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 p-value associated with the test statistic in this problem is approximately equal to
A)0.0100.
B)0.0051.
C)0.0026.
D)0.0013.

Question

Quizplus · Accepted Answer

We need to test the hypothesis:
Null hypothesis: p <= 0.25  (proportion of households with Blu-ray players is less than or equal to 0.25)
Alternate hypothesis: p > 0.25 (proportion of households with Blu-ray players is greater than 0.25)

The sample proportion is: p-hat = 96/300 = 0.32
The test statistic can be calculated as:
z = (p-hat - p) / sqrt(p*(1-p)/n) = (0.32 - 0.25) / sqrt(0.25*0.75/300) = 2.75
where n = 300 is the sample size

The p-value for this one-tailed test can be calculated using a standard normal distribution table or calculator as P(Z > 2.75) = 0.0026 (rounded to four decimal places).

Since the p-value (0.0026) is less than the significance level of 0.05, we reject the null hypothesis. Therefore, there is evidence that the proportion of households with Blu-ray players in the area is greater than 0.25, and the Blu-ray rental chain should open a new store in the area.

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