Question

If probability of type II error of a statistical test is 0.2 then power of the test is

• A. 0.2
• B. 5
• C. 20%
• D. 0.8

Hint:

To maximize the quality of a statistical test, we aim to minimize $\beta$, which in turn maximizes the power ($1 - \beta$) of the test.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In hypothesis testing, the power of a statistical test is the probability that the test correctly rejects a false null hypothesis $H_0$.
Key Formula or Approach:
The power of a test is mathematically related to the probability of committing a Type II error ($\beta$) by the formula:
\[ \text{Power} = 1 - \beta \]

Step 2: Detailed Explanation:
We are given:
Probability of Type II error, $\beta = 0.2$
Using the power formula:
\[ \text{Power} = 1 - 0.2 = 0.8 \]
Therefore, the power of the test is 0.8 (or 80%).

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