The owner of restaurant that serves continental food wants to study characteristics of his customers. He decides 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.
• 18 customers purchased dessert.
a.) Construct a 95% confidence interval estimate of the population mean amount spent per customer in the restaurant.
b.) Construct a 90% confidence interval estimate of the population proportion of customers who purchase dessert.
The owner of a competing restaurant wants to conduct a similar survey in her restaurant. This owner does not have access to the information of the owner of the first restaurant. 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 within ±0.04?
e.) Based on your answers to ( c ) and (d), how large a sample should the owner take?