[R] Confidence intervals - a statistical question, nothing to do with R

[Moshe Olshansky]

Dear list,

I have r towns, T1,...,Tr where town i has population Ni. For each town I randomly sampled Mi individuals and found that Ki of them have a certain property. So Pi = Ki/Mi is an unbiased estimate of the proportion of people in town i having that property and the weighted average of Pi is an unbiased estimate of the proportion of the entire population (all r towns) having this property.
I can compute confidence intervals for the proportion of people having that property for each city (in my case Mi << Ni and so binomial distribution is a good approximation to Ki).
My question is: how can I compute confidence interval for the proportion of people in the entire population (r towns) having that property? Either analytical or numerical (simulation?) method will be all right.

Thank you in advance,

Moshe.