Question

Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .01 level of significance. In this situation the true level of significance of this test is

Answer 1

The true true level of significance of this test is more than 0.01.

Explanation:

No standard deviation and we are told that the investigator still used z rather than the more appropriate t - distribution.

This method of using the z-distribution when standard deviation is unknown will definitely result in a smaller critical value and this in turn simply means that the p-value will be smaller than what it should really be.

Thus, it means the critical value is getting closer to the mean value than the way it should be.

Therefore, means that for a given significance of 0.01 and using the z-distribution under this no standard deviation situation, the true true level of significance of this test is more than 0.01.