Chapter 10, Problem 48CE

The owners of the Westfield Mall wished to study customer shopping habits. From earlier studies, the owners were under the impression that a typical shopper spends 0.75 hour at the mall, with a standard deviation of 0.10 hour. Recently the mall owners added some specialty restaurants designed to keep shoppers in the mall longer. The consulting firm, Brunner and Swanson Marketing Enterprises, was hired to evaluate the effects of the restaurants. A sample of 45 shoppers by Brunner and Swanson revealed that the mean time spent in the mall had increased to 0.80 hour.

1. a. Develop a hypothesis test to determine if the mean time spent in the mall changed. Use the .10 significance level.
2. b. Suppose the mean shopping time actually increased from 0.75 hour to 0.79 hours. What is the probability of making a Type II error?
3. c. When Brunner and Swanson reported the information in part (b) to the mall owners, the owners believed that the probability of making a Type II error was too high. How could this probability be reduced?