Which statement best defines a Type II error in hypothesis testing?

Which statement best defines a Type II error in hypothesis testing?

• A. Incorrectly rejecting a true null hypothesis.
• B. Failing to reject a true null hypothesis.
• C. Failing to reject a false null hypothesis.
• D. The probability of observing the test statistic under the null hypothesis.

Answer: (C)

A Type II error occurs when there really is an effect (the null hypothesis is false), but the test fails to detect it and you do not reject the null. It’s a false negative: you conclude there’s no difference when a difference actually exists. The statement that captures this is failing to reject a false null hypothesis. This contrasts with rejecting a true null hypothesis (Type I error) and failing to reject a true null hypothesis (a correct decision). The probability of observing a test statistic under the null relates to the p-value, not to the error type. The chance of missing a real effect is the test’s power, which you can improve by larger sample size, less variability, or a more sensitive test.

A Type II error occurs when there really is an effect (the null hypothesis is false), but the test fails to detect it and you do not reject the null. It’s a false negative: you conclude there’s no difference when a difference actually exists. The statement that captures this is failing to reject a false null hypothesis.

This contrasts with rejecting a true null hypothesis (Type I error) and failing to reject a true null hypothesis (a correct decision). The probability of observing a test statistic under the null relates to the p-value, not to the error type. The chance of missing a real effect is the test’s power, which you can improve by larger sample size, less variability, or a more sensitive test.