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. State the test of interest to the rental chain. A) H₀ : π ≤ 0.32 versus H₁ : π 0.32 B) H₀ : π ≤ 0.25 versus H₁ : π 0.25 C) H₀ : π ≤ 5,000 versus H₁ : π 5,000 D) H₀ : μ ≤ 5,000 versus H₁ : μ 5,000

Question

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. State the test of interest to the rental chain. A) H₀ : π ≤ 0.32 versus H₁ : π > 0.32 B) H₀ : π ≤ 0.25 versus H₁ : π > 0.25 C) H₀ : π ≤ 5,000 versus H₁ : π > 5,000 D) H₀ : μ ≤ 5,000 versus H₁ : μ > 5,000

Quizplus · Accepted Answer

The test of interest is a hypothesis test for the population proportion of households in the area that have DVD players (denoted by π). The null hypothesis (H₀) is that π is less than or equal to a certain value (which is not specified in the options provided). The alternative hypothesis (H₁) is that π is greater than this value. To determine the appropriate null value for π, we first note that the sample proportion of households with DVD players is 96/300 = 0.32. If we assume that this is a reasonable estimate of the population proportion, then the null value for π should be 0.32 (since the chain will open if π is greater than 0.32). We can then use this value to choose the appropriate option. Option A has a null value of 0.32, but the alternative hypothesis is one-sided (π>0.32) rather than two-sided, which is not appropriate for our problem. Option C has a null value of 5000, which is not a proportion and does not make sense in this context. Option D has a null value of 5000, which is the number of households rather than the proportion of households, and again does not make sense in this context. Option B has a null value of 0.25, which is less than the sample proportion of 0.32. This is appropriate, since the null hypothesis should represent the chain's default position of not opening the store unless there is strong evidence in favor of there being enough households with DVD players. The alternative hypothesis is that π is greater than 0.25, which is consistent with the chain's goal of finding a sufficient number of households. Therefore, option B is the best choice.

A Major DVD Rental Chain Is Considering Opening a New