What's the critical region?

What's the critical region?

• A. The region in which your result would be statistically significant
• B. The region where p > 0.05
• C. The central area of the sampling distribution
• D. The region that is critical

Answer: (A)

In hypothesis testing, the critical region is the part of the sampling distribution under the null hypothesis that would lead you to reject the null. It consists of the extreme values of the test statistic that occur with probability equal to the chosen significance level, alpha. If your observed result falls in this region, you conclude the result is statistically significant at that alpha level. This is why the correct idea is that the critical region is where results would be statistically significant. For example, with a two-tailed test at alpha = 0.05, the critical region lies in the two tails beyond the 2.5th and 97.5th percentiles. The central area, by contrast, is where results are not extreme enough to reject the null, and a region defined as the p > 0.05 region would not indicate significance. The phrase “region that is critical” is vague without linking it to alpha and the extreme values; the meaningful definition is the set of outcomes that lead to rejecting the null.

In hypothesis testing, the critical region is the part of the sampling distribution under the null hypothesis that would lead you to reject the null. It consists of the extreme values of the test statistic that occur with probability equal to the chosen significance level, alpha. If your observed result falls in this region, you conclude the result is statistically significant at that alpha level.

This is why the correct idea is that the critical region is where results would be statistically significant. For example, with a two-tailed test at alpha = 0.05, the critical region lies in the two tails beyond the 2.5th and 97.5th percentiles. The central area, by contrast, is where results are not extreme enough to reject the null, and a region defined as the p > 0.05 region would not indicate significance. The phrase “region that is critical” is vague without linking it to alpha and the extreme values; the meaningful definition is the set of outcomes that lead to rejecting the null.