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. Which of the following tests will be the most appropriate?
A)t test for the mean.
B)Z test for the proportion.
C)Pooled-variance t test.
D)Separate-variance t test.

Question

Quizplus · Accepted Answer

Since we are interested in testing the proportion of households with favorable views, a Z test for proportion is the most appropriate. The sample size (n=300) is large enough to assume normality due to the central limit theorem. Also, since we don't have information on the population variance, we cannot use a t-test for the mean. Pooled-variance t test and separate-variance t test are also not applicable in this case as we are not comparing means of two populations. Since we want to test the proportion of households in favor of the brand, the most appropriate test would be the Z test for the proportion. This test allows us to determine if the proportion of households with a favorable view is statistically significant and greater than the threshold of 5,000 out of 20,000 households.

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