Chapter 9.3, Problem 78E

a)

To determine

The Type-I and Type-II error in the given setting and type of error could have made in.

Explanation of Solution

Given:A significance test is performed to test the claim that the first year students at the university study 2.5 hours per night during the school week. A skeptic suspects that the study less than 2.5 hours on average.The p value of a significance test as 0.0622

Concept used:Type-I error : Rejecting the true null hypothesis or it is also known as false positive.

Type-II error: Non rejection of a false null hypothesis or it is also known as false negative.

Type-I error : Concluding that the first year students at the university study less than 2.5 hours per night during the school week when they actually study 2.5 hours per night during school week.

Type-II error: Concluding that the first year students at the university study 2.5 hours per night during the school week when they actually study less than 2.5 hours per night during school week.

It is concluded that the first year students at the university study 2.5 hours per night during school week. So we could have committed Type-II error.

b)

To determine

The change which give the test a higher power to detect µ = 120 minutes.

Explanation of Solution

For maximizing the power of test, either we have to increase the sample size or increase the significance level.

The two significance levels given are 0.01 and 0.10. As $\alpha =0.10$ is higher level of significance, it gives the test higher power.