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 decision on the hypothesis test using a 3% level of significance is A) to reject H₀in favor of H₁. B) to accept H₀in favor of H₁. C) to fail to reject H₀in favor of H₁. 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 deviation of the sampling distribution is sqrt(0.32 * 0.68 / 300) = 0.034. The z-score for the sample proportion is (0.32 - 0.25) / 0.034 = 2.06. The p-value for the z-score is 0.039, which is less than the level of significance of 0.03. Therefore, we reject the null hypothesis and conclude that there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players.

A Major DVD Rental Chain Is Considering Opening a New