I'm really having a hard time understanding how standard error works and its driving me crazy. Okay, let's start from the top.
-Assume we have a distribution that's none normal. We don't know the population mean or standard deviation since the population is too big and we don't have time to get all the values.
-Now out of that huge population, let's say we take a sample size of 50 values and calculate the mean. We do this repeatedly for 20 times. So now we have 20 sample means. We plot these 20 means to get a sample distribution.
Question 1: In my above example, I only calculated 20 sample means. In statistic textbooks, does it assume that we calculate an infinite amount of sample means and create a continuous distribution? It never mentions this so I'm already confused. And in practice, we can't calculate an infinite amount of sample means. This has been confusing me because we need to know what 'n' is and I don't know if n is the size of the sample (i.e. 50) or the number of samples we take (i.e. 20). I want to say 'n' is 50 but that assumes that the number of samples is infinite, which is impractical. So why learn something that's impractical?
Oh and this brings me to another question. In the textbook, it says that if we know the population standard deviation, then the standard error is just:
Standard error = population standard deviation / sqrt(n)
My question is, why in the world do we even learn this? If we know what the population standard deviation is, that means we must know what the population mean is. So why calculate a sample mean to try to estimate the population mean when we already know what it is?
Ugh...I have so many more questions too but to keep it simple, I'll ask these first!
Thanks for the help!