Chapter 9.3, Problem 77E

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 Variety A has the higher mean yield when compared to yield of Variety B.

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 Variety A has higher mean yield than Variety B when actually it is not.

Type-II error: Concluding that the Variety A has lower mean yield than Variety B, when actually Variety A has higher yield.

It is concluded that the Variety A has higher yield. So we could have committed Type-II error.

b)

To determine

The two ways of increasing the power of the test to detect µ = 0.5

Explanation of Solution

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

The two ways of increasing the power of test are

1. Increasing the sample size.

2. Increasing the level of significance.