Consider the following hypothesis test.

Sample 1		Sample 2

Enter negative values as negative numbers.

a. What is the value of the test statistic? (to 2 decimals)

-1.53

b. What is the -value? (to 4 decimals)

0.12602

c. With , what is your hypothesis testing conclusion?

Do not reject the null hypothesis

2. Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation’s largest supermarkets (Consumer Reports website). Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with meaning the respondent is completely satisfied in terms of all factors. Sample data representative of independent samples of Publix and Trader Joe’s customers are shown below.

a. Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers.

equal to 0

not equal to 0

b. Assume that experience with the Consumer Reports satisfaction rating scale indicates that a population standard deviation of is a reasonable assumption for both retailers. Conduct the hypothesis test and report the -value.

0.331

I. Reject . There is not sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers.

II. Do not reject . There is not sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers.

III. Reject . There is sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers.

IV. Do not reject . There is sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers.

c. Which retailer, if either, appears to have the greater customer satisfaction?

Cannot be determined

Provide a confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. Enter negative values as negative numbers, if any.

-1.0141 3.0141

3. Consider the following data for two independent random samples taken from two normal populations.

Sample 1	10	7	13	7	9	8
Sample 2	8	7	8	4	6	9

a. Compute the two sample means. (to nearest whole number)

b. Compute the two sample standard deviations. (to 2 decimals)

2.28

1.79

c. What is the point estimate of the difference between the two population means?

d. What is the confidence interval estimate of the difference between the two population means? (to 2 decimals and enter negative value as negative number)

-0.17 4.17

4. The increasing annual cost (including tuition, room, board, books and fees) to attend college ) to attend college has been widely discussed in many publications including Money magazine. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Click on the datafile logo to reference the data. Round degrees of freedom to the preceding whole number.

Private Colleges
52.8	43.2	45.0	33.3	44.0
30.6	45.8	37.8	50.5	42.0
Public Colleges
20.3	22.0	28.2	15.6	24.1	28.5
22.8	25.8	18.5	25.6	14.4	21.8

a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places.

42.50

22.30

6.98

4.53

b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place.

20.2

Interpret this value in terms of the annual cost of attending private and public colleges.

20200

c. Develop a confidence interval of the difference between the mean annual cost of attending private and public colleges.confidence interval, private colleges have a population mean annual cost 14696 to 25704 more expensive than public colleges.

5. Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services. Higher ratings on the client satisfaction survey indicate better service with the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has years of experience, whereas consultant B has year of experience. Use and test to see whether the consultant with more experience has the higher population mean service rating. Round degrees of freedom to previous whole number.

a. State the null and alternative hypotheses.

is less than or equal to 0

is greater than 0

b. Compute the value of the test statistic. (to 2 decimals)

1.99

c. What is the p-value? Use Table 2 from Appendix B to find the values that bound the test statistic.

0.025 0.05

d. What is your conclusion?

Reject the null hypothesis

6. Bank of America’s Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. Using data from a sample of credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). Using the difference data, the sample mean difference was , and the sample standard deviation was .

a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

equal to 0

not equal to 0

b. Use level of significance. Can you conclude that the population means differ?

differ

What is the -value? (to 6 decimals)

0.000008

c. Which category, groceries or dining out, has a higher population mean annual credit card charge?

Grocerices

What is the point estimate of the difference between the population means? Round to the nearest whole number.

850

What is the confidence interval estimate of the difference between the population means? Round to the nearest whole number.

499.7987 1200.203

7. The College Board SAT college entrance exam consists of two sections: math and evidence-based reading and writing (EBRW). Sample data showing the math and EBRW scores for a sample of students who took the SAT follow. Click on the datafile logo to reference the data.

Student	Math	EBRW	Student	Math	EBRW
1	540	474	7	480	430
2	432	380	8	499	459
3	528	463	9	610	615
4	574	612	10	572	541
5	448	420	11	390	335
6	502	526	12	593	613

a. Use a level of significance and test for a difference between the population mean for the math scores and the population mean for the EBRW scores.

2.34

What is the -value? Round your answer to four decimal places.

.0394

What is your conclusion?

I. Reject . We cannot conclude that there is a significant difference between the population mean scores for the SAT math test and the SAT writing test.

II. Do not reject . We cannot conclude that there is a significant difference between the population mean scores for the SAT math test and the SAT writing test.

III. Reject . We can conclude that there is a significant difference between the population mean scores for the SAT math test and the SAT writing test.

IV. Do not reject . We can conclude that there is a significant difference between the population mean scores for the SAT math test and the SAT writing test.

b. What is the point estimate of the difference between the mean scores for the two tests?

What are the estimates of the population mean scores for the two tests?

514

489

Which test reports the higher mean score?

Math test

8. A personal fitness produces both a deluxe and a standard model of a smoothie blender for home use. Selling prices obtained from a sample of retail outlets follow.

a. The manufacturer’s suggested retail prices for the two models show a price differential. Use a level of significance and test that the mean difference between the prices of the two models is .

Do not reject the null hypothesis (Ho=10) W

b. What is the confidence interval for the difference between the mean prices of the two models?

6.44 11.27

9. Consider the hypothesis test below.The following results are for independent samples taken from the two populations.

a. What is the -value (to 4 decimals)? Use Table 1 from Appendix B.

0.0248

b. With , what is your hypothesis testing conclusion?

Conclude the difference between the proportions is greater than 0

10. Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel, May , ). Hotel occupancy data for February in two consecutive years are as follows

Current Year	Previous Year
Occupied Rooms	1,470	1,360
Total Rooms	1,750	1,700

a. Formulate the hypothesis test that can be used to determine whether there has been an increase in the proportion of rooms occupied over the one-year period.

less than or equal to 0

greater than 0

b. What is the estimated proportion of hotel rooms occupied each year (to decimals)?

Current year 0.84

previous year 0.80

c. Conduct a hypothesis test. What is the -value (to decimals)? Use Table 1 from Appendix B.

0.0011

Using a level of significance, what is your conclusion?

can canclude

d. What is the confidence interval estimate of the change in occupancy for the one-year period (to decimals)?

0.0144 0.0656

Do you think area officials would be pleased with the results?

pleased an increase

11. The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are as follows.

Kitchen	Master Bedroom	Kitchen	Master Bedroom
25.2	18.0	23.0	17.8
17.4	22.9	19.7	24.6
22.8	26.4	16.9	21.0
21.9	24.8	21.8
19.7	26.9	23.6

a. Develop a point estimate of the difference between the population mean remodeling costs of kitchens and master bedrooms. (Enter negative values as negative numbers. Report in thousands of dollars with no commas in your answer.)

-1.6

b. Develop a confidence interval for the difference between the two population means. (to 1 decimal and enter negative values as negative numbers)

-4.30787 1.10787

12. Country Financial, a financial services company, uses surveys of adults age and older to determine whether personal financial fitness is changing over time. A recent sample of adults showed indicating that their financial security was more than fair. Just a year prior, a sample of adults showed indicating that their financial security was more than fair.

a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.

equal to

not equal to

b. Conduct the hypothesis test and compute the -value. Round your answer to four decimal places.

0.0072

At level of significance, what is your conclusion?

I. Reject . There is not sufficient evidence to conclude that the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.

II. Reject . There is sufficient evidence to conclude that the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.

III. Do not reject . There is not sufficient evidence to conclude that the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.

IV. Do not reject . There is sufficient evidence to conclude that the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.

c. What is the confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.

0.0164 0.1036

13. Each year, over million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention has launched studies of drug-resistant gonorrhea (CDC.gov website). Of cases tested in Alabama, were found to be drug-resistant. Of cases tested in Texas, were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a level of significance. What is the -value, and what is your conclusion?

Test statistic = 2.37 (to 2 decimals)

-value = 0.0178 (to 4 decimals)

Conclusion Reject the null hypothesis

Choose the correct option.

There is a significant difference in drug resistance between the two states. Alabama has the higher drug resistance rate.

True

14. Find the following chi-square distribution values from Table 11.1 or Table 3 of Appendix B. (to decimals)

a. with

11.070

b. with

27.488

c. with

9.591

d. with

23.209

e. with

9.390

14. In , Mike Krzyewski and John Calipari topped the list of highest paid college basketball coaches (Sports Illustrated website). The following sample shows the head basketball coach’s salary for a sample of schools playing NCAA Division I basketball. Salary data are in millions of dollars.

University	Coach’s Salary	University	Coach’s Salary
North Carolina State	2.2	Miami (FL)	1.5
Iona	0.5	Creighton	1.3
Texas A&M	2.4	Texas Tech	1.5
Oregon	2.7	South Dakota State	0.3
Iowa State	2.0	New Mexico State	0.3

a. Use the sample mean for the schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division I basketball (to decimals).

$ 1.47 million

b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to decimals).

$ 0.8756 million

c. What is the confidence interval for the population variance (to decimals)? Use Table 11.1.

($ 0.36 million, $ 2.56 million)

d. What is the confidence interval for the population standard deviation (to decimals)? Use Table 11.1.

($ 0.60 million, $ 1.6 million)

15. In , Americans spent a record-high billion on Halloween-related purchases (the balance website). Sample data showing the amount, in dollars, adults spent on a Halloween costume are as follows.

10	70	21	61
30	37	32	43
54	16	15	99
45	31	65	28

a. What is the estimate of the population mean amount adults spend on a Halloween costume (to decimals)?

41.06

b. What is the sample standard deviation (to decimals)?

23.83

c. Provide a confidence interval estimate of the population standard deviation for the amount adults spend on a Halloween costume (to decimals). Use Table 11.1.

17.60 36.88

15. The competitive advantage of some small American factories such as In Tolerance Contract Manufacturing lies in their ability to produce parts with very narrow requirements, or tolerances, that are typical in the aerospace industry. Consider a product with specifications that call for a maximum variance in the lengths of the parts of . Suppose the sample variance for parts turns out to be . Use , to test whether the population variance specification is being violated.

Last option

First option

Test statistic = 43.75 (to 2 decimals, if required)

Greater than 0.10

option 1

16. Find the following distribution values from Table 4 of Appendix B (available online).

a. with degrees of freedom and

3.33

b. with degrees of freedom and

2.76

c. with degrees of freedom and

4.5

d. with degrees of freedom and

1.94

17. In its Auto Reliability Survey, Consumer Reports asked subscribers to report their maintenance and repair costs. Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of automobiles years old showed a sample standard deviation for annual repair costs of and a sample of automobiles years old showed a sample standard deviation for annual repair costs of .

a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. Let year old automobiles be represented by population .

Less than or equal to

greater than

b. At a level of significance, what is your conclusion?

2.25

between 0.025 and 0.05

Do not conclude

18. The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Jelly Belly Candy Company is testing two machines that use different technologies to fill three pound bags of jelly beans. The file Bags contains a sample of data on the weights of bags (in pounds) filled by each machine.Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements? Click on the datafile logo to reference the data.

0.0489

0.0059

8.2844

Reject

Machine 1

19. Battery life is an important issue for many smartphone owners. Public health studies have examined “low-battery anxiety” and acute anxiety called “nomophobia” that results when a smartphone user’s phone battery charge runs low and then dies (Wall Street Journal, May , ). Battery life between charges for the Samsung Galaxy S9 averages hours when the primary use is talk time and hours when the primary use is Internet applications. Because the mean hours for talk time usage is greater than the mean hours for Internet usage, the question was raised as to whether the variance in hours of usage is also greater when the primary use is talk time. Sample data showing battery life between charges for the two applications follows. Click on the datafile logo to reference the data.

a. Formulate hypotheses about the two population variances that can be used to determine whether the population variance in battery life is greater for the talk time application. Consider the talk time use as population and Internet use as population .

Less than or equal to

greater than

b. What are the standard deviations of battery life for the two samples (to decimals)?

7.36

4.77

c. Conduct the hypothesis test and compute the -value.

0.091506

Using a level of significance, what is your conclusion?

Do not reject cannot conclude

20. Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of days of operation shows a sample mean of rooms occupied per day and a sample standard deviation of rooms.

a. What is the point estimate of the population variance (to nearest whole number)?

900

b. Provide a confidence interval estimate of the population variance (to nearest whole number). Use Table 11.1.

567 1690

c. Provide a confidence interval estimate of the population standard deviation (to decimal). Use Table 11.1.

23.8 41.1

21. According to the Corporate Travel Index compiled by Business Travel News, the average daily cost for business travel in the United States rose to per day (Executive Travel website). The file Travel contains sample data for an analogous study on the estimated daily living costs for an executive traveling to various international cities. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs. Click on the datafile logo to reference the data.

a. Compute the sample mean (to decimals).

260.16.

b. Compute the sample standard deviation (to decimals).

70.69

c. Compute a confidence interval for the population standard deviation (to decimals). Use Table 11.1.

53.76 103.24

22. Filling boxes with consistent amounts of its cereals are critical to General Mills’ success. The filling variance for boxes of Count Chocula cereal is designed to be ounces² or less. A sample of boxes of Count Chocula shows a sample standard deviation of ounces. Use to determine whether the variance in the cereal box fillings is exceeding the design specification. Use Table 11.1.

option 1

option 3

Test statistic = 51.20 (to decimals)

do not reject

Interpret: The population variance appears to be exceeding the standard.

False

23. A sample of days over the past six months showed that that Philip Sherman, DDS, treated the following numbers of patients: , , , , , , , , and . If the number of patients seen per day is normally distributed, would an analysis of these sample data reject the hypothesis that the variance in the number of patients seen per day is equal to ? Use level of significance. Use Table 3 from Appendix B.

equal to

not equal to

Calculate the variance and test statistic. (to 2 decimals)

12.69

10.16

What is your conclusion?

do not reject

24. Stable cost reporting in a manufacturing setting is typically a sign that operations are running smoothly. The accounting department at Rockwell Collins, an avionics manufacturer, analyzes the variance of the weekly costs reported by two of its production departments. A sample of cost reports for each of the two departments shows cost variances of and , respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use (to decimals).

equal to

not equal to

Test statistic = 2.35

Do not reject

25. During the first weeks of the television season, the Saturday evening 8:00 P.M. to 9:00 P.M. audience proportions were recorded as ABC , CBS , NBC , and Independents . A sample of homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC homes, CBS homes, NBC homes, and Independents homes. Test with to determine whether the viewing audience proportions changed.

Find the test statistic and p-value. (Round your test statistic to two decimal places. Use Table 3 of Appendix B.)

Test statistic = 6.62

between 0.05 and 0.10

Conclusion

no significant

26. The following table contains observed frequencies for a sample of .

Column Variable
Row Variable	A	B	C
P	35	50	40
Q	15	20	40

Test for independence of the row and column variables using .

Compute the value of the test statistic (to 2 decimals).

8.91

between 0.01 and 0.025

conclude the row

27. In , Addison Group and Kelton surveyed the work preferences and attitudes of working adults spread over three generations — Baby Boomers, Generation X, and Millennials (Society for Human Resource Management website). One question asked individuals if they would leave their current job to make more money at another job. The file Millennials contains the sample data, which is also summarized in the following table.

Conduct a test of independence to determine whether interest in leaving a current job for more money is independent of employee generation.

Compute the value of the test statistic (to decimals). Do not round your intermediate calculation.

6.13

What is the -value? Use Table 3 of Appendix B.

Between 0.025 and 0.05

Using a level of significance, what is your conclusion?

is not

28. The Wall Street Journal Corporate Perceptions Study surveys readers and asks how each rats the quality of management and the reputation of the company for over worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good, and fair categorical scale. Assume the sample data for respondents below applies to this study.

Reputation of Company
Quality of Management	Excellent	Good	Fair
Excellent	40	25	5
Good	35	35	10
Fair	25	10	15

a. Use level of significance and test for independence of the quality of management and the reputation of the company.

Compute the value of the test statistic (to 2 decimals). Do not round intermediate calculations.

17.03

Use Table 3 of Appendix B to find the -value.

less than 0.005

not independent

b. If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.

have the same rating and associated

29. Use the sample data below to test the hypotheses

Populations
Response	1	2	3
Yes	150	150	94
No	100	150	106

Using a level of significance, what is the -value? Use Table 3 of Appendix B.

between 0.01 and 0.025

What is your conclusion?

cannot conclude

30. The following sample data represent the number of late and on time flights for the Delta, United and US Airways.

Airline
Flight	Delta	United	US Airways
Late	39	51	56
On Time	261	249	344

a. Formulate the hypotheses for a test that will determine whether the population proportion of late flights is the same for all three airlines.

All

Not

b. Conduct the hypothesis test with a level of significance. What is the -value? Use Table 3 of Appendix B.

greater than 0.10

What is your conclusion?

Unable to reiect the null hypothesis that the population proportions are same

c. Compute the sample proportion of late flights for each airline.

0.130

0.170

0.140

.146

31. Kate Sanders, a researcher in the department of biology at IPFW University, studied the effect of agriculture contaminants on the stream fish population in northeastern Indiana. Specially designed traps collected samples of fish at each of four stream locations. A research question was, Did the differences in agricultural contaminants found at the four locations alter the proportion of the fish population by gender? Observed frequencies were as follows.

Stream Locations
Gender	A	B	C	D
Male	49	44	49	39
Female	41	46	36	44

a. Focusing on the proportion of male fish at each location, test the hypothesis that the population proportions are equal for all four locations. Use a level of significance.

Not all population

What is the -value? Use Table 3 of Appendix B.

greater than 0.10

What is your conclusion?

option 4

b. Does it appear that differences in agricultural contaminants found at the four locations altered the fish population by gender?

32. Social media is popular around the world. Statista provides estimate of the number of social media users in various countries in as well as the projections for . Assume that the results for surveys in the United Kingdom, China, Russia, and the United States are as follows.

a. Conduct a hypothesis test to determine whether the proportion of adults using social media is equal for all four countries. Using a level of significance.

Not all population

What is the -value? Use Table 3 of Appendix B.

less than 0.01

What is your conclusion?

not equal

b. What are the sample proportions for each of the four countries? Round your answers to two decimal places.

0.60

0.43

0.49

Which country has the largest proportion of adults using social networking sites?

United states

c. Using a level of significance, conduct multiple pairwise comparison tests among the four countries. Round , and to two decimal places. Round to four decimal places.

0.60 0.43 .17 800 500 0.0786 Yes

0.60 0.49 0.11 800 800 0.0717 yes

0.60 0.64 0.04 800 1000 0.0644 No

0.43 0.49 0.06 500 700 0.0814 No

0.43 0.64 0.21 500 1000 0.0750 Yes

0.49 0.64 0.15 700 1000 0.0678 Yes

What is your conclusion?

UK vs US Vs C vs R

32. Historically, the industries with the most complaints to the Better Business Bureau have been banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of complaints are contained in the file BBB. Click on the datafile logo to reference the data.

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