The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?
A) Z-test of a population proportion
B) t-test of a population proportion
C) Z-test of a population mean
D) t-test of population mean

Question

Quizplus · Accepted Answer

Since we are testing a proportion (i.e. the proportion of new compact-car owners who would have purchased the inflatable air bags), we would use a Z-test of a population proportion. The sample size (n=200) is large enough for us to assume that the sampling distribution of the sample proportion is approximately normal, allowing us to use a Z-test. The null hypothesis would be that the true proportion is 0.30, and we would use the sample proportion (79/200) and standard error formula to calculate the test statistic and p-value.

The Marketing Manager for an Automobile Manufacturer Is Interested in Determining