Another question on population vs. sample The problem that bugs me can be boiled down to: "What is population? (Really)." This is my thought experiment I've dealing with for a few days.
There is a researcher A, who gathers data from $N = 20$ observations on some variable. He gets $\bar{x_A} = 17.21$. He thinks that he can't measure all the population, 'cause "the amount of money, time" is too much to do that (the usual story, lecturers tell the students).
But there is also a researcher B, who happened to collect the data from entire population, because it turns out that it's feasible, it's like $N=100$ people, but researcher A didn't know that. You can think of some rare genetic diseases. Not that many people have them, so it's quite possible to get the data from all patients suffering from the condition - at least in some thought experiments like this.
The researcher B finally gets $\bar{x_B} = 18.82$. Obviously, $\bar{x_A} \neq \bar{x_B}$.
Questions:
[1] Is really the entire set of observations the population? I know that it may sound stupid (yes, it does), but I wonder if there is some catch in here?
If it is, then - according to what they say - you can't use inferential statistics and you can't do eg. (statistical) significance tests when you are the researcher B. Or maybe is the population some theoretical entity and the researcher B's data is not a population?
[2] It is also said, that if you can get the data from all observations in population, you get the population's parameter, so you may write $\mu$ instead of $\bar{x_B}$. So The researcher B 's $\bar{x_B}$ becomes $\mu = 18.82$ -... right?
[3] Is the researcher A's mean $\bar{x_A} = 17.21$ somehow wrong?
[4] Can you point me to some valuable literature? :-) I feel I need to educate myself on this.

Good questions.

*

*This is debated. Under the super-population view, no. Under the finite population view, yes.


*According to the finite population view, yes.


*According to the finite population view, yes. According to the super-population view, researcher B still has a sample, but it's a larger and better sample than researcher A's sample.


*See this paper and references therein.
