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Chi Square Test of Independence on Purchase of Clothing

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15. Where do women most often buy casual clothing? Data from the U.S. Shopper Database provided the following percentages for women shopping at each of the various outlets.

Outlet Percentage Outlet Percentage
Wal mart 24 Kohl's 8
Traditional department 11 Mail Order 12
JCPenney 8 Other 37

The other category included outlets such as Target, Kmart, and Sears as well as numerous smaller specialty outlet. No individual outlet in this group accounted for more than 5% of the women shoppers. A recent survey using a sample of 140 women shoppers in Atlanta, Georgia found 42 Wal-Mart, 20 traditional department store, 8 J.C. Penney, 10 Kohl's, 21 mail order, and 39 other outlet shoppers. Does this sample suggests that women shoppers in Atlanta differ from the shopping preferences expressed in the U.S. Shopper Database? What is the p-value? Use a = .05. What is your conclusion?

17. The Wall Street Journal's Shareholder Scoreboard tracks the performance of 1000 major U.S. companies. The performance of each company is rated on the annual total return, including stock price changes and the reinvestment of dividends. Ratings are assigned by dividing all 1000 companies into five groups from A (top 20%), B (next 20%), to E (bottom 20%) Shown here are the one-year ratings for a sample of 60 of the largest companies. Do the largest companies differ in performance from the performance of the 1000 companies in the Shareholder Scoreboard? Use a = .05

5 8 15 20 12

23. With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage. The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purpose of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies.
Health Insurance
Size of Company Yes No Total
Small 36 14 50
Medium 65 10 75
Large 88 12 100

a. Conduct a test of independence to determine whether a employee health insurance coverage is independent of the size of the company. Use a = .05. What is the p-value, and what is your conclusion?
b. The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Use percentage based on the preceding data to support this conclusion.

25. Negative appeal is recognized as an effective method of persuasion in advertising. A study in The Journal of Advertising reported the results of a content analysis of guilt and fear advertisements in 24 magazines. The number of ads with guilt and fear appeals that appeared in selected magazine types follows.

Type of Appeal

Number of Ads Number of Ads
Magazine Type with Guilt Appeals with Fear Appeals

News and opinions 20 10
General editorial 15 11
Family Editorial 30 19
Business/financial 22 17
Female-oriented 16 14
African-American 12 15

Use the chi-square test of independence with a .01 level of significance to analyze the data.

What is your conclusion?

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Solution Summary

Chi square test of Independence.
Null Hypothesis, Alternative Hypothesis, Significance Level, Critical Value and P value are discussed. Interpretation of the results are also given.