One Tailed Test
When the alternative hypothesis is onesided like or , then the rejection region is taken only on one side of the sampling distribution. It is called onetailed test or onesided test. When is onesided to the right like, the entire rejection region equal to is taken in the right end of the sampling distribution.
The test is called onesided to the right. The hypothesis is rejected if the calculated value of a statistic, say falls in the rejection region. The critical value is which has the area equal to to its right. The rejection region and acceptance region are shown in Figure. The null hypothesis is rejected when (calculated) .
If the alternative hypothesis is onesided to the left like , the entire rejection region equal to is taken on the left tail of the sampling distribution. The test is called onesided or onetailed to the left. The critical value is which cuts off the area equal to to its left. The critical region is and is shown in Figure.
For some important values of , the critical values of for twotailed and one tailed tests are given below:
Critical Value of

Twosides test

Onesided test

Onesided to the left


and




and




and




and


