A random sample of analyst earnings has mean of $2.84 and a standard deviation of $0.40. What can we say about the 90% confidence interval for earnings next period if: A. the sample size is 20? B. The sample size is 40? What probabilistic statement could we make at the 90% confidence level: C. if the sample size were 15? D. If the sample size were 60?

Please clarify you query in a detailed way

It’s a bogus question because the set-up just isn’t right, but the point they are trying to make is that you don’t know anything about the shape of the dist’n of “analyst earnings” so you don’t really know anything about the distn of the average of analyst earnings. EXCEPT - if the sample size is large, we can probably use the central limit theorem. I’ll bet your book defines large as “> 30” so for A the answer is nada and b the answer is the usual CLT C.I. for the mean and similarly for C and D.

Joey, hightly appreciated by your enthusiasm. This exam is in comprehensive problems of Schweser 2008 book and its answer is that we can use the central limit theorem for only D answer. Thought as you but i can not understand why the book say that the B answer is can not?

Read the book again. It mentioned clearly (I vaguely recollect). If I jog my memory… You cannot answer either A or B because it talks of the ‘actual’ “earnings next period”. A and B talk about the actual population, while stats are for the earnings estimate. For C and D, use Joey’s writeup.

Ohhhh…thank nodoubt very much. You make me clear my confusing. I take no notice on wording of this exam. A & B are for “earnings next period”, but C&D for “probabilistic statement”. Thanks all of you once again.

You have to eb really careful on these questions - the devil is in the details. One little word can change the meaning of the question.