# A sampling question from notes SS3 reading 10

A random sample of analysit earnings estimates has a 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? C what probabilistic statement could we make at 90% level if the sample size were 15? D what probabilistic statement could we make at 90% confidence level if the sample size were 60?

a. 2.84 +/- t(19,0.05) * 0.4 / sqrt(20)

Be careful. The question didn’t say the observations were from a normal distribution (nor did it say Simon says but that’s not relevant here). Using the usual 30 dividing line they probably want you to say that you can’t say anything on a and c. Also, you are giving C.I.'s for the mean (which is appropriate) but they are asking about next period so you actually need a prediction interval, not a confidence interval. Too bad they don’t teach prediction intervals.

This question is a tad tricky…I would analyse the question in the following manner: 1. What is the size of population? (It’s not given in the question, so how can I tell whether a sample size of 20 is small, & sample size of 40 is large, how about sample size of 60?) 2. If point 1 is determined + normal or lognormal distribution is stated, then following the summary table in reading 10. A more appropriate decision on whether to use z or t-distribution can be determined. Feedbacks please…

Joey made a good point here. the answer from notes: you can not say anything for A and B, b/c you do not have information on NEXT period you can not say anything for C either, b/c you can not assume normal distribution, and the sample size < 30 for D, cpk gave the same answer as notes. but my question is since you do not have information on NEXT period, how can you say anything on C and D? Aren’t they the same as A and B?

Did the answers really say that? Wow…Good for them.

For d, cpk is not talking about next period, but the current period.

JoeyDVivre Wrote: ------------------------------------------------------- > For d, cpk is not talking about next period, but > the current period. but the question is about next period, what is the difference between B and D? are they the same kind of question?

The question is a little ambiguous - particularly for me right now - but I think D) is the best answer,