# Two-Tailed Test

When the rejection region is taken on both ends of the sampling distribution, the test is called a two-sided test or two-tailed test. When we are using a two-sided test, half of the rejection region equal to is taken on the right side and the other half equal to is taken on the left side of the sampling distribution. Suppose the sampling distribution of the statistic is a normal distribution and we have to test the hypothesis against the alternative hypothesis which is two-sided. is rejected when the calculated value of is greater than or it is less than .

Thus the critical region is or, and it can also be written as .

When is rejected, then is accepted. The two-sided test is shown in the figure below.