If the Type I error (α) for a given test is to be decreased, then for a fixed sample size n:
A) the Type II error (β) will also decrease.
B) the Type II error (β) will increase.
C) the power of the test will increase.
D) a one-tailed test must be utilized.

Question

Quizplus · Accepted Answer

When the Type I error (α) is decreased, it means the criteria for rejecting the null hypothesis are made more stringent. This generally leads to a higher chance of not rejecting the null hypothesis when it is false, thereby increasing the Type II error (β). The power of the test, which is 1-β, would decrease as a result, not increase, and changing to a one-tailed test is a separate decision that doesn't directly relate to the relationship between α and β.

If the Type I Error (α) for a Given Test