# Confidence intervals for stratified sampling

Let's suppose that I divided my population $N$ into 3 groups:

$N_1$, $N_2$ and $N_3$

I used stratified sampling to get samples which are representativie for each group, let's call them

$n_1$,$n_2$ and $n_3$.

The sum, of course, is equal to $n$. Now I want to compute the confidence interval for the mean, sigma unknown. Can I use the well known procedure for each group $n_1$,$n_2$ and $n_3$ to get the range of the unknown mean of, respectively,$N_1$, $N_2$ and $N_3$ or it's possible only to find the confidence interval respect to $n$, i.e compute a confidence interval to find only the range of the mean of $N$?

Confidence interval is: $\overline{x} \pm t^{*} \frac{s}{\sqrt{n}}$

• To what "well known procedure" do you refer? What do you mean by "confidence interval for $n$," given that you know the value of $n$ (and it's not even a parameter to be estimated in the first place)? – whuber Oct 28 '17 at 15:03
• I want to find the range in which, with some probability, the mean of my population will be. To do this I use the information of my sample to do inference on all the population. Since my population is stratified, I used stratified sampling. Can I use the formula for each stratified sample? Given that I compute the sample mean for each sub-sample and use the sample sd of each one. I added the formula. – Kolmogorovwannabe Oct 28 '17 at 15:10
• It depends on how you selected the strata and their sizes. In no case will simply adding the confidence limits be correct. – whuber Oct 28 '17 at 15:12
• My stratas have different sizes, for example each strata represents a group of bank users. The sum of each strata is my sample. I want to know if it is correct to apply that formula to each strata, using for each one its own mean, sd and numerosity to have a range in which the corresponding mean of the group in population is. – Kolmogorovwannabe Oct 28 '17 at 15:17
• I added details in the question that may help the reader. – Kolmogorovwannabe Oct 28 '17 at 15:28