Question

A test of H₀: μ = 60 versus H₁: μ ≠ 60 is performed using a significance level of 0.01. The p-value is 0.033.
If the true value of μ is 53, does the conclusion result in a Type I error, a Type II error, or a correct decision?

a- Type II error

b-Type I error

c- Correct decision

d-

Answer 1

Solution:

Given: A test of H₀: μ = 60 versus H₁: μ ≠ 60 is performed using a significance level of 0.01.

p-value = 0.033.

Decision Rule:
Reject null hypothesis H0, if p-value < 0.01 level of significance, otherwise we fail to reject H0

Since  p-value = 0.033. > 0.01 level of significance, we fail to reject H0.

That means we conclude that: mean μ = 60 is correct.

But we are given that: the true value of μ is 53, that means null hypothesis actually not true or it is False.

So here we fail to reject H0, in fact null hypothesis is False.

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

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

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

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

Thus according to definitions stated above, we have made Type II Error.

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

a- Type II error