Question

ch 18 if the probability that you fail to reject the null hypothesis is 20%, when in fact 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
0.90
0.20
0.80
it is not possible to determine the power without knowing the sample size.

Explanation:

Step1: Recall the formula for power of a test

The power of a test is given by \(1 - \beta\), where \(\beta\) is the probability of Type - II error (failing to reject the null hypothesis when it is false).

Step2: Identify \(\beta\) from the problem

We are given that the probability of failing to reject the null hypothesis when we should have (Type - II error) is \(20\%=0.2\). So, \(\beta = 0.2\)

Step3: Calculate the power

Using the formula \(Power=1 - \beta\), substitute \(\beta = 0.2\) into the formula. Then \(Power = 1-0.2=0.8\)

Answer:

0.80