Question

In a one-tail test for the population mean, if the null hypothesis is not rejected when the alternative hypothesis is true, then:

• A. Make adjustments with level of significance
• B. A Correct Decision Is Made
• C. A Type II Error Is Committed
• D. A Type I Error Is Committed

Hint:

Remember the simple definitions: - Type I Error = False Positive (rejecting a true $H_0$). - Type II Error = False Negative (failing to reject a false $H_0$).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In statistical hypothesis testing, decision outcomes can lead to correct choices or two types of errors depending on the true state of the population.

Step 2: Detailed Explanation:
Let us review the error matrix in hypothesis testing:
1. Type I Error ($\alpha$): Occurs when we reject the null hypothesis ($H_0$) when it is actually true.
2. Type II Error ($\beta$): Occurs when we fail to reject (or do not reject) the null hypothesis ($H_0$) when the alternative hypothesis ($H_1$) is true (meaning $H_0$ is false).
Based on the question:
- The alternative hypothesis is true, which implies that the null hypothesis is false.
- The decision made is to not reject the null hypothesis.
This decision represents a failure to detect a true effect, which fits the definition of a Type II error.

Step 3: Final Answer:
A Type II Error is committed.