Which of the is/are true?
I. The probability of type II error equals 1 - significance level.
II. A higher significance level is makes it easier to reject a null hypothesis.
III. Minimizing the chance of a Type I error minimizes the probability of Type II error.
IV. The higher the probability of Type II error, the higher is the chance that the alternative will be accepted when it is true.
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A. B. C. D. E. F. G. H.A
The probability of Type I (not type II) error equals 1 - the significance level.
The significance level represents an upper bound on the probability that the null hypothesis is true given the observed sample. The higher this level is set, the easier it is to say that the null is false (though the probability that you are making a mistake in rejecting the null also becomes higher!).
Type I and Type II errors represent two different types of errors and are not directly related. A relationship like (III) appears tempting but is not true.
For the purposes of CFA Level I exam, (IV) can be taken to be true, though technically, it is not entirely accurate. It holds only if the alternative hypothesis is exactly complementary to the null hypothesis i.e. the null hypothesis and the alternative hypothesis span the entire range of values that the variable being tested can take. If you set up the alternative hypothesis incorrectly, then rejection of the null does not necessarily imply that the alternative is true; it could also imply that you have not taken all the possibilities into consideration. For e.g., suppose a theory does not rule out the possibility that a variable X can be negative but you mistakenly set up the hypotheses as Ho: X = 0, H1: X > 0. Then clearly, even if you reject the null hypothesis, it does not imply that X can take only positive values. Recognizing such mistakes in setting up a hypothesis test is crucial.