A major videocassette 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 videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The p-value associated with the test statistic in this problem is approximately equal to
A) 0.0026.
B) 0.0013.
C) 0.0100.
D) 0.0051.

Question

Quizplus · Accepted Answer

We need to conduct a hypothesis test to determine if the proportion of households with VCRs in the area is greater than 0.25 (5,000/20,000).

H0: p <= 0.25 (null hypothesis)
Ha: p > 0.25 (alternative hypothesis)

We can use a one-sample proportion test with a significance level of 0.05.

The test statistic is:
z = (0.32 - 0.25) / sqrt[(0.25)(0.75)/300] = 3.06

The p-value associated with this test statistic is P(Z > 3.06) = 0.0026.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of households with VCRs in the area is greater than 0.25. Therefore, the chain should open a new store in the area.

A Major Videocassette Rental Chain Is Considering Opening a New