2. 8.62 Scarlett and Heather, the owners of an upscale restaurant in Dayton, Ohio, want to study the dining characteristics of their customers. They decide to focus on the amount of money spent by customers. The results from a sample of 60 customers are as follows: Amount spent: sample mean = $38.54, sample standard deviation = $7.26.

a. Construct a 95% confidence interval estimate for the population mean amount spent per customer in the restaurant.

Jeanine, the owner of a competing restaurant, wants to conduct a similar survey in her restaurant. Jeanine does not have access to the information that Scarlett and Heather have obtained from the survey they conducted. Answer the following question:

b. What sample size is needed to have 95% confidence of estimating the population mean amount spent in her restaurant to within $1.50, assuming that the standard deviation is estimated to be $8?