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 27 minutes. The owner has randomly selected 17 customers
And delivered pizzas to their homes in order to test whether the mean delivery time actually
Exceeds 27 minutes. What assumption is necessary for this test to be valid?
A)The population variance must equal the population mean.
B)The sample mean delivery time must equal the population mean delivery time.
C)None. The Central Limit Theorem makes any assumptions unnecessary.
D)The population of delivery times must have a normal distribution.

Question

Quizplus · Accepted Answer

For the validity of the test, especially with a relatively small sample size (n=17), it's assumed that the population from which the sample is drawn has a normal distribution. This assumption is crucial when applying statistical tests that rely on normality, such as t-tests for means. The Central Limit Theorem does suggest that the sampling distribution of the sample mean approaches a normal distribution as the sample size becomes large, but with smaller samples, the original distribution's shape is more influential.

A Local Eat-In Pizza Restaurant Wants to Investigate the Possibility