Hypothesis test level of significance

[tiger]

Suppose that you are performing a one-tailed hypothesis test. "Assuming that everything else remains constant, a decrease in the test's level of significance (a) leads to a higher probability of rejecting the null hypothesis". Is the statement true or false? Please elaborate.

[vicki]

Assuming that everything else remains constant, when the level of significance decreases, the critical value becomes smaller for a right-tailed test and greater for a left-tailed test, thus it is easier to reject H0. The probability of rejecting the null hypothesis increases.