For each of the following statements, state whether the statement is true or false, and justify your answer:

(a) The significance level of a hypothesis test is equal to the probability that the null hypothesis is true.

(b) If the significance level of a hypothesis test is decreased, the power would be expected to increase.

(c) If a null hypothesis is rejected at the significance level of α, the probability that the null hypothesis is true equals α.

(d) A type I error occurs when the test statistic falls in the rejection region of the test.

Hypothesis testing:

The two types of errors occur while performing hypotheses tests.

Type I error: Chance of rejecting the null hypothesis, though it is true.
Type II error: Chance of not rejecting the null hypothesis, though it is false.
The power of the test is the chance of rejecting the false null hypothesis.

Errors are the wrong decisions, and the power of the test is the correct decision for hypothesis testing.