The S&P 500 index has expected return of 9% per year with standarddeviation of 15%. Assuming that returns are normally distributed, what is the range of returns that can be expected over one year with a 95% level of confidence?

9% (+/-) 1.96*15% [-20.4%, 38.4%]

It is correct. My question is “I get confused sometime”: When we use the standard error to caulate the confidence interval?

You use the standard error when you are not told that the distribution is normal (generally they will say sample mean, sample standard deviation, and give you the number of observations N)

When you are using a Sample to make a prediction of the Population Parameters, use the Std Error of the Sample Mean. This is because (this is not mathematical, it is something you have to think about) you are using a smaller # to predict a much larger #. So your error term needs to reflect that difference. in the above, the S&P 500 index is the population itself. So no need for the Std Error of the “sample” because they have given you the entire Population Mean and std. If they had instead given you the mean of 30 companies on the S&P 500 is 9% and their sample std dev is 15% --> your answer would have changed to 9 +/- 1.96 * 15/sqrt(29) instead of the above. Hope this answers your question. CP

strangedays Wrote: ------------------------------------------------------- > It is correct. > > My question is “I get confused sometime”: > > When we use the standard error to caulate the > confidence interval? good one – I think when you are looking at a sample, you use SEE ? they gave us no sample size here, so we can eschew it r(standard error) right away.

cpk123 Wrote: ------------------------------------------------------- > When you are using a Sample to make a prediction > of the Population Parameters, use the Std Error of > the Sample Mean. This is because (this is not > mathematical, it is something you have to think > about) you are using a smaller # to predict a much > larger #. So your error term needs to reflect that > difference. > > in the above, the S&P 500 index is the population > itself. So no need for the Std Error of the > “sample” because they have given you the entire > Population Mean and std. > > If they had instead given you the mean of 30 > companies on the S&P 500 is 9% and their sample > std dev is 15% --> your answer would have changed > to > > 9 +/- 1.96 * 15/sqrt(29) > > instead of the above. > > Hope this answers your question. > > CP cpk123 gave you a great explanation, except you are supposed to take the square root of N, not (N-1) for the standard error N-1 is degrees of freedom for the T distribution, or what you should use when calculating a sample variance - but the number under the square root sign in the denominator will be just ‘N’ for the std. error

guys thank you very much! I am going revising my practice test that I did today and feeling very depressed

supersharpshooter Wrote: ------------------------------------------------------- > cpk123 Wrote: > -------------------------------------------------- > ----- > > When you are using a Sample to make a > prediction > > of the Population Parameters, use the Std Error > of > > the Sample Mean. This is because (this is not > > mathematical, it is something you have to think > > about) you are using a smaller # to predict a > much > > larger #. So your error term needs to reflect > that > > difference. > > > > in the above, the S&P 500 index is the > population > > itself. So no need for the Std Error of the > > “sample” because they have given you the entire > > Population Mean and std. > > > > If they had instead given you the mean of 30 > > companies on the S&P 500 is 9% and their sample > > std dev is 15% --> your answer would have > changed > > to > > > > 9 +/- 1.96 * 15/sqrt(29) > > > > instead of the above. > > > > Hope this answers your question. > > > > CP > > cpk123 gave you a great explanation, except you > are supposed to take the square root of N, not > (N-1) for the standard error > > N-1 is degrees of freedom for the T distribution, > or what you should use when calculating a sample > variance - but the number under the square root > sign in the denominator will be just ‘N’ for the > std. error nice