Confidence Intervals and Hypothesis Testing
Concept

Critical Region

The critical region, determined by the significance level α, is the set of values that will lead to rejecting the null hypothesis H_0. In a standard normal distribution, this region is located in the tails of the distribution. The cutoff value of the region is a critical value given by the z-value of α. The tests of significance — left, right, or two-tail — determine whether there are one or two critical regions.
Critical Values
Significance Level Left-Tail Test
H_a:μ
Two-Tail Test
H_a:μ≠ k
Right-Tail Test
H_a:μ>k
α=1 % -2.326 ±2.576 2.326
α=5 % -1.645 ±1.960 1.645
α=10 % -1.282 ±1.645 1.282

This table shows the typical significance levels and their corresponding critical values. It is worth noting that the area of the critical region(s) is equal to the significance level α.

critical regions
Exercises