Question

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a knee airbag 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 knee airbag. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you reach?

Question 4 options:

A)	There is sufficient evidence that the proportion is 0.30.

B)	There is not sufficient evidence that the proportion is not 0.30.

C)	There is sufficient evidence that the proportion is not 0.30.

D)	There is not sufficient evidence that the proportion is 0.30.

Answer 1

Let denotes the population proportion.

To test against

Here

sample proportion of people who indicated that they would have purchased the knee airbag

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if

Now,

The value of the test statistic

and P-value

Since P-value = 0.001685 < 0.05, so we reject H₀ at 5% level of significance and we can conclude that:

ans-> c) There is sufficient evidence that the proportion is not 0.30.