Tutorial One Tailed Test


One Tailed Test


   


When the alternative hypothesis is one-sided like or, then the rejection region is taken only on one side of the sampling distribution. It is called one-tailed test or one-sided test. When is one-sided to the right like, the entire rejection region equal to is taken in the right end of the sampling distribution.
The test is called one-sided 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 one-sided to the left like, the entire rejection region equal to is taken on the left tail of the sampling distribution. The test is called one-sided or one-tailed 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 two-tailed and one tailed tests are given below:

Critical Value of

Two-sides test

One-sided test

One-sided to the left

and

and

and

and



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