Problem 1: A 20-minute consumer survey mailed to 500 adults aged 25–34 included a $5 Starbucks gift certificate. The same survey was mailed to 500 adults aged 25–34 without the gift certificate. There were 65 responses from the first group and 45 from the second group. (a) Perform a two-tailed test comparing the response rates (proportions) at α = .05. (b) Form a confidence interval for the difference of proportions, without pooling the samples. Does it include zero?
Problem 2: Are women’s feet getting bigger? Retailers in the last 20 years have had to increase their stock of larger sizes. Wal-Mart Stores, Inc., and Payless ShoeSource, Inc., have been aggressive in stocking larger sizes, and Nordstrom’s reports that its larger sizes typically sell out first. Assuming equal variances, at α = .025, do these random shoe size samples of 12 randomly chosen women in each age group show that women’s shoe sizes have increased? (See The Wall Street Journal, July 17,2004.) ShoeSize1
Born in 1980: 8 7.5 8.5 8.5 8 7.5 9.5 7.5 8 8 8.5 9
Born in 1960: 8.5 7.5 8 8 7.5 7.5 7.5 8 7 8 7 8