Question

A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, u, of cars rented in the U.S. this year. The consumer group has reason to believe that the mean monthly mileage of cars rented in the U.S. this year is less than last year's mean, which was 2800 miles. The group plans to do a statistical test regarding the value of u. It chooses a random sample of monthly mileages and computes the mean of the sample to be 2625 miles and the standard deviation to be 750 miles. Based on this information, answer the questions below. What are the null hypothesis (H) and the alternate hypothesis (H) that should be used for the test? ? Huis ? H: u is? In the context of this test, what is a Type I error? the hypothesis that u is? ? when, A Type I error is ? in fact, u is? Suppose that the group decides to reject the null hypothesis. What sort of error might it be making?

Answer 1

Here we are testing whether this years's mean rented mileage is less than last year's. The null hypothesis will therefore be opposite of this claim.

The last years mean = 2800

(Mean mileage is greater or equal to 2800)

Ho Gu> 2800

(Mean mileage is less than 2800)

Ho :μ< 2800

Type 1 error is to reject the null hypothesis when it is true.

Reject the null hypothesis : Means that the mean mileage < 2800

When null is true : Mean in fact is $\geq$ 2800

A type 1 error is to reject  the null hypothesis that $\mu$ is less than 2800 when in fact $\mu$ is greater than or equal to  2800.

If the group is deciding to reject the nul hypothesis then it can make

type 1 error.