 # Hypothesis testing

I hope I’m not making a mess. Here it is, question L1 – 04186 from Stalla PassMaster. An analyst samples performance claims and actual results for 3 managers shown in the table below. Which of the following actions regarding the managers’ claims is correct if the analyst uses a two-tail test with 24 observations and a 95% confidence interval? Manager __ Claimed performance __ Observed performance __ Observed standard deviation A ______ 14.1% ______ 12% _____ 6.5% B ______ 10.8% ______ 12.8% _____ 4.3% Manager A Manager B (a) Reject Reject (b) Reject Accept © Accept Reject (d) Accept Accept

24 observations. Find T 0.025, 23 = 2.069 Manager A: 12 +/- 2.069 * (6.5/sqrt(24)) if 14.1 lies in that interval – Accept [9.255, 14.74] – Accept Manager B: 12.8 +/- 2.069 * (4.3/sqrt(24)) If 10.8 lies in that interval – accept [10.98,14.62] So Accept, Reject

Thanks cpk123 That’s what my calculus gave me too, but the answer in the PassMaster is (b), Reject Accept. I wrote to Stalla for clarification. I’ll post the answer.

Yeap, our calculus is good.

For manager A, the calculated t stat is (0.12-0.141)/(0.065/sqrt 24)= -0.32 Critical region is t2.069 based on 23 d.f… Therefore for manager A we fail to reject H0. For manager B the calculated t stat is (0.02)/(0.043/sqrt 24)=2.28. Therefore we reject H0. I think there’s a problem with the answer given too…

HydrogenRainbow, in fact it is the other way arround in the numerator (“Claimed” is the hypothesised value, the X bar). I received confirmation that selecting © is correct. This will be in Errata soon.

Two-sided tests are symmetric so it makes no difference

HydrogenRainbow Wrote: ------------------------------------------------------- > For manager A, the calculated t stat is > (0.12-0.141)/(0.065/sqrt 24)= -0.32 > Critical region is t2.069 based on > 23 d.f… Therefore for manager A we fail to reject > H0. > For manager B the calculated t stat is > (0.02)/(0.043/sqrt 24)=2.28. Therefore we reject > H0. I think there’s a problem with the answer > given too… Your formula and conclusion are correct, but the math is off: For manager A, the calculated t stat is > (0.12-0.141)/(0.065/sqrt 24)= -1.58

Oh yeah…my mistake abt the t stat I did stumble on the numerator…but yeppers like what Joey has said, since it is a 2-tailed test it does not matter…so it was kinda by luck that I’d still get the same result =/

What’s a hydrogen rainbow anyway?

The thing with this problem is that manager B’s performance was better than expected, yet the poor guy gets rejected:) The other one’s performance ended up being in the “cushion”, he gets accepted:) Kind of unfair :))

Yeah, but it’s an odd problem. A performance claim is not the mean of some distribution that the observed performance is sampled from so the whole problem set-up is dopey. The study guides do an absolutely awful job of teaching any statistics.

JoeyDVivre Wrote: ------------------------------------------------------- > What’s a hydrogen rainbow anyway? It technically isnt a rainbow since there are only 3 (or is it 4…cant really remmember) lines in the line absorption spectrum of hydrogen. perhaps some physics phd holder here can give the correct explanation…i suck totally at physics Joey- what is a good text for stats?

An Introduction to Probability Theory and Its Applications by William Feller

thanks whodey your msg helped! T stat = UNKNOWN VARIANCE = s only given (stnd. dev.) Z stat = KNOWN VARIANCE = o only give (population variance)

HydrogenRainbow Wrote: ------------------------------------------------------- > An Introduction to Probability Theory and Its > Applications by William Feller Sure. Make sure to read both volumes before the CFA exam. Feller’s academic grandfather is Hilbert who is my great^4-grandfather so we’re family.

That is a lousy book for stats for people on this form. Unless you want to continue your academic studies into Measure Theroy Vol II is a killer. Volume I should only be touched by undergraduate math majors. ------------------------------------------------------- > HydrogenRainbow Wrote: > -------------------------------------------------- > ----- > > An Introduction to Probability Theory and Its > > Applications by William Feller > >

My response was supposed to be sarcastic.

Heh. OK, on a more serious note, I think you can try Statistics for Mgmt and Economics by Keller and Warrack. Seems like a decent book to me and I think it should work just nice for you all