# 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 $\alpha /2$ is taken on the right side and the other half equal to $\alpha /2$ 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 ${H_o}:\theta = {\theta _o}$ against the alternative hypothesis ${H_1}:\theta \ne {\theta _o}$ which is two-sided. ${H_o}$ is rejected when the calculated value of $Z$ is greater than ${Z_{\alpha /2}}$ or it is less than $- {Z_{\alpha /2}}$.

Thus the critical region is $Z > {Z_{\alpha /2}}$ or$Z <- {Z_{\alpha /2}}$, and it can also be written as $- {Z_{\alpha /2}} < Z < {Z_{\alpha /2}}$.

When ${H_o}$ is rejected, then ${Z_1}$ is accepted. The two-sided test is shown in the figure below.