Calling All Coffee Drinkers / Hypothesis Testing

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jbnjc

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A national survey of lawyers found that lawyers drank an average of 6.8 cups of coffee each week. A random sample of 36 stockbrokers found that the stockbrokers drank an average of 6.2 cups of coffee each week with a standard deviation of 0.5. At the 5% significance level, which of the following is most accurate?


A. Stockbrokers drink the same amount of coffee per week as lawyers

B. Stockbrokers definitely drink less coffee per week than lawyers

c. The analyst cannot conclude that stockbrokers drinkg the same amount of coffee per week as lawyers

D. Stockbrokers drink more coffee per week than lawyers.
 
Answer B. z statistic equals -7.2 what is surely beyond any non-rejection intervals
 
CFAMontreal Wrote:
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> Answer B. z statistic equals -7.2 what is surely
> beyond any non-rejection intervals


You are wrong, Hypothesis testing does not "definitely" prove anything. Try again.

Would like to see you calculations.

Thanks
 
z=(6.2-6.8)/(0.5/sq.root 36) = -0.6/0.0833 = -7.2

I agree - not dedinitely, but at 5% significance level we can say that lawyers and brokers don't drink the same amounts of coffee
 
Test Stat here is Z = (6.2 - 6.8)/(0.5/Sqrt(36)) = -7.2 as calculated by CFAMontreal.

Your hypothesis test rejected A so it's out at any even remotely reasonable level of significance.

D) is out because all indications are that lawyers drink more than stockbrokers.

B) doesn't look that bad to me, but the "definitely" word is a problem <shrugs>.

C) is a correct answer but it's substanceless. There is no way in any situation to conclude that stockbrokers drink the same amount as lawyers. In fact, if we gathered all the data down to the last milliliter, they dont drink the same amount of coffee.

This question is a silly mess beginning with the misleading set-up that the amount of coffee consumed by lawyers is known but the amount of coffee consumed by stockbrokers needs to be estimated. In fact, if you were doing this experiment you would almost certainly be doing a two-sample test.

This question would never, ever in a million years make it through the review process to get anywhere close to the CFA exam. Where did you get it?
 
jbnjc Wrote:
-------------------------------------------------------
> CFAMontreal Wrote:
> --------------------------------------------------
> -----
> > Answer B. z statistic equals -7.2 what is
> surely
> > beyond any non-rejection intervals
>
>
> You are wrong, Hypothesis testing does not
> "definitely" prove anything. Try again.

I also don't think that tone is appropriate for a guy trying to help you.
 
JoeyDVivre, thanks a lot for your comments...I agree with them.

Re tone of jbnjc, it is OK...I like it ;) it is better to motivate someone thinking than just to show the correct answer immediately, and I would say: oh, yes, it is correct, it is easy...I finished QM review couple of weeks ago, so it was kinda good to refresh it and find out that I am wrong in y way of thinking. Nobody will be able to tel me that during the test. So we all learn here ;) Thanks to jbnjc as well!
 
CFAMontreal Wrote:
-------------------------------------------------------
> z=(6.2-6.8)/(0.5/sq.root 36) = -0.6/0.0833 = -7.2
>
> I agree - not dedinitely, but at 5% significance
> level we can say that lawyers and brokers don't
> drink the same amounts of coffee



Why did you calculate the Z statistic, we know a 5% level of signifcance, gives a confidence interval of 95% which means z stat is 1.96 X standared error which is
.05 / sq rt of 36 = .0833 around the Hu = 6.8 , Xmin = 6.64 Xmax = 6.64, the X = 6.96

sample mean of 6.2 lies outside acceptance range so answer of 6.64 to 6.96 so reject the null hypothesis that Hu=6.8 if favor of Ha does not = 6.8. Why the 7.2?
 
Sorry if my directness was insulting, that was not my intention. I apologize if I offended anyone. I am direct however, as we approach the exam we will have little time to "beat around the bush".... again sorry.

Respect fof all level 1 candidates,

Jbnjc
 
I solved this problem the other way around. Your approach is also good...

which one can be quicker during the exam? and more reliable?
 
I understand how you calculated the -7.2 z score but unsure how that proved that number was out of any possible acceptance range so quickly with out the long way.. ... please enlighten me about the "more" reliablity factor. I can see it is definitely quicker.

Thanks
 
in that particular situation, I didn't remember all exact z values for confidence levels (if needed, I have to spend extra 30 seconds to write it down for me...still not automatic, this stuff), but I know that the biggest one is 2.57 for 99%, so my calculated z-value was definitely out of all confidence levels. So without any doubts, Ho rejected. If the z value were about 3 or lower, then I would look it up - the value of z-statistic for 95% confidence level (or 5% significance level)...am I clear and am I correct?
 
CFAMontreal Wrote:
-------------------------------------------------------
> in that particular situation, I didn't remember
> all exact z values for confidence levels (if
> needed, I have to spend extra 30 seconds to write
> it down for me...still not automatic, this stuff),
> but I know that the biggest one is 2.57 for 99%,
> so my calculated z-value was definitely out of all
> confidence levels. So without any doubts, Ho
> rejected. If the z value were about 3 or lower,
> then I would look it up - the value of z-statistic
> for 95% confidence level (or 5% significance
> level)...am I clear and am I correct?


Bravo. Thank you!
 
Numbers to Remember:
2.58 99% CI
2.33 98% CI
1.96 95% CI
1.645 90% CI
1.28 80% CI

You will never need another, I promise.

But 7.2 is way the heck out of the ball park. I used to teach the CI way of doing hypothesis tests, but I really hate it now. The problem is that CI's are for a very specific problem (a point estimate and a standard error) and hypothesis testing is much more general. For example, on Level II you have at least Durbin-Watson tests and ANOVA tables, both of which are hypothesis tests with no clear interpretation as CI's.

Since you need to learn both approaches anyway, it's better to separate them from the beginning. Calculate a CI when you are asked for an estimate and calculate a hypothesis test when you are asked to prove some binary outcome.
 
jamespucyk Wrote:
-------------------------------------------------------
> B


No, the answer is C.
 
Your right, I only read the question and not the answers... LOL... I won't make that same mistake in June.

*EDIT* It's cus hypothesis testing don't prove nuttin' definative. The sample can be from a tail end or not representative of the population, etc.



Edited 1 time(s). Last edit at Saturday, September 2, 2006 at 01:54AM by jamespucyk.
 
jamespucyk Wrote:
-------------------------------------------------------
> Your right, I only read the question and not the
> answers... LOL... I won't make that same mistake
> in June.
>
> *EDIT* It's cus hypothesis testing don't prove
> nuttin' definative. The sample can be from a tail
> end or not representative of the population, etc.


Given your history on this forum you are forgiven!

Much RESPECT,

jbnjc
 
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