I know what confidence interval mean in random sampling, but I'm confused what does CI mean in the whole population. Is there any difference? Or I could see the whole population as a "big" random sample since the random sample is equally useful as the whole population?
Thanks
A confidence interval describes an interval for a parameter for which (based on some assumptions) you feel confident it falls in. When talking about a "random sample" versus "whole population", there are two main possibilities.
The parameter in consideration is known exactly from sampling the data. E.g., "What percent of the population is male?" A random sample will give you an estimate, plus some confidence interval based on the standard error. However, the closer your sample is to the entire population, the size of your confidence interval rapidly approaches zero. Once you have the entire population, you know the exact percentage of sexes, for example.
You are performing a regression, or otherwise trying to model relationships between variables. For example, you may want to find the relationship between weight versus sex and age. The parameters you are trying to estimate are $b_1$ and $b_2$ in $weight = b_1 \cdot age + b_2 \cdot sex + error$. Even if you have the whole population, that doesn't give you perfect information, since the error is unknown. In most cases, there is uncertainty, and you will still have a confidence interval.
