R help - Nov 2009 - Confidence intervals - a statistical question, nothing to do with R

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.

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at
r-project.org] On
> Behalf Of Moshe Olshansky
> Sent: Wednesday, November 18, 2009 3:21 PM
> To: R-help at r-project.org
> Subject: [R] Confidence intervals - a statistical question, nothing to do
with R
> 
> 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.
> 
You might want to look at the survey package for getting appropriate variance
estimates.

Hope this is helpful,

Dan

Daniel J. Nordlund
Washington State Department of Social and Health Services
Planning, Performance, and Accountability
Research and Data Analysis Division
Olympia, WA  98504-5204