Question

Margaret manages a fast food restaurant and she is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling the cup with water. She selected a random sample of 90 customers who asked for a water cup when placing an order and found that 33 of those customers filled the cup with a soft drink from the beverage fountain.

Construct 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. Write a sentence interpreting the interval you found. Margaret believes that each customer who asks for a water cup, but fills it with a soda costs the restaurant $0.25. Suppose that in the month of April 3000 customers ask for a water cup when placing an order. Use the confidence interval constructed in question #1 to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soda. If Margaret can provide strong evidence that a good amount of the customers who ask for a water cup actually fill the cup with soda, the restaurant will move the soda machine behind the counter and not let customers “self serve.” This will alienate customers, but save the restaurant money.

Describe the consequences a Type I error in this situation. If Margaret can provide strong evidence that a good amount of the customers who ask for a water cup actually fill the cup with soda, the restaurant will move the soda machine behind the counter and not let customers “self serve.” This will alienate customers, but save the restaurant money.

Describe the consequences a Type II error in this situation. If you were Margaret, would you worry more about a Type I or Type II error? Why?

Answer 1