Jack and Rose, the owners of an upscale restaurant in 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 showed:Amount of money spent: * = $38.54 and 5 = $7.26Eighteen customers purchased a dessert.
a/ Construct a 95% confidence interval estimate for the population mean amount of money spent per customer in the restaurant.
b/ Construct a 90% confidence interval estimate for the population proportion of customers who purchase dessert.Cathy, the owner of a competing restaurant, wants to conduct a similar survey in her restaurant. Cathy does not have access to the information that Jack and Rose have obtained from the survey they conducted. Answer the following questions:
c/ What sample size is needed to have 95% confidence level of estimating the population mean amount of money spent per customer in her restaurant with a margin of error not exceeding $1.5, assuming that the standard deviation is estimated to be $8?
d/ How many customers need to be selected to have 90% confidence level of estimating the population proportion of customers who purchase dessert with a margin of error of 4% and assuming that a sample proportion is estimated to be 0.5?
e/ Based on your answers to (c) and (d), how large a sample should Cathy take?