The marketing manager for an automobile manufacturer is inte

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?

Solution

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.

It means our null hypothesis is H₀ : p = 0.30

And the alternative hypothesis is the proportion is different from 0.30 , H₁ : p 0.30 .

Where , p = population proportion.

Given that, n = number of new compact-car owners = 200

x = new compact-car owners would have purchased the knee airbag = 79

phat = x / n = 79 / 200 = 0.395 = sample proportion.

And also we have given that decision do not reject the null hypothesis and from this statement we have to conclude that proportion may be 0.30.

Hence the answer.