Final answer:
The power of a study with a Type II error of 20% is 80%. Power is calculated as 1 - β, where β is the probability of a Type II error. The power of a test measures its ability to correctly identify a true alternative hypothesis. The correct answer is A) 80%.
Step-by-step explanation:
If you design a study to have a Type II (beta) error of 20%, the power of your study is calculated as 1 minus the probability of the Type II error.
Given that the probability of a Type II error (denoted as β) is 20%, the power of your study would be 1 - 0.20, which equals 80%. Therefore, the correct answer is A) 80%.
Type I error is denoted by α and it is the probability of rejecting the null hypothesis when it is actually true. In contrast, Type II error, denoted by β, is the probability of failing to reject the null hypothesis when it is false.
The power of the test (1 - β) quantifies the likelihood that the test will correctly identify a true alternative hypothesis, so a high power is desirable and indicates a lower chance of making a Type II error.