The owner of restaurant A wants to study the characteristics of his customers. He decides to focus on two variables: the amount of money spent by customers and whether the customer orders dessert. The results from a sample of 62 customers are as follows:
Amount spent: the mean = $40.11 and the standard deviation = $7.41
20 customers purchased dessert
a. Construct and interpret a 90% confidence interval estimate of the population proportion of customers who purchase dessert.
Lower limit: ............
Upper limit: ............
The owner of a competing restaurant B wants to conduct a similar survey in his restaurant.
b. Based on his competitor's information, he tries to find the sample size he needs to have 95% confidence to estimate the population mean amount spent in his restaurant to within $2.7.
What is the sample size? ...............
He decides to sample the number he found above, and the results are:
Amount spent: the mean = $35.32 and the standard deviation = $15.65
25 customers purchased dessert
c. Construct a 99% confidence interval for the difference in the mean spent in both restaurants. Based on this confidence interval, what conclusion can you draw about the mean amount spent in restaurant B compared to the mean amount spent in restaurant A?
Lower limit: .............
Upper limit: .............