### CFA Practice Question

Which of the is (are) false?

I. A high p-value is necessary to reject a null hypothesis.
II The higher the significance level, the greater is the chance that the null will be rejected when it is false.
III. The higher the probability of Type II error, the higher is the chance of rejecting the null when it is false.
A. I and II.
B. I and III.
C. I, II and III.
Explanation: You can think of the p-value as the maximum probability that the null hypothesis is true despite observing the value of the test statistic that you have in the sample at hand. Thus, the lower the p-value, the greater is your confidence in rejecting the null hypothesis.

The significance level represents an upper bound on the probability that the null hypothesis is true given the observed sample and the testing procedure. Hence, if you reject the null at the 5% significance level, for e.g., then the probability that the null is true despite your statistical evidence to the contrary could be as high as 5% (but no more, under the assumptions of the test).

A Type II error refers to the event that we will fail to reject the null when it is false. The higher the probability of a Type II error, the lower the chance of rejecting the null when it is false.

User Comment
escempep I think II is right,
since Type II error = not rejecting a false null Hyp
then 1-Type II error = reject a false null hyp
and we know that 1-Type II error = Type I error = level of significance

Then Wider the level of significance, higher the probability to reject a fall null hyp.

Is someone ok with that?
schelsea Type I Error is rejecting a True null hypothesis. Rejecting a false null hypothesis would be the correct decision.
JCopeland Correct. Type I Error is the likelihood that the null hypothesis will be rejected when it is true. It also increases the liklihood that Ho will be rejected whether it is true or false. What makes it an error is the fact that you are rejecting something that is actually true. If you are rejecting something that is not true (or false) it is a correct rejection and not an error at all. Because significance level is used interchangable with alpha and Type I. II is not true. Hence, the answer is C, they are all false.
pfcasey I strongly believe that II is a TRUE statement.
Higher significance => Higher P(Type I Error)
=> Lower P(Type II Error)
=> Higher Power
And Power is defined as P(reject H0 when it's false)
Therefore II is true and B is correct answer.
chandsingh Does higher significance mean 80% instead of 95% or 99% instead of 95%?
mc42086 Significance=Alpha=P(Type 1 Error)
Confidence Level = 1-Significance
So Higher Conf = Lower Significance
So 80% instead of 95% does mean higher significance.

That being said I agree with the II should be correct or at least is not neccesarily false?
"... the greater is the chance that the null will be rejected when its FALSE"

alpha (level of significance) is type I error which measures the probability the null will be rejected when TRUE. Therefore, its also false.
tommyguard3 Still not convinced II is false

"...the greater is the chance that the null will be rejected when its false"

Alpha=significance=type 1 error=probability the null will be rejected when true...as the probability of rejecting a true Null increases so does the probability of rejecting a false null.

Therefore while it is not the full explanation of significance it is still a true statement not false.
merc10112 I agree with grew0001, if II said...

"...the greater the chance the null will be rejected when it's TRUE"

Then the statement would be correct, but it says FALSE.

So its false.