Calculating confidence in part of a sample (explain like I'm in the humanities please :) ) Working on a two-part project. First, we're estimating the total size of a very large population. Each member of the population has a standardized random 15-digit identifier, and we have guessed using a brute force method until discovering enough extant identifiers (20,000) to estimate the population size, with a confidence calculated using standard error of the mean. That part is ok.
The second part is a description of the 20k sample: demographics, etc. What I need to figure out is how to calculate the CI/error% of particular subsets of that sample. So if there's a group of 1,000 within the sample of 20,000 with unusual characteristics, I want to be able to describe those characteristics. Let's say it's a sample of people where one dimension of the data is income. There's a group of 1,000 CEOs in the group with a much higher income than everyone else. What I want to know how to figure out is how statistically significant the mean income of that 1,000 would be. It seems like it would require some compounding of the standard error of the sample with regard to the population and the sub-sample of CEOs in relation to the sample. Am I overthinking this?

Reading some of your follow-up comments, it sounds like you want to provide descriptive statistics with confidence intervals.
The uncertainty around the total population size generally isn't a problem. Typically, you'd just assume that the total population is infinite. This is a conservative approach. The you follow the standard approach for computing confidence intervals.
A more precise approach takes the size of the population into account. The idea here is that if you have a population of 100 and a sample of 99, you actually almost know the mean of the population. There's a formula to shrink your variance estimate by this ratio. It's called the finite population correction.
In your case, there's some uncertainty about the total population, but if your estimate of the total population is unbiased, then your estimate of this ratio is unbiased and you're okay. You can see this with a little math. See my answer here to a similar question.
So you have two options, 1) just assume your sample of 1,000 CEO's is from an infinite population of CEO's or 2) apply a finite population correction using your estimate for the population size.
Unless you've sampled a large ratio of the total population, 1) and 2) will be about the same. So if you just want to keep it simple, you should go with 1). In which case, yes, you're probably over thinking things. :)
