Question

What is needed to calculate the critical region for the t-test for a single sample?

A. Alternative hypothesis only

B. Alpha and Alternative Hypothesis only

C. df, alpha, and alternative hypothesis

D. df and alternative hypothesis only

Answer 1

Solution:

To calculate the critical region for the t-test for a single sample , we need :

i) df : Degrees of Freedom = n -1

ii) Level of significance = which is the area of rejection region

iii) Alternative hypothesis which decides whether test is one tailed or two tailed.

So if test is one tailed , then we assume Level of significance = as one tailed area and look in t table for One tailed area as size of Level of significance = and for associated degrees of freedom, then we find corresponding t critical value, which is the boundary point of rejection region.

In case of two tailed test, we assume Level of significance = as two tailed area and look in t table for two tailed area as size of Level of significance = for associated degrees of freedom, then we find corresponding t critical value. In this case we have two critical regions. So we have two t critical values and these two values are boundary points of rejection region in left and right tail.

Thus in order to get the critical region for the t-test for a single sample , we need :

C. df, alpha, and alternative hypothesis