CFA Practice Question

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CFA Practice Question

A consumer group wants to prove that average hospital costs are more than $931 per day. The group randomly samples 60 accounts and finds a sample mean of $950. The hypothesis test is at an a-level of 5% and assumes a σ of $50. The null hypothesis is H0: ______.

A. μ <= 931
B. μ >= 931
C. μ <= 950
Correct Answer: A

The alternative hypothesis, Ha, is what is to be proved; in this case, we want to prove that the average costs are above $931. So, we have Ha: μ > 931. This leaves the null hypothesis as H0: μ <= 931.

User Contributed Comments 19

User Comment
tssverma why prove alternative hypotheses. Why not prove null hypotheses
DAS11 This doesn't sound right to me either. I thought you prove null and the alternative hypothesis is accepted when null is rejected, therefore you try to prove/reject null.
closer It's the opposite. If you want to prove that the cost > 931, then you should try to reject cost <=931 which is the null. If you can reject that cost <= 931 is not true, then cost > 931.
awellman I think on subtle point here is that we want to test for greater than (not equal to). Since there is no greater than test, by definition we have to prove that its not less than or equal to.
Nightsurfer Good insight.
Bibhu Awellman has given some good points.
whiteknight No..check the last question.....we take null hypothesis as something we want to prove...clearly seen in the last question...and try to disprove it....thats the alt hypothesis..
bobert whiteknight. I was with you until I reread the section after looking at the last question. Let me try to verify for you and all who are still confused.

You have the two types of hypothesis, NULL and ALTERNATIVE.

Null is the one we either REJECT or FAIL TO REJECT. There is no acceptance of the null. Think null, nothing, nothing right. The null can either be wrong because the test statistic has no correlation with the population and is not within the confidence interval, OR it could be within the confidence interval by mistake in which case we assume it is correct by test standards and fail to reject it.

The ALTERNATIVE hypothesis is the hypothesis we choose if there is sufficient evidence to show the null is wrong.

This makes sense because the NULL + ALTERNATIVE should cover all possible variables being tested.

So for these questions it says, "A consumer group wants to prove that the average hospital costs are more than $931 per day."
At the end asks: "The null hypothesis is H0:_______."

As I just said, the null hypothesis is what is NOT right. (AKA trying to show what is true by disproving the rest)

Since the group wants to prove that the avg cost is >931, we need to figure out if we can reject the opposite, which is the null.

Therefore H0: μ <= 931

And lastly, remember:
H0 + H1 = (μ <= 931) + (μ > 931)= All possible variables being tested.
sergashev prove the opposite not to be subject to datamining
studyprep We make/pick Ho in such a way, that we don't get/fall into Type 1 error. Making type 1 error is more serious than making type II. (Type 1 means false positive, that is fail to reject while it is false). So for this question we made Ho<=931, so here even if we made type 1 error, it would not be that bad it would be other wise.
mordja solid work Bobert
rfvo Yip, N1 !!
anastasiya to make things even clearer for those who got confused in stating the null and alternative H (incl. me): see example 2 on page 469, Reading 11 of the CFA textbook.
SuperKnight Just to clarify something. A false positive (type I error) is when you reject the null hypothesis even though its true. Hence, you think you have some significant proof but you're wrong. A good example is putting someone in jail that didn't commit the crime, you find them guilty even though they are innocent. The other error would be a Type II error, false negative, which is failing to reject the null hypothesis even though its false. Same example, you let someone go even though they did commit the crime.
apiccion In an experiment the NULL HYPOTHESIS is something you wish to DISPROVE. There are two outcomes to the NULL HYPOTHESIS:
(i) The null hypothesis is rejected
(ii) The null hypothesis is not rejected

Warning warning! Danger danger!
(ii) is NOT the same as saying that the null hypothesis is proved.
dcfa @studyprep -
type I error=rejecting a null hypothesis when it is actually true
type II error=failure to reject null when it is actually false
vsimco A good way of thinking of this is

What do you want to prove? That Hospital Costs are more than > x. Why is this the alternative hypothesis? Because we want to show even when we "assume that null hypothesis is correct" that we would still reject the null. If we did not reject the null, we do not accept the null all we have done is failed to reject it. Rejection gives a meaningful result for the alternative hypothesis, No rejection does not give a meaningful result for the hypothesis.

Its basically like a case in a court of law. The burden of proof is on the accuser. I.e in the alternative hypothesis.
ashish100 i'm basically picking the opposites right now. which is not bad in a sense that i can just pick the other answer with my logic lol

but damn this is confusing
ashish100 bobert did a good job explaining it tho. thanks bobert.
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