There's a nationwide dataset of the average scores on test, by school (each school has one entry in the dataset). There are significant differences between the means and SDs among the states. A subset is made for Florida. When calculating the standard error of the mean for Florida, do I use the nationwide SD (population SD), or Florida's SD? There are 110 values for FL, and the SD is 25% larger than with the nationwide dataset.
Under the CLT, the sample mean and SD is supposed to approach the population mean and SD upon repeated sampling, but that won't happen when FL is different. So the "population," from FL's perspective, is FL, and with repeated sampling in FL (if possible), the mean and SD would approach a "true" FL.
I'm thinking the issue is with non-random sampling, except studies that compare traits among males and females consider the samples to be random - and FL is a trait, like M/F is.