Margin of error for stratified survey sample

#1
Hi all, apologies for cross-posting: I posted this in another forum last week; it received over 100 views but no responses!

I have a stratified sample of respondents to a survey with the following make-up:



So the total population is 7468 (and the total sample size is 1,008).

I have also applied a set of weights to the data, which yields the following effective sample sizes:



The effective total sample size is 727.

What I'm trying to find out is the margin of error for a sample proportion of 0.5 for the WHOLE weighted sample at the 95% confidence level (I can work it out for each of the strata). Can anyone help me?

We can assume the data is normally distributed due to the central limit theorem.

Also respondents were selected via a stratified proportionate sampling design: stratum 5 was oversampled and stratum 6 was undersampled to accommodate (not sure if this makes a difference).

I've Googled this and nothing at all definitive comes up.

Many thanks in advance for any advice!
 
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Dason

Ambassador to the humans
#2
We can assume the data is normally distributed due to the central limit theorem.
I don't really understand what you're asking but what you say here is not really correct. The CLT doesn't tell you if the data is normally distributed or not - it tells you about the sampling distribution about sums/means of random variables.
 
#3
Many thanks Dason. We can safely ignore that sentence then!

I'm asking for the formula for the margin of error for a proportion, from a stratified sample.

The normal formula for the margin of error for a proportion of a simple random sample (with Finite Population Correction included) is:



...where z is the critical value.

But what is the formula for a stratified sample?

The only thing online I could find is this:

http://www.promesa.co.nz/Help/EP_est_stratified_random_sample.htm

Is this correct??