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.


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