Final answer:
If a study is designed with a beta error of 20%, the power of the test would be 80%. Power is determined by subtracting the beta error from one, and it represents the probability of correctly rejecting a false null hypothesis.
Step-by-step explanation:
A Type II error (also known as a beta error, β error) occurs when a statistical test fails to reject a false null hypothesis. The student's question involves the relationship between Type II error and power of the test, which is defined as 1 - β. Therefore, if a study is designed to have a beta error of 20%, the power of that study is calculated as 1 - 0.2, resulting in a power of 80%. It's important to aim for a high power, typically as close to one as possible, to increase the likelihood of correctly rejecting a false null hypothesis when it is indeed false.
Statisticians can improve the power of a test by increasing the sample size or by making the test more sensitive to the effect being tested, thus reducing the probability of making a Type II error. A power analysis can be conducted before carrying out the test to evaluate whether the sample size is sufficient to detect the desired effect with the chosen alpha level (α).