When computing a t-test, it is important to distinguish between directional and nondirectional hypotheses as the direction will determine the rejection regions. Describe how the rejection regions would differ according to the type of hypothesis you would use.
If P = .01, then directional would look for P = .01. If nondirectional, you would look for P = .005 in either direction.
When computing a t-test, the rejection regions determine at what point we reject the null hypothesis. The rejection regions are defined by the critical value(s) or the p-value(s) associated with a specific level of significance (α), which represents the probability of making a Type I error.
In the case of directional hypotheses, we have a specific expectation or prediction about the direction of the relationship between variables. For example, we may predict that there will be either a positive or negative relationship between two variables. In this case, we have a one-tailed test and the rejection region is concentrated on one side of the distribution.
If our directional hypothesis predicts a positive relationship, we will use an upper-tailed test. The critical region or rejection region will be in the upper tail of the t-distribution. We will compare the calculated t-value to the critical value associated with the desired level of significance (α). If the calculated t-value falls in the upper tail of the distribution and exceeds the critical value, we reject the null hypothesis.
On the other hand, if our directional hypothesis predicts a negative relationship, we will use a lower-tailed test. The critical region or rejection region will be in the lower tail of the t-distribution. Again, we compare the calculated t-value to the critical value associated with the desired level of significance (α). If the calculated t-value falls in the lower tail of the distribution and is less than the critical value, we reject the null hypothesis.
In contrast, when dealing with nondirectional hypotheses, we do not make any specific predictions about the direction of the relationship between variables. We are only interested in comparing means or looking for a difference. In this case, we have a two-tailed test, and the rejection region is distributed across both tails of the t-distribution.
For a two-tailed test, we divide the desired level of significance (α) into two equal parts, allocating one part to each tail of the distribution. We then compare the calculated t-value to the critical values associated with the upper and lower tails. If the calculated t-value falls in either tail and exceeds the corresponding critical values, we reject the null hypothesis.
In summary, the rejection regions in a t-test differ based on the type of hypothesis being used. Directional hypotheses have a one-tailed test and a rejection region concentrated on the predicted side of the distribution, while nondirectional hypotheses have a two-tailed test and a rejection region distributed across both tails of the distribution.