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Confidence Interval and Hypothesis Testing using Chi-square

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#7: In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded.

Commercial A Commercial B
Number Who Saw Commercial 150 200
Number Who Received Message 63 60

a. Use a = 0.05 and test the hypothesis that there is no difference in the recall proportions for the two commercials.
b. Compute a 95% confidence interval for the difference between the recall proportions for the two populations.

#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 (The Wall Street Journal, January 28, 2004).

Outlet Percentage

Wal-Mart 24%
J.C. Penney 8%
Kohl's 8%
Mail order 12%
Other 37%

The other category included outlets such as Target, Kmart, and Sears as well as numerous specialty outlets. 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 stores, 8 J.C. Penney, 10 Kohl's, 21 mail order, and 39 other outlet shoppers. Does this sample suggest that women shoppers in Atlanta differ from the shopping preferences expressed in the U.S. Shoppers Database? What is the p-value? Use a = 0.05. What is your 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 type follows.

Use the chi-squared test of independence with a 0.01 level of significance to analyze the data. What is your conclusion?

Magazine type
Type of Appeal

Number of Ads with Guilt Appeal Number of Ads with Fear Appeal
News and opinion 20 10
General editorial 15 11
Family-oriented 30 19
Female-oriented 16 14
African-American 12 15

Solution Summary

Answers to 3 questions on Confidence Interval and Hypothesis Testing have been provided:

1) z- test is used to test the hypothesis that there is no difference in the recall proportions for two commercials and 95% confidence interval is calculated for the difference between the recall proportions for two populations.
2) chi-square test is used to test the hypothesis that women shoppers in Atlanta differ from the shopping preferences expressed in the U.S. Shoppers Database.
3) chi-squared test of independence is used to analyze the data on negative appeal

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