Question

What is a Type II error in hypothesis testing?

• A. Rejecting a true null hypothesis
• B. Failing to reject a false null hypothesis
• C. Accepting a true null hypothesis
• D. Rejecting both null and alternative hypotheses

Hint:

Remember: \textbf{Type I Error} = False positive (rejecting a true \(H_0\)). \textbf{Type II Error} = False negative (failing to reject a false \(H_0\)).

Answer 1

The Correct Option is B

Concept: In hypothesis testing, two types of errors can occur when making statistical decisions about the null hypothesis \(H_0\).

• Type I Error: Rejecting the null hypothesis when it is actually true.
• Type II Error: Failing to reject the null hypothesis when it is actually false.

Type I error is often denoted by \(\alpha\), while Type II error is denoted by \(\beta\).
Step 1: Identify the definition of Type II error.} A Type II error occurs when a researcher does not reject the null hypothesis even though it is false. In other words, the test fails to detect an effect or difference that actually exists. Thus, the correct answer is Failing to reject a false null hypothesis.