A major Blu-ray 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 Blu-ray players.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players.The decision on the hypothesis test using a 5% 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

To solve this problem, we will use a hypothesis test with the following hypotheses:

H0: p <= 0.25 (less than or equal to 25% of households have Blu-ray players)
Ha: p > 0.25 (more than 25% of households have Blu-ray players)

We chose 0.25 as the null hypothesis proportion because 5,000 out of 20,000 households is equivalent to 0.25 or 25%.

Next, we need to calculate the test statistic using the formula:

z = (p-hat - p0) / sqrt(p0 * (1-p0) / n)

where p-hat is the sample proportion, p0 is the null hypothesis proportion, and n is the sample size.

Plugging in the values, we get:

z = (0.32 - 0.25) / sqrt(0.25 * 0.75 / 300) = 2.53

Using a z-table or calculator, we find that the p-value is approximately 0.005.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 25% of households in the area have Blu-ray players. Therefore, the Blu-ray rental chain should open a new store in the area.

The correct answer is choice A: to reject H0 in favor of Ha.

A Major Blu-Ray Rental Chain Is Considering Opening a New