OneTailed Test
When the alternative hypothesis $${H_1}$$ is onesided like $$\theta > {\theta _o}$$ or $$\theta < {\theta _o}$$, then the rejection region is taken only on one side of the sampling distribution. This is called a onetailed test or onesided test. When $${H_1}$$ is onesided to the right like $$\theta > {\theta _o}$$, the entire rejection region equal to $$\alpha $$ is taken in the right end of the sampling distribution.
Here the test is called onesided to the right. The hypothesis $${H_o}$$ is rejected if the calculated value of a statistic, say $$Z$$, falls in the rejection region. The critical value is $${Z_\alpha }$$ which has the area equal to $$\alpha $$ to its right. The rejection region and acceptance region are shown in the figure below. The null hypothesis $${H_o}$$ is rejected when $$Z$$ (calculated) $$ > {Z_\alpha }$$.
If the alternative hypothesis is onesided to the left like $$\theta < {\theta _o}$$, the entire rejection region equal to $$\alpha $$ is taken on the left tail of the sampling distribution. The test is called onesided or onetailed to the left. The critical value is $$ – {Z_\alpha }$$, which cuts off the area equal to $$\alpha $$ to its left. The critical region is $$Z < – {Z_\alpha }$$ and is shown in the figure below.
For some important values of $$\alpha $$, the critical values of $$Z$$ for twotailed and one tailed tests are given below:
Critical Value of $$Z$$
$$\alpha $$

Twosided test

Onesided test

Onesided to the left

$$0.10{\text{ }}(10\% )$$

$$ – 1.645$$and $$ + 1.645$$

$$ + 1.282$$

$$ – 1.282$$

$$0.05{\text{ }}(5\% )$$

$$ – 1.96$$and $$ + 1.96$$

$$ + 1.645$$

$$ – 1.645$$

$$0.02{\text{ }}(2\% )$$

$$ – 2.326$$and $$ + 2.326$$

$$ + 2.054$$

$$ – 2.054$$

$$0.01{\text{ }}(1\% )$$

$$ – 2.575$$and $$ + 2.575$$

$$ + 2.326$$

$$ – 2.326$$
