A major videocassette 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 videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. Which of the following tests will be the most appropriate?
A) t test for mean
B) separate-variance t test
C) Z test for proportion
D) pooled-variance t test

Question

Quizplus · Accepted Answer

The appropriate test in this scenario is the Z test for proportion because we are comparing a proportion (the number of households with VCRs) to a specified value (5,000 out of 20,000 households). The sample size of 300 is large enough for the Central Limit Theorem to apply, allowing us to use the normal distribution and calculate a z-score to make the comparison. The other tests listed (t tests) are appropriate for comparing means, not proportions.

A Major Videocassette Rental Chain Is Considering Opening a New