A major DVD rental 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 are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The rental chain's conclusion from the hypothesis test using a 3% 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 DVD players 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 error of the sample proportion 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 P(Z > 2.33) = 0.01, which is less than the level of significance of 0.03. Therefore, the rental chain should reject the null hypothesis and conclude that more than 5,000 of the 20,000 households in the area are equipped with DVD players. This evidence suggests that the rental chain should open a new store in the area.

A Major DVD Rental Chain Is Considering Opening a New