.

1) It has been claimed that a majority of Americans have adequate health insurance. In a survey in which 200 people were interviewed, it was found that 57% have adequate health insurance. Test the claim at the 5% level of significance.

2) A journalist asserts that at most 40% of the population favors a national lottery. In a random sample of 400 adults, 184 expressed support for a national lottery. At the 1% significance level, what should be concluded about this claim?

In these problems, assume that the 78 people in the class survey constitute a random sample of Mendocino College students.

3) A researcher studying demographics thinks that a minority of Mendocino College students are not graduates of a Lake or Mendocino County high school. If 20 of the people surveyed are not graduates of a Lake or Mendocino County high school, test the claim at the 1% significance level.

4) Another researcher is studying consumer habits of community college students and claims that three-fourths of Mendocino College students own cars made in 2004 or later. Test the claim at the 10% significance level, given that 53 people surveyed had cars from 2004 or later.

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Assignment # 9 – On material from Lecture #21

In Problems 1-4, state the equation of the regression line and the value of the sample correlation coefficient, to the nearest thousandth. 1) Using age as the predictor variable and number of pets as the response variable.

2) Using height as the independent variable and shoe size as the dependent variable.

3) Using shoe size as the predictor variable and age as the response variable.

4) Using shoe size as the independent variable and height as the dependent variable.

Predict the following, rounding to the nearest tenth, using 0.600 as the cut-off for r:5) The height of a person who wears a size 10 shoe.

6) The number of pets owned by a person who is 40 years old.

7) The age of a person with size 11 shoes.

8) The shoe size of a person who is 62 inches tall.

In the regression analysis involving height as the independent variable and shoe size as the dependent variable, find the residual to the nearest tenth for9) Person #9

10) Person #19

11) Person #34

12) Person #49

In the regression analysis involving shoe size as the independent variable and height as the dependent variable, find the residual to the nearest tenth for 13) Person #17

14) Person #23

15) Person #64

16) Person #71

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Assignment #10 – On material from Lecture #22

For each problem, a) State the hypotheses (and identify the claim),

b) Fill in the chart for O, p, E, and (O−E )2

E (round E’s and (O−E )2

E ’s to the nearest thousandth if necessary, and make a diagram showing the c

2 test value and the p-value (to the nearest thousandth),

c) State your decision whether to reject H0 , andd) Summarize the results.

1) A children’s raincoat manufacturer claims that customers prefer certain colors over others. He selected a random sample of 50 raincoats sold and noted their colors. There were 21 yellow, 12 red, 9 green, and 8 blue. Test his claim at α=0 .10 .

2) According to a recent census report, 68% of families have two parents present, 23% have only a mother present, 5% have only a father present, and 4% have neither parent present. A random sample of families from a large school district revealed that 146 had two parents, 34 mother only, 7 father only, and 13 neither. Test the claim that the school district’s distribution differs from the census at α=0 .01 .

3) The population distribution of federal prisons nationwide by serious offenses is the following: violent offenses, 12.6%; property offenses, 8.5%; drug offenses, 60.2%; weapons, 8.2%; immigration, 4.9%; other, 5.6%. A warden claims that his prison has the same percentages. A survey of 500 prisoners at his prison finds 64 violent offenders, 40 property offenders, 326 drug offenders, 42 weapons offenders, 25 immigration offenders, and 3 with other offenses. Test the warden’s claim at α=0 . 05 .

4) A quality control engineer claims that defective items are manufactured with the same frequency each day of the work week. A week is randomly selected at her factory, and the number of defective items produced each day is recorded. There were 32 on Monday, 16 on Tuesday, 23 on Wednesday, 19 on Thursday, and 40 on Friday. Test her claim at α=0 . 05 .

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