Answer to Question #278354 in Statistics and Probability for love

Question

Suppose a statistician chose to test a hypothesis at ∝= 0.01. The critical value for a right-tailed test is +2.33. If the test value were 1.97, what would the decision be? What would happen if, after seeing the test value, she decided to choose ∝= 0.05? What would the decision be? Explain the contradiction if there is one.

Answer 1

SOLUTION

α=0.01 and the critical value for the right-tailed test is +2.33.

So if the test value was 1.97, the decision would be not to reject the null hypothesis.

If α is chosen as 0.05 for a right-tailed test the critical value is obtained as 1.65. Thus in this case the decision would be to reject the null hypothesis

The contradiction is that in the first case the null hypothesis is not rejected while in the second case it is rejected. This happens since in the second case the probability of type 1 error has been increased.