### CFA Practice Question

Which statement(s) is (are) true?

I. The probability of a Type II error equals 1 - significance level.
II. A higher significance level makes it easier to reject a null hypothesis.
III. Minimizing the chance of a Type I error minimizes the probability of a Type II error.
IV. The higher the probability of a Type II error, the higher the chance that the alternative will be accepted when it is true.
A. II and IV
B. I and III
C. II only
Explanation: 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.

Technically, IV 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 example, suppose a theory does not rule out the possibility that a variable X can be negative but you mistakenly set up the hypothesis 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.

User Comment
humphrey IV is false.
type II error: rejecting null hypothesis when it is actually true. the higher the probability of type II error, the higher it is to accept the alternative (H1) when it is false.
ticomico If you want to be serious about the question, it is impossibe even to accept the null hypothesis. You can fail to reject, but never accept the null hypothesis.
ticomico I think IV is not probability of type II error but power of the test. The power of the test is the probability of correctly rejecting the null when it is false. Higher the power of the test, higher the probability of 'rejecting the Ho when it is false'. Touché
gruszewski the higher the probability of type II error (mistakingly rejecting true null), the higher the probability of accepting the alternative, no matter alternative is true or false
ahan I agree with ticomico. Type II error is that mistakenly accept (or should say fail to reject) a false hypothesis. The IV question should be poewr of test.
rockeR Listen to me right now.
Type II error is the failure to reject the null hypothesis when it is actually false.
This implies that as the probabilty of a TypeII error increase,the power of the test declines.
Thus the anwser IV is wrong!
danlan prob(type II error)=1-power of test
cocomilk the answer is wrong. a higher significant level, say 99%, makes it HARDER to reject the null hypothesis.
siramarc cocomilk: which is a higher significant level, 0.1 or 0.01? It is 0.1! You got the opposite right.
boddunah type I error= rejecting a true null hypothesis.
type II error = do not reject false null hypothesis.
mindi i agree with rockeR.

type II error is accepting a false H0, so the higher the probability of a type II error, the higher chance that the NULL hypothesis is accepted when it is FALSE
ashish100 what a shit show on these comments sections for the comments.

anyways, if anyone else was wondering.

Probability of Type II Error = 1 - Power of test.

So power of test increase, probability of Type II error decrease.