What defines the critical region in hypothesis testing?

What defines the critical region in hypothesis testing?

• A. The region defined by the p-value threshold.
• B. The region of values where the null hypothesis is always accepted.
• C. The region composed of the extreme sample values that are very unlikely under the null.
• D. The region where the test statistic is exactly equal to the mean.

Answer: (C)

The main idea is that the critical region is the set of sample outcomes that would lead you to reject the null hypothesis at the chosen significance level. It’s formed from the extreme values of the sampling distribution under the null—those outcomes that are very unlikely if H0 is true. For example, in a two‑tailed test at 5% significance, the critical region consists of the far ends of the distribution (beyond the usual cutoff values); if your observed data falls in this region, you reject H0. The other descriptions don’t capture this focus on extreme, unlikely outcomes that trigger rejection.

The main idea is that the critical region is the set of sample outcomes that would lead you to reject the null hypothesis at the chosen significance level. It’s formed from the extreme values of the sampling distribution under the null—those outcomes that are very unlikely if H0 is true. For example, in a two‑tailed test at 5% significance, the critical region consists of the far ends of the distribution (beyond the usual cutoff values); if your observed data falls in this region, you reject H0. The other descriptions don’t capture this focus on extreme, unlikely outcomes that trigger rejection.