dreary, look at the next ups-post. There you can see that i wrote onetailed instead of twotailed.
Stalla.
Ok. I wont use it 
The lesson learned is not to over-interpret what the statement says: He says he beats it by 3%, take him for his word!
No, no, dreary, i am pure quant, and i know, when to be straight and when to read it normal. and the provided answer to the question (i taught for years a lot of statistic classes at university) is a low quality one. Honestly: a two tailed test makes in this world for this question no sense. Ask others - if you don’t believe me: Posted by: JoeyDVivre (IP Logged) [hide posts from this user] Date: May 10, 2008 08:07PM Both 1-tail…
It’s not a quant issue! It’s reading skills, sorry don’t mean to be rude.
Sigh. Of course that’s not right. In hypothesis testing you are always setting a standard and trying t prove something. Think that you are a prosecutor in a criminal trial trying to prove something beyond a reasonable doubt. In example #1, the manager says “he beats the Russell 2000 by 3% per year”. That’s a claim that needs to be proven. In this case, there is this weird data set and they try to disprove the claim (could a new manager claim that he beats the Russell by 10,000 % per year and you would sit around impotent to contest that claim?). In the normal universe, the manager would need to prove that claim and Ha would be mu > 3%. Here, they set up this weird thing where they want you to show mu < 3% but in either case, it is 1-tailed. In the second one you have a problem, but it’s not formulating Ha which is Mu < 0.5. (Hypothesis tests on things like current ratio can be a problem as you are relying really heavily on a CLT for distinctly non-normal data that may not even be “proper” r.v.'s).
Joey, nice to discuss with u: "In example #1…In the normal universe, the manager would need to prove that claim and Ha would be mu > 3%. Here, they set up this weird thing where they want you to show mu < 3% but in either case, it is 1-tailed. " This is not weird. It is just a question of perspective: If you are the manager you set: Ha mu > 3%. If you are for example an auditor from the cfa conduct program you set: Ha: mu < 3 % It is very important to set the hypothesis without a look at the sample result. Here we are a (i assume: critical) analyst, so Ha: mu < 3 %.
I say I beat the Russel by 3%. The Russel is 10% and my return is 15%. My claim is WRONG. Don’t quant me left or right on this one I beat it actually by 5%! Therefore my advertising claim is NOT correct. Think of it as a situation in which beating by 3% only is the goal, whereas if you beat by anything different from 3%, you lose. How would you formulate your hypothesis then?
Dreary, nice to discuss with u: under these assumptions u are right. But it is an advertisment (so more return is better for the investor). If it is a constant return asset or something like that: yes you would be right. But look at the text: “An investment manager advertises that he beats the Russell 2000 by 3% per year.” Who would test H0 mu=3 % vs HAmu <>3%.? nobody would be interested in this test, if it’s not as constant return thing. cfaisok
I agree that is what they mean by their advertisement and that we should *in practice* test it as one-tailed, but for *exam purposes*, you would be over-interpreting. Cheers.
you can write to cfai a mail and ask - if you think that you and stalla are right. I wouldn’t bet too much on a 2-tailed one
Analyst A: I bet you I will beat Russell by 3%. Analyst B: $500 that you will not! Time goes by, and “A” beats Russell by 5%. Did he win the bet?
Let’s run 100 meters. here my advertisement: I will beat dreary by 3 seconds. We run 10 times (sample) You need in the mean 20 seconds. My mean time is 10.3 seconds. Standard deviation=0,5 sec Will anybody come and tell me I that my null hypothesis here is wrong? Wrong, because I was too fast? In the mean I was much faster… Nobody should reject my adversisment hypothesis - even in an exam.
You bet a beat of 3 seconds, you beat him by 10. My money on Dreary:) good for you, you are in good shape:) But if you don’t beat by exactly 3 seconds - as you advertised, Dreary wins the bet:)
that’s nice, that you two hold together… Remember map, i didn’t write “exactly”. The manager didn’t write “exactly” in his advertisement. Then you and dreary would be right. I didn’t see any “exactly” today. It’s nice to have discussions with u 2. Kind regards, cfaisok P.S. if you are in doubt, call cfai --------------------------------------------------------------------------------------------- Additional confusion for you: what you say map - that the parameter must be hit. Due to the fact that the random variable is continously distributed the probability that the parameter mu has a value of exactly 3 seconds is zero. To come back to the original question and to make it ridiculous: Let us sue the manager. Since the return is continously distributed, the probability that a return is bet by exactly 3 % is ex ante 0 %. => The probabilty that the advertisement is wrong (without knowing the true parameter - ex ante) is 100 %.
cfaisok Wrote: ------------------------------------------------------- > Let’s run 100 meters. > > here my advertisement: I will beat dreary by 3 > seconds. > > We run 10 times (sample) > > You need in the mean 20 seconds. > My mean time is 10.3 seconds. > Standard deviation=0,5 sec > > Will anybody come and tell me I that my null > hypothesis here is wrong? Wrong, because I was too > fast? > > In the mean I was much faster… Nobody should > reject my adversisment hypothesis - even in an > exam. a) I would bet big that you can’t do a 10.3 100 M. b) If you can do a 10.3 100 M your std dev should be < .1 sec c) Your advertisement isnt really the stuff of hypothesis testing. It is not clear what the population is that you are making inferences about (all possible 100 meter times you and Dreary could do? the difference between you and Dreary in all 100 M races?) and we usually don’t think of race times as random samples from a distribution. In particular, there is little chance that they are independent.
> Since the return is continously distributed, the probability that a return is bet by exactly 3 % is ex ante 0 %. => The probabilty that the advertisement is wrong (without knowing the true parameter - ex ante) is 100 %. Another reason to reject the null.
a) you get one point for your answer --> you guessed right b) you don’t have a reasonable and adeqate basis for this conclusion --> zero points for this ethic topic c) it is a good/bad as your last “law” example, Joey - it was just an educational move. Of course a race time can be seen as a random variable. And of course they are not perfectly independant. If we talk about a difference test, we have the same problem in dreary’s original question, too. There is the same lack of information. “all possible 100 meter times you and Dreary could do? the difference between you and Dreary in all 100 M races?” It is not defined in the managers advertisement as well. --> i’ll give you one point Joey: you scored 66,67 %. (failed) Quant 100 % (passed) Ethics 0 % (failed)
@dreary, no it’s not. Because if your statement was right then two tailed tests for continously distributed random variables wouldn’T make any sense. (As i wrote: to confuse) My statement was right, but your conclusion wrong.