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 decision on the hypothesis test using a 3% level of significance is A) to fail to reject H₀ in favor of H₁. B) to reject H₀ in favor of H₁. C) to accept H₀ in favor of H₁. D) We cannot tell what the decision should be from the information given.

Question

Quizplus · Accepted Answer

We want to test the hypothesis whether more than 5,000 households in the area have VCRs. Let p be the proportion of households in the area with VCRs. 
Null hypothesis: p <= 0.25 (assuming 5,000/20,000=0.25)
Alternative hypothesis: p > 0.25
The sample proportion of households with VCRs is 96/300 = 0.32. 
Under the null hypothesis, the test statistic is:

z = (0.32 - 0.25) / sqrt(0.25 * 0.75 / 300) = 3.16

Using a 3% level of significance, the critical value for a one-tailed test is 1.88. Since the test statistic is greater than the critical value, we reject the null hypothesis. We have evidence to support the claim that more than 5,000 households in the area have VCRs. Therefore, the chain should open the new store.

A Major Videocassette Rental Chain Is Considering Opening a New