Question

In the hypothesis testing, which of the following defines the size of power of the test?

• A. 1- (Probability of accepting null hypothesis when it is true)
• B. 1- (Probability of rejecting null hypothesis when it is true)
• C. 1- (Probability of accepting null hypothesis when it is false)
• D. 1 + (Probability of rejecting null hypothesis when it is not true)

Answer 1

The Correct Option is C

To understand the size of the power of a test in hypothesis testing, we first need to comprehend some fundamental concepts:

• Null Hypothesis (\(H_0\)): It is the hypothesis that there is no effect or no difference, and it is assumed to be true until evidence suggests otherwise.
• Alternate Hypothesis (\(H_1\)): It is the hypothesis that indicates the presence of an effect or a difference.
• Type I Error (\(\alpha\)): The probability of rejecting the null hypothesis when it is true. This is also referred to as the significance level of the test.
• Type II Error (\(\beta\)): The probability of accepting the null hypothesis when it is false.
• Power of the Test: It is defined as the probability of correctly rejecting the null hypothesis when it is false, which can be expressed as \(1 - \beta\).

Now, let's analyze the given options to identify which one correctly explains the size of the power of the test:

1. The option "1- (Probability of accepting null hypothesis when it is true)" describes \(\alpha\), which is related to the Type I Error but not the power of the test.
2. The option "1- (Probability of rejecting null hypothesis when it is true)" is incorrect because it refers to a scenario involving a true null hypothesis, similar to Type I Error, but it does not describe the power of the test.
3. The option "1- (Probability of accepting null hypothesis when it is false)" defines \(1 - \beta\), which is indeed the power of the test. This measures the ability of a test to detect a true effect when it exists.
4. The option "1 + (Probability of rejecting null hypothesis when it is not true)" is mathematically incorrect and does not logically relate to the concept of power in hypothesis testing.

Therefore, the correct answer is the third option: "1- (Probability of accepting null hypothesis when it is false)." This directly correlates with the definition of the power of a test, which is defined as \(1 - \beta\).