The Inland Empire Food Store Company has stated in its advertising that the average shopper will save more than $5.00 per week by shopping at Inland stores. A consumer group has decided to test this assertion by sampling 50 shoppers who currently shop at other stores. It selects the customers and then notes each item purchased at their regular stores. These same items are then priced at the Inland store, and the total bill is compared. The data in the file Inland Foods reflect savings at Inland for the 50 shoppers. Note that those cases where the bill was higher at Inland are marked with a minus sign.
a. Set up the appropriate null and alternative hypotheses to test Inland’s claim.
b. Using a significance level of 0.05, develop the decision rule and test the hypothesis. Can Inland Empire support its advertising claim?
c. Which type of hypothesis error would the consumer group be most interested in controlling? Which type of hypothesis test error would the company be most interested in controlling? Explain your reasoning.