Question

what does a type ii error signify in hypothesis testing?
a. correctly rejecting the null hypothesis.
b. correctly accepting the null hypothesis.
c. rejecting a true alternative hypothesis.
d. failing to reject a false null hypothesis.

Explanation:

In hypothesis testing, a Type II Error occurs when we fail to reject the null hypothesis \(H_0\) even though the alternative hypothesis \(H_1\) is true. That is, we fail to reject a false null hypothesis.

• Option a: Correctly rejecting the null hypothesis is not a Type II Error. It is a correct decision.
• Option b: Correctly accepting the null hypothesis (when it is true) is a correct decision, not a Type II Error.
• Option c: Rejecting a true alternative hypothesis is not the definition of a Type II Error.
• Option d: This matches the definition of a Type II Error.

Answer:

d. Failing to reject a false null hypothesis.