Inferential Stats: Estimating Pop St. Deviation/Variance - Chi Square

#1
Hello,

I have questions regarding some elements of Estimating a Population Standard Deviation via the Chi Square method... Please note that I am not asking for directions on how to do this, as I know how, but require more background information on the subjects. I would appreciate answers that are concise and directly answer my questions.

Background notes: I was taught this via a college stats course. We used the Chi-square model ONLY to estimate st. dev/variance.

1. Why the Chi Square Model?
In the case of estimating a pop. mean, we use T-distribution. This is because Sigma is unknown in a practical sense... What is the unknown parameter that forces us to use this model? Can anyone provide more info on why we use this model?

2. What are the model requirements for this method?
So, I am reading that the Chi-Square Model can ONLY be used when the population sampled from is NORMAL. So, what model requirements must be satisfied before using the method? Does the central limit theorem apply? Does N>20n ?

3. If the population sampled from is not normal, what other methods must be used other than Chi-Square?


Please answer precisely and if you can, provide some online materials to support your claims. Thank you very much.

-new member.