# What is the probability that the study will show a significant difference in efficacy between the two drugs?

You are conducting a research study and wish to know whether two different drugs are equally effective.
H0 [null hypothesis]: Drugs A and B are equally effective.
Ha [alternative hypothesis]: Drug B is more effective than A.
Your study uses an alpha-level of alpha=0.05. The power of the test was 0.80.
If the alternate hypothesis is actually true, what is the probability that the study will show a significant difference in efficacy between the two drugs?

1. 0.05

2. 0.20

3. 0.80

4. 0.95

5. It is impossible to determine from the information given

Explanation

A Type II Error occurs when the alternative hypothesis is true, but the null hypothesis is not rejected. In other words, this is the ability of the test to find a significant difference. The probability of commiting a Type II Error is beta. The power of a test = (1 - beta). Therefore, the chance of committing a Type II Error is 0.20. However, the chance of correctly identifying a significant difference between the two drugs is equal to the power, which is 0.80.
A Type I Error occurs when the null hypothesis is true, but is rejected in favor of the alternative hypothesis. The probability of a Type I Error is also known as the alpha level of the test.