I am a noob trying to learn some statistics and I didn’t find (or understand) answers to my question.
I’m currently learning about the normal distribution, the Central Limit Theorem and confidence intervals. My question is as following; since we can know the mean of a population in a sample (n>30) to which the CLT applies, should we use population formulas on this sample? For example,if I want to calculate the Standard Error of this sample, should I use the population or the sample formula?
In my head, since the mean of the sample = the mean of the population, then I could be able to calculate the variance (and then the Standard Error) using the population formula on this sample. But it’s confusing me and i’m not sure anymore.
Subsequently, to calculate the confidence interval of the mean of this same sample, should I use the formula for “known population variance and normally distributed” dataset? I assume that in order for the CLT to apply, you have to have access to a population’s data, and so you can know this population’s variance.
I’m just really confused about the CLT I guess; does it apply only on samples you get from a whole population’s dataset? Or can it apply on a sample directly? (or a sample n>30 you take from a sample) Because if it’s the case and if my assumption on my first question is correct, I have trouble understanding why we would need a formula for confidence intervals where we don’t know the population’s variance.
Thanks for bearing with me, I hope I have been clear enough (english is not my primary language) for you to understand me. If you can help me, don’t hesitate, any help (on my questions, or any link to any ressources I could use) is appreciated!