Question

What can be concluded by failing to reject the null hypothesis?

• A.

  either that the null hypothesis is correct or that the test procedure is not strong enough (i.e. that the sample size is not large enough)  to reject the null hypothesis

• B.

  that the null hypothesis is correct, therefore the alternative hypothesis should be rejected

• C.

  that the function of the alternative hypothesis is incorrect

• D.

  that the alternative hypothesis is correct, therefore the null hypothesis should be rejected

Answer 1

If we fail to reject the null hypothesis, either that the null hypothesis is correct or that the test procedure is not strong enough (i.e. that the sample size is not large enough)  to reject the null hypothesis. It is not direct that the null hypothesis is accepted and alternative hypothesis is rejected. So the correct option should be A.

Answer 2

The correct answer is A. Failing to reject the null hypothesis means that there is not enough evidence to support the alternative hypothesis. It does not necessarily mean that the null hypothesis is true or that the alternative hypothesis is false. It could mean that the null hypothesis is correct, or it could indicate that the test procedure is not strong enough (e.g., due to a small sample size) to detect a significant difference and reject the null hypothesis.