Which of the following is/are true?
I. If a test always rejects the null, its significance level is zero.
II. If a test always accepts the null, the probability of type II error equals zero.
III. If the p-value exceeds the significance level, you cannot reject the null.
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A. B. C. D.C
The lowest significance level at which the null hypothesis can be rejected is called the p-value of the test. Thus, if the p-value is less than the significance level, the null hypothesis can be rejected at that significance level; otherwise, you must fail to reject the null. The significance level in hypothesis testing refers to the probability that we will reject the null when it is true. Hence, if we always reject the null, the probability of rejecting it when it is true equals 1. A Type II error occurs when we fail to reject the null when in fact it is false. Therefore, if we always accept the null, we will never reject it even when it is false. So the probability of Type
II error will equal 1.