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 two variables: the amount of money spent by customers and whether customers order dessert. The results from a sample of 60 customers are as follows:

• Amount spent: X = $38.54, S = $7.26.

• Eighteen customers purchased dessert.

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

b. Construct a 90% confidence interval estimate for the population proportion of customers who purchase dessert. 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 questions:

c. 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?

d. How many customers need to be selected to have 90% confidence of estimating the population proportion of customers who purchase dessert to within ± 0.04?

e. Based on your answers to (c) and (d), how large a sample should Jeanine take?