How much evidence is there that μ exceeds 30 mph?
9.102 Consumer Reports (January 2005) indicates that profit margins on extended warranties are much greater than on the purchase of most products.5 In this exercise we consider a major electronics retailer that wishes to increase the proportion of customers who buy extended warranties on digital cameras. Historically, 20 percent of digital camera customers have purchased the retailer’s extended warranty. To increase this percentage, the retailer has decided to offer a new warranty that is less expensive and more comprehensive. Suppose that three months after starting to offer the new warranty, a random sample of 500 customer sales invoices shows that 152 out of 500 digital camera customers purchased the new warranty. Letting p denote the proportion of all digital camera customers who have purchased the new warranty, calculate the p-value for testing H0: p = .20 versus Ha: p > .20. How much evidence is there that p exceeds .20? Does the difference between and .2 seem to be practically important? Explain your opinion.
9.103 Fortune magazine has periodically reported on the rise of fees and expenses charged by stock funds.
a Suppose that 10 years ago the average annual expense for stock funds was 1.19 percent. Let μ be the current mean annual expense for all stock funds, and assume that stock fund annual expenses are approximately normally distributed. If a random sample of 12 stock funds gives a sample mean annual expense of with a standard deviation of s = .31%, use critical values and this sample information to test H0: μ ≤ 1.19% versus Ha: μ > 1.19% by setting α equal to .10, .05, .01, and .001. How much evidence is there that the current mean annual expense for stock funds exceeds the average of 10 years ago?