A pizza 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 have a favorable view of its brand.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view.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

To find the p-value, we need to use a one-sample proportion test.

The null hypothesis is that the proportion of households with a favorable view of the pizza chain is less than or equal to 0.25 (5,000/20,000). The alternative hypothesis is that the proportion is greater than 0.25.

We can use a normal approximation since the sample size is large enough (n*p >= 10 and n*(1-p) >= 10, where n = 300 and p = 0.25 under the null hypothesis).

The test statistic is z = (0.32 - 0.25) / sqrt(0.25 * 0.75 / 300) = 2.12, where 0.32 is the sample proportion of households with a favorable view.

The p-value is the probability of observing a test statistic as extreme or more extreme than 2.12, assuming the null hypothesis is true. This is a one-tailed test, so we look up the area to the right of 2.12 in the standard normal table, which is approximately 0.0162.

Therefore, the p-value is 0.0162, which is closest to 0.0026 (option C).

A Pizza Chain Is Considering Opening a New Store in an Area