Looks like we just replied to nostrademons at the same time, but we slightly disagree. You say that the dependence on population size is slow (sqrt) but I say there is no dependence for most cases. Are you sure you aren't confusing the dependence of confidence on sample size as opposed to population size? See, e.g.,

http://en.wikipedia.org/wiki/Statistical_significance#Signal...

I could be making a mistake somewhere.