Confidence intervals and large-sample confidence
Hi, out there!
I really need some help/hints on this:
"Suppose a research report is to include 20 confidence intervals, each at the 0.95 level. Although one would expect some relationships, suppose the intervals are based on independent statistics.
a) About how many of the intervals would you expect actually to include the true value of the parameter being estimated?
b) What is the probability that all 20 intervals will contain the true values of the parameters being estimated?"
I've been reading the whole chapter, in my textbook (Berry & Lindgren: Statistics), and I simply can't find it!
Thanks in advance
Re: Confidence intervals and large-sample confidence
For a) you need to consider what the confidence interval represents: a 95% interval represents that 95% of the time the interval will contain the true parameter.
Now if something is independent, you need to consider the independence criterion which is P(A and B) = P(A)P(B). So if you have the probability of one interval containing the true parameter, then you have to consider the probability corresponding to your statement (i.e. what you expect actually to include the true value) and then find the frequency (which is multiplying this probability by the number of items in your population which in this case is 20 intervals).
Part b) is the same but consider the extension to twenty variables of P(A and B) = P(A)P(B) for independent A and B (except that we have twenty intervals not two).