Reference: Q22. Concept Checkers. Reading #10.
Annual returns on small stocks have a popn mean of 12% and a popn std devn of 20%. If returns are normally distributed, a 90% confidence intvl on mean returns over a 5-yr period is: Doubt: I am not able to connect “anual returns” and “5-yr period” in this question. I saw the soln, but still it is not very intuitive.
I think they meant a 90% confidence interval on mean _ annual _ returns over a 5-year period. The only thing the 5 years signifies is that that’s the period over which they gathered their annual return data; you’re not constructing a confidence interval for 5-year returns.
Ambiguous wording.
So, why do we have to use 5 yr in our calculation? Why can’t we just construct a confidence interval for annual returns?
I have noticed that whenever a sample size is given, confidence intervals based on that sample size are constructed. The reason I need confidence interval is because I am using a sample, not the population for my analysis. From what I can make of it, they want us to test the accuracy (loosely put term) of the mean annual returns over a 5-yr sample period; hence, the confidence interval over a 5 year period.
They gathered 5 years’ of returns, so n = 5; that’s the sample size they want you to use.
As I say, the wording’s not clear.
(Perhaps they had annual returns of -18%, 12%, 22%, 2%, and 42%. These would be . . . I don’t know . . . average annual returns for small stocks for five years, say. It’s not clear. I wouldn’t worry about this one; on the real exam it won’t be ambiguous.)
I am sorry that I couldn’t state my question clearly. What I wanted to ask is when we use a sample size, we construct a confidence interval over that size or over the whole of the population? Over that size, right? So, we are cobtructing a confidence interval for annual reyurns over a 5-yr period, right? If that be the case, thanks a lot for your patience 
In this problem we are constructing a confidence interval for the 5-year mean annual return. That’s why we use standard error (not standard deviation), and 5 is our sample size.
Yes, you’re correct.
(On a side note, it’s fascinating to see you write, “If that _ be _ the case . . . .” Most Americans would (incorrectly) write, “If that is the case . . .” because they’ve never been taught that the present subjunctive of “to be” is “be.” I applaud your education.)
(Years ago, as an undergraduate mathematics student, I was in a class called “Introduction to Mathematical Methods”; is was a class designed to teach us how to construct proofs, which is a skill we would need in our upper division courses. One day the professor complained about the dismal grammar in the papers he handed back. That evening, when working on my homework, I started a proof with “If x _ be _ an element of set A . . .” When he returned it after grading it, he had crossed out “be” and written in “is”. After class I asked him why, if he were so concerned about our grammar, he would cross out “be” (the proper present subjunctive) and write in “is” (the present tense, but not subjunctive). His reply: it sounded like something out of the King James Bible.)
Comment removed. Sorry if I offended anyone. Please note that it was not my intention to offend anyone.
It will not do you good to romanticize the quality of US education. Yes, some MIT professors are good; that’s why they put up their video lecture notes. However, there are plenty of Indian professors who teach well and post their lecture videos on Youtube, too. The best introductory stochastic processes book I read was written by an Indian guy and published by an Indian publisher. Same with intermediate analysis. And the free on-line learning site, Khan Academy, is famously run by an Indian guy.
Incidentally, if you keep having trouble with basic stats/quant methods portion, you might want to check out the Khan Academy videos explaning concepts. They’re very short and conscise, and you don’t have to wade through hour-long lecture to get to the part that you’re having trouble with.
Thanks
Comment removed. Kindly accept my apologies. It was not meant to offend anyone. In case, I have offended anyone becuase of my stupidity, I apologize again. Everybody makes mistakes. I hope I deserve a second chance.