The owners of the Franklin Park Mall wished to study customer shopping habits. From earlier studies the owners are under the impression that a typical shopper spends 0.75 hours at the mall, with a standard deviation of 0.10 hours. Recently the mall owners added some specialty restaurants designed to keep shoppers in the mall longer. The consulting firm, Brunner and Swanson Marketing Enterprises, has been 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 hours.

a. Develop a test of hypothesis to determine if the mean time spent in the mall is more than 0.75 hours. Use the .05 significance level.
b. Suppose the mean shopping time actually increased from 0.75 hours to 0.77 hours. What is the probability this increase would not be detected?
c. When Brunner and Swanson reported the information in part (b) to the mall owners, the owners were upset with the statement that a survey could not detect a change from 0.75 to 0.77 hours of shopping time. How could this probability be reduced?