If the significance level is decreased to 1%, how would the power of the test change?

When the significance level is decreased to 1%, this means that the threshold for rejecting the null hypothesis (which indicates that the observed effect is statistically significant) becomes more stringent. In practical terms, you are less likely to declare a result significant unless there is strong evidence against the null hypothesis.

When the significance level is lowered, the likelihood of making a Type I error (incorrectly rejecting a true null hypothesis) decreases. However, this adjustment typically leads to a decrease in the power of the test.

Power is the probability that a test correctly rejects a false null hypothesis (i.e., it detects an effect when there is one). A lower significance level can result in increased difficulty in finding statistically significant results, especially when sample sizes remain fixed. This is due to the fact that with a more stringent criterion, fewer results are likely to meet this new standard, thereby resulting in decreased power to detect true effects.

In conclusion, decreasing the significance level to 1% would lead to a decrease in the power of the test, contrary to the selected answer. Power is inherently tied to the significance level chosen for the test; therefore, as you adjust that level downward, the ability to detect true positives is diminished.