When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the ________.
A) probability of Type II error decreases
B) probability of incorrectly rejecting the null hypothesis increases
C) probability of incorrectly not rejecting the null hypothesis increases
D) probability of incorrectly not rejecting the null hypothesis decreases

Question

Quizplus · Accepted Answer

When the probability of a Type I error decreases, it means that the significance level is reduced, and the probability of incorrectly rejecting the null hypothesis is also reduced. However, this also means that the probability of correctly rejecting the null hypothesis (i.e., avoiding a Type II error) is also reduced, resulting in an increased probability of incorrectly not rejecting the null hypothesis. Therefore, the answer is C.

When Conducting a Hypothesis Test for a Given Sample Size