A pizza chain is considering opening a new store in an area that currently does not have any such
Stores.The chain will open if there is evidence that more than 5,000 of the 20,000 households in
The area have a favorable view of its brain.It conducts a telephone poll of 300 randomly selected
Households in the area and finds that 96 have a favorable view.The pizza chain's conclusion from
The hypothesis test using a 5% level of significance is:
A) to open a new store.
B) not to open a new store.
C) to delay opening a new store until additional evidence is collected.
D) we cannot tell what the decision should be from the information given.

Question

Quizplus · Accepted Answer

The sample proportion of households with a favorable view of the pizza chain is 96/300 = 0.32. The sample size is 300, which is large enough to use the normal distribution to approximate the sampling distribution of the sample proportion. The standard deviation of the sampling distribution is sqrt(0.32 * 0.68 / 300) = 0.03. The z-score for the sample proportion is (0.32 - 0.25) / 0.03 = 2.33. The p-value for the hypothesis test is the area under the normal distribution to the right of the z-score, which is 0.01. Since the p-value is less than the level of significance of 0.05, we reject the null hypothesis and conclude that there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of the pizza chain. Therefore, the pizza chain should open a new store.

A Pizza Chain Is Considering Opening a New Store in an Area