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 value of the test statistic in this problem is approximately equal to:
A)2.80
B)2.60
C)1.94
D)1.30

Question

Quizplus · Accepted Answer

The test statistic for this problem involves calculating the z-score, which measures the number of standard deviations a sample proportion is away from the population proportion.

The formula for the z-score is:

z = (p̂ - p) / √(p(1-p)/n)

where:
p̂ = sample proportion (favorable views / total sample size)
p = population proportion (5,000 / 20,000 = 0.25)
n = sample size (300)

Plugging in the values, we get:

z = (0.32 - 0.25) / √(0.25(1-0.25)/300) ≈ 2.80

Therefore, the best choice is A, with a test statistic of approximately 2.80.

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