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 own DVD players.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players.
- The value of the test statistic in this problem is approximately equal to
A) 1.94.
B) 1.30.
C) 2.60.
D) 2.80.

Question

Quizplus · Accepted Answer

We can use a one-sample proportion test to determine if there is enough evidence to suggest that more than 5,000 out of 20,000 households own DVD players.

The null hypothesis is that the proportion of households owning DVD players is 0.25 (5,000/20,000) or lower. The alternative hypothesis is that the proportion is greater than 0.25.

We can calculate the test statistic using the formula:
z = (p - P) / sqrt(P*(1-P)/n)
where p is the proportion of households owning DVD players in our sample, P is the hypothesized proportion under the null hypothesis, and n is the sample size.

In this case, p = 96/300 = 0.32, P = 0.25, and n = 300. Plugging these values into the formula, we get:
z = (0.32 - 0.25) / sqrt(0.25*(1-0.25)/300) ≈ 2.80

The corresponding p-value is less than 0.005, assuming a one-tailed test. This means that we can reject the null hypothesis at the 0.01 level of significance and conclude that there is enough evidence to suggest that more than 5,000 out of 20,000 households own DVD players in the area. Therefore, the DVD rental chain can consider opening a new store in this area.

A Major DVD Rental Chain Is Considering Opening a New