Question

State the critical value(s) for the following two-tailed t test at a 0.05 level of significance: t([infinity]). ±1.645 ±1.96 the same as for a two-tailed z test at a 0.05 level of significance both ±1.96 and the same as for a two-tailed z test at a 0.05 level of significance.

Answer 1

± 1.96 and the same as for a two-tailed z test at a 0.05 level of significance.

Explanation:

We are given the following information in the question:

We perform a two-tailed hypothesis at a 0.05 level of significance.

We have to state the critical values for the same.

Z-critical:

`z_(critical)\text{ at}~\alpha_(0.05) = \pm 1.96`

T-critical:

The critical value for t depends upon the degree of freedom which is obtained from the sample size.

If n is the sample size, then , n - 1 is the degree of freedom.

`t_(critical)\text{ at infinite degree of freedom and}~\alpha_(0.05) = \pm 1.96`

which is the same as the z-critical