What is a rejection region?
The rejection region is the interval, measured in the sampling distribution of the statistic under study, that leads to rejection of the null hypothesis H 0 in a hypothesis test.
How do you determine the appropriate rejection region?
The rejection region is the region where, if our test statistic falls, then we have enough evidence to reject the null hypothesis. If we consider the right-tailed test, for example, the rejection region is any value greater than c 1 − α , where c 1 − α is the critical value.
When is a null hypothesis rejected in one tailed test?
One-Tailed Test. 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 the figure below. The null hypothesis is rejected when (calculated) .
When is one-sided to the right like one tailed test?
One-Tailed 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. Here 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.
Which is the critical region of the one tailed test?
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 the figure below.
When is the rejection region taken only on the right side?
When the alternative hypothesis is one-sided like or , then the rejection region is taken only on one side of the sampling distribution. This is called a 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.