A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 30 minutes. The owner has randomly selected 22 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 30 minutes. What assumption is necessary for this test to be valid? A. The population variance must equal the population mean.

Question:

(A) The population variance must equal the population mean.

(B) None. The Central Limit Theorem makes any assumptions unnecessary.

(C) The population of delivery times must have a normal distribution.

(D) The sample mean delivery time must equal the population mean delivery time.

(E) None of the above

The correct option is;

(C) The population of delivery times must have a normal distribution

Step-by-step explanation:

Here, we note that the pizza restaurant wants to test the possibility of starting to deliver pizzas based on comparison of the mean delivery time to a preferred mean and the outcome will aid the decision whether to reject the previous (null) assumption or hypothesis or to accept it.

Therefore, to meet the requirement of the investigation, the population of delivery times must be normally distributed or must have a normal distribution.