Question

Given below are two statements
Statement I: Probability of rejecting null hypothesis when it is true is known as level of significance.
Statement II: Probability of rejecting null hypothesis when it is false or alternate hypothesis is true is known as power of the test.
In light of the above statements, choose the correct answer from the options given below

• A. Statement I is true but Statement II is false
• B. Statement I is false but Statement II is true
• C. Both Statement I and II are false
• D. Both Statement I and II are true

Hint:

- Level of significance ($\alpha$) = $P(\text{Reject } H_0 \mid H_0 \text{ is true})$
- Power of the test ($1-\beta$) = $P(\text{Reject } H_0 \mid H_0 \text{ is false})$

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Statistical hypothesis testing is evaluated based on the probabilities of making correct decisions versus committing errors.

Step 2: Detailed Explanation:
Let us analyze both statements:
- Statement I: The error of rejecting the null hypothesis $H_0$ when it is actually true is defined as a Type I error.
The maximum probability of committing a Type I error is known as the level of significance ($\alpha$). Thus, Statement I is true.
- Statement II: The action of rejecting the null hypothesis $H_0$ when $H_0$ is false (meaning the alternative hypothesis $H_1$ is true) is a correct statistical decision.
The probability of making this correct decision is defined as the power of the test ($1 - \beta$, where $\beta$ is the probability of a Type II error). Thus, Statement II is true.
Since both statements are correct, the correct answer is that both Statement I and II are true.

Step 3: Final Answer
The correct option is (D).