3.[16] The owner of a restaurant serving continental food wants to study characteristics of customers of his restaurant. In particular, he decides to focus on two variables: the amount of money spent by customers and whether or not customers order dessert. The results from a sample of 60 customers are as follows:

Amount spent: mean = $38.54; standard deviation = $7.26

18 customers purchased dessert

a)[4] Set up a 95% confidence interval estimate of the population average amount spent per customer in the restaurant.

b)[4] Set up a 90% confidence interval estimate of the population proportion of customers who purchase dessert.

Assuming the owner of a competing restaurant wishes to conduct a similar survey in her restaurant (and does not have access to the information obtained by the owner of the first restaurant), answer the following:

c)[2] If she wants to have 95% confidence of estimating the true population average amount spent in her restaurant to within $1.50 and the standard deviation is assumed to be $8, what sample size is needed?

d)[4] If she wants to have 90% confidence of estimating the true proportion of customers who purchase dessert to within 0.04, what sample size is needed? Use both the pilot study and worst-case scenario.

e)[2] Based on your answers to c and d, what size sample should be taken? Explain.