Power is the probability of rejecting the null hypothesis when there is a true effect. Which option matches this definition?

• A. The probability of rejecting the null when the null is true
• B. The probability of failing to reject the null when the alternative is true
• C. The probability of rejecting the null when the alternative is true
• D. The probability of detecting any effect regardless of true status

Answer: (C)

Power is the probability that a statistical test will reject the null hypothesis when there is a real effect. In other words, it reflects the test's ability to detect true differences. This is the probability of rejecting the null given that the alternative is true, which is equal to 1 minus beta (where beta is the chance of a Type II error, failing to reject the null when there is a real effect). The option that describes rejecting the null when the alternative is true matches this definition. The other statements correspond to different ideas: rejecting the null when the null is true is the Type I error rate (alpha); failing to reject the null when the alternative is true is the Type II error rate; and detecting any effect regardless of true status doesn’t capture the conditional probability that power represents.