If the decision from a hypothesis test is to fail to reject the null hypothesis when in reality the null hypothesis is true, the test has:
A) made a correct decision.
B) made a type I error.
C) made a type II error.
D) proved Ha true.

Question

Quizplus · Accepted Answer

When the decision from a hypothesis test is to fail to reject the null hypothesis when in reality the null hypothesis is true, it means that the test has not falsely rejected a true statement, which is the correct decision. This is not a type I error, as a type I error occurs when the null hypothesis is rejected when it is actually true. It is also not a type II error, as a type II error occurs when the null hypothesis is not rejected when it is actually false. The test has not proven Ha true, as failing to reject the null hypothesis does not automatically prove the alternative hypothesis true.

If the Decision from a Hypothesis Test Is to Fail