Originally Posted by

**hatsoff** I only understand about half of what was posted (I'm still wading through calc 3, and haven't made it to stats/probability), but from what I can gather, it seems that in this case the confidence of a $\displaystyle \hat{p}$ score does not depend at all on the total population, but on the sample size $\displaystyle n$ alone.

So, if $\displaystyle n_1=n_2$, and $\displaystyle \hat{p_1}=\hat{p_2}$, then the confidence for each $\displaystyle \hat{p}$ value is the same, no matter how different are the sizes of the population... or do I have this completely wrong?

I mean, obviously the population sizes would place absolute limits on the error. For example, if you sample 10 members of a population of 100, and you get 5 positive results, then your error cannot be more than 45%, whereas if you had a 5/10 result from a pop. of 1000, your error could technically be as great as 49.5%. When working with larger numbers (in the millions, e.g.), does the ratio of n/pop. matter, or is it simply n that makes a difference, independent of the pop. size?