Question

What are critical regions?

Answer 1

For hypothesis testing , critical region is the area under the standardized distribution ( z , t etc)  corresponding to level of significance ( alpha level : 5% , 1% etc) such that if the value of the test statistic falls within it , we reject the null hypothesis. Critical region depends on the level of significance . It increases with level of significance . Critical region also depends on whether its one tailed or two tailed test. For one tailed tailed test critical region is at one tail , for two tailed test its on both tail.The critical region is the value greater than ( right tailed test ) or less than( left tailed test ) the critical value and for two tailed test its less than lower tail critical value and greater than upper tail critical value. The critical value can be obtained from critical value table of the standardized distribution.

For example , for z test with level of significance 5% , critical value of z (two  tailed) = +/- 1.96

critical value (left tailed ) = -1.65 , critical value (right tailed ) = 1.65

Critical region for two tailed test is z < -1.96 or  z > 1.96 ( that is if value of test statistic z falls below -1.96 or above 1.96, we reject the null hypothesis)

Critical region for left  tailed test is z < -1.65  ( that is if value of test statistic z falls below -1.65, we reject the null hypothesis)

Critical region for right tailed test is z > 1.96 ( that is if value of test statistic z falls above 1.65, we reject the null hypothesis)

The critical regions are shown below