If the probability that you fail to reject the null hypothesis is 20% when you should have rejected it because there is a real effect that you were unable to detect, given your data, the power of the test is:

(A) 0.8.

(B) 0.9.

(C) β.

(D) It is not possible to determine the power without knowing the sample size.

Correct Option: (A) 0.80.

Step-by-step explanation:

The type II error is an error made during statistical hypothesis testing.

The type II error is defined as the probability of failing to the reject the null hypothesis when the null hypothesis is false.

The type II error is related to the power of the test (β) as follows:

P (Type II Error) = 1 - β

Given:

P (Type II Error) = 0.20

Compute the power of the test as follows:

P (Type II Error) = 1 - β

β = 1 - P (Type II Error)

= 1 - 0.20

= 0.80

Thus, the power of the test is 0.80.