Answer in Statistics and Probability for Biostat101 #250478
Suppose a statistician chose to test a hypothesis at . the critical value for a right-tailed test is . If the test value was , what would the decision be? What would happen if, after seeing the test value, she decided to choose ? What would the decision be? Explain the contradiction, if there is one.
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 in not rejected while in the second case it is rejected. This happen since in the second case the probability of type 1 error has been increased.