Estimating Population mean given a sample, and the population size

Question

For my study, I have population size known (in order of millions), and a sample data (about 30 sample size). I can estimate population mean using 95% confidence interval by t distribution or normal distribution.

The question is, because the population size and sample size vary too much, can I somehow use population size as a parameter to estimate its mean? Intuitively, the greater the difference between population and sample size is, the larger the interval should be.

Answer 1

This seems to be the typical problem of surveys. As usual (and counterintuitive) the population size seldom matters for estimating any means. Only important is the sample size, the larger the better. So the answer to your problem is: The population size is of little importance.