Question

A test is made of H0: μ = 25 versus H1: μ ≠ 25. The true value of μ is 28 and H0 is rejected. Determine whether the outcome is a Type I error, a Type II error, or a correct decision.

      
a-Correct decision

       
b-Type II error

       
c-Type I error

Answer 1

Solution:

Given:

H0: μ = 25 versus H1: μ ≠ 25.

The true value of μ is 28

H0 is rejected.

We have to determine whether the outcome is a Type I error, a Type II error, or a correct decision.

Following are the definitions of Type I , Type II and correct decision.

1) Type I Error : Reject null hypothesis , in fact it is True.

2) Type II Error : Fail to reject null hypothesis , in fact it is False.

3) Correct decision: Reject H0, when it is False  or   Fail to reject H0, when it is True.

Since null hypothesis H0 is rejected and it is given that the true value of μ is 28, that means null hypothesis H0: μ = 25 is False.

That is:

Null hypothesis H0 is rejected, actually is False

Thus according to above definition, it is a Correct decision.

This correct answer is:

a-Correct decision