What is true regarding type II errors in hypothesis testing?

• A. The null hypothesis is not rejected when the null hypothesis is true.
• B. The null hypothesis is rejected when the alternative hypothesis is true.
• C. The null hypothesis is not rejected when the alternative hypothesis is true.
• D. The null hypothesis is rejected when the null hypothesis is true.

Answer: (C)

Type II error is when you fail to reject the null hypothesis even though the alternative hypothesis is true. In other words, there is a real effect, but your test doesn’t detect it and you conclude there is no effect.

The statement described matches that situation: you don’t reject the null even though there is an actual difference or effect indicated by the alternative. This is the essence of a Type II error, and its probability is called beta. The complement, 1 minus beta, is the test’s power—the chance of correctly detecting a true effect. Power increases with larger sample size, greater effect size, or a higher significance level.

Why the other ideas don’t fit: rejecting the null when the null is true is a false positive, known as a Type I error. Rejecting the null when the alternative is true is the correct, desirable outcome and reflects the test’s power rather than an error. Not rejecting the null when the alternative is true precisely describes a Type II error.