Question

A significance test is going to be performed using a significance level of α = 0.05. Suppose that the null hypothesis is actually true. If the significance level was lowered to α = 0.01, which of the following would be true?

a. The probability of a Type I error would increase.
b. We don't have enough information to reason about Type I error probabilities.
c. The probability of a Type I error would decrease.
d. The probability of a Type I error would stay the same.

Answer 1

c. The probability of a Type I error would decrease.

Lowering the significance level from 0.05 to 0.01 reduces the probability of a Type I error, meaning fewer null hypotheses will be incorrectly rejected when they are indeed true.

Step-by-step explanation:

If the significance level of a test is lowered from α = 0.05 to α = 0.01, the probability of committing a Type I error, which is rejecting the null hypothesis when it is actually true, would decrease.

This is because the level of significance of the test (α) directly corresponds to the probability of a Type I error occurring.

This means that by lowering α, fewer hypothesis tests will lead to the null hypothesis being incorrectly rejected when it is true.

Therefore, the correct answer is:
c. The probability of a Type I error would decrease.