# Establishing null hypothesis

Came across this Schweser question: You are testing to see if the mean of a population is less than 133. A random sample of 50 observations had a mean of 130. Assume a standard deviation of 5. The test is to be made at the 2% significance level. Question: 29 - 18627 The null hypothesis is: A) P > 133 B) P = or < 133 C) P = or > 133 D) P = 133 The answer is C. Why not B? Is it because it included an equal sign, so it is not the best answer? Can P < 133 be an answer? Thanks in advance

You are trying to figure out if the mean of a population is LESS than 133. You usually set up you null to be the conditions you aren’t trying to determine (in this case GREATER or EQUAL to 133). Then if you can reject your null, you are closer to proving that the mean is LESS than 133 (although you haven’t proved it)!

null hyp always contains the = sign so only b c and d qualify based on that. The alt. hyp is what is being tested: so ha: p < 133 based on that null is p = or > 133 © would be correct.

it is more significant to reject something than to accept it! that’s the logic behind it.

I disagree with barthezz. It is more significant to accept something than reject it. If we reject “A”, we are leaving the possibility of everything besides “A”. If we accept “B”, we are saying “B” is the only answer.

apcarlso, You have to reject C and not A. The text says: You are testing to see if the mean of a population is LESS than 133. Thus it won’t make sense to test for A. Because as you said you would be left with B,C and D. You have to reject C) that is P = or > 133 as cpk123 pointed out.

cpk123 Wrote: ------------------------------------------------------- > null hyp always contains the = sign > so only b c and d qualify based on that. > > The alt. hyp is what is being tested: so ha: p < > 133 > > based on that null is p = or > 133 © would be > correct. Uh oh, don’t let Joey see this post. He is liable to go off on some statistical rant…

mwt9 not sure what is wrong with it… CP mwvt9 Wrote: ------------------------------------------------------- > cpk123 Wrote: > -------------------------------------------------- > ----- > > null hyp always contains the = sign > > so only b c and d qualify based on that. > > > > The alt. hyp is what is being tested: so ha: p > < > > 133 > > > > based on that null is p = or > 133 © would be > > correct. > > > Uh oh, don’t let Joey see this post. He is liable > to go off on some statistical rant…

bart- i made a poor choice to illustrate my point with letters… suffice it to say, i agree with your last post.

Ho: P >= 130 Ha: P < 130 Answer is undoubtedly C I usually follow the same trick as cpk123 stated… - Dinesh S

cpk123 Wrote: ------------------------------------------------------- > null hyp always contains the = sign cpk123, that’s a wrong statement. if in the intial problem is replaced to “you are testing to see if the mean of the population is less or equal than 133”, then null hypothesis is Mean > 133. since distribution of the mean is continuous, one point is not going to make a difference. however, your statement is still incorrect.

maratikus Wrote: > cpk123, that’s a wrong statement. if in the > intial problem is replaced to “you are testing to > see if the mean of the population is less or equal > than 133”, then null hypothesis is Mean > 133. > In this case… Ho: P <= 133 Ha: P > 133 [One tailed test…] Correct me if I have completely messed up the logic?? - Dinesh S

No comments… that’s all I can say… it helps me remember the way to set up the hyp. maybe it’s wrong… but do not want to beat in something new so close to the exam.

Dinesh - I agree with Maratikus. If the question was: “You are testing to see if the mean of a population is less than or equal to 133…” then: Ho : P > 133 Ha : P <= 133 You want to accept Ha and reject Ho. Since you suspect the mean <= 133…

apcarlso, actually I made also a mistake since you never accept a hypothesis. you reject it or fail to reject it. that is the proper wording.

Ho : P > 133 Ha : P <= 133 that would be completely WRONG!!! please read page 454-455 of the CFAI text book to see that your setup of the Ha is wrong because it contains the = sign in it.

cpk123 Wrote: ------------------------------------------------------- > Ho : P > 133 > Ha : P <= 133 > that would be completely WRONG!!! > > please read page 454-455 of the CFAI text book to > see that your setup of the Ha is wrong because it > contains the = sign in it. Perfect… we can’t have a EQUAL sign in alternative hypo, so your setup is kinda wrong, apcarlso. - Dinesh S

Thanks for the headsup guys… don’t have the texts with me, but will brush up when I get home.

> that would be completely WRONG!!! > > please read page 454-455 of the CFAI text book to > see that your setup of the Ha is wrong because it > contains the = sign in it. cpk123, I looked at the CFAI textbook and what they say is consistent with you said. In this particular situation I disagree with what they say (I also disagree with how they define hedge fund fees, etc). We had a discussion about null hypothesis a couple of months ago. The fact that I disagree is a very minor thing, not practical to argue about it 2.5 weeks before the exam.