The manager of a local supermarket wants to estimate the average amount customers spend at his store on Fridays. He would like to study the buying behavior of each customer who makes a purchase at the store on a typical Friday. However, the manager’s assistant, who is currently enrolled in a managerial statistics course at a local college, urges the manager to save his scarce time and money by studying a sample of customer purchases. The available frame of relevant customer purchases is provided in file P8_51.XLS. 

a. What sample size would be required for the supermarket manager to be approximately 95% sure that his estimate of the average customer expenditure on Fridays is within $25 of the true mean? Assume that his best estimate of the population standard deviation σ  is $72. 

b. Choose a simple random sample of the size found in part a. 

c. Compute the observed sampling error based on the sample you have drawn from the population given in P8_51.XLS. How does the actual sampling error compare to the maximum probable absolute error established in part a? Explain.