Which of the following statements are not correct?
A) It is possible that the null hypothesis may be rejected when it is true.
B) It is impossible that the null hypothesis may be rejected when it is true.
C) It is possible that the null hypothesis may not be rejected when it is false.
D) All of the above statements are correct.
E) None of the above statements are correct.

Question

Quizplus · Accepted Answer

It is possible to make a Type I error (rejecting the null when it's true), but it's not impossible to make a Type II error (failing to reject the null when it's false). So statement A is correct. However, it is impossible to reject the null hypothesis when it is true (since the null hypothesis is taken to be true by default), so statement B is not correct. Statement C is correct since "not rejecting the null" means failing to find evidence against it, but this evidence may be weak or inconclusive. Therefore, the correct answer is B.

Which of the Following Statements Are Not Correct