Question

Power of a statistical test is defined as

• A. one minus probability of rejecting the Null hypothesis when it is true
• B. one minus probability of not rejecting the Null hypothesis when it is not true
• C. probability of rejecting the Null hypothesis when it is true minus probability of not rejecting the Null hypothesis when it is not true
• D. probability of not rejecting the Null hypothesis when it is not true

Hint:

The power of a statistical test is a measure of the test's ability to detect an effect when one exists, and is calculated as \( 1 - \beta \), where \( \beta \) is the probability of a Type II error.

Answer 1

The Correct Option is B

Step 1: Understand the concept of the power of a statistical test.
The power of a statistical test is the probability that the test will correctly reject a false null hypothesis. In other words, it measures the ability of a test to detect a true effect (if there is one) and avoid Type II errors (failing to reject a false null hypothesis).
Step 2: Analyze the options.
- Option (A) is incorrect because it represents the complement of the Type I error rate (probability of rejecting a true null hypothesis).
- Option (B) is correct. The power of a statistical test is the probability of rejecting the null hypothesis when it is false (true positive rate), which is defined as \(1 - \beta\), where \( \beta \) is the probability of not rejecting the null hypothesis when it is false.
- Option (C) is incorrect because it refers to the difference between rejecting the null hypothesis when it is true and not rejecting the null hypothesis when it is false, which doesn't directly define power.
- Option (D) is incorrect because it represents the probability of failing to reject the null hypothesis when it is false, which relates to Type II error.
Final Answer: \[ \boxed{\text{one minus probability of not rejecting the Null hypothesis when it is not true}} \]