Need help with the Interval Estimate of the Variance (Two-tailed Chi-Square)
So we were solving the following problem in my Inferencial Statistics class the other day:
We wish to estimate the variance of the nistamine concentration in an ointment. It is known from long time experience that it's distribution follows a normal distribution. A sample of 9 ointments is taken, yielding the following nistamine levels (in millions of units/g): 1, 0.9, 1.5, 2.8, 3.1, 3.2, 2.5, 1.9, 2. Estimate the variance using two confidence intervals at the 99% and 95% confidence levels.
Thing is the teacher gave us the standard formula for Confidence Intervals of Vartiance- (two tailed)
I solved the problem using the formula as it is, multiplying the (n-1) by the variance (because the problem is talking about the variance s^2), however, the teacher and the rest of the class got a different result. When I asked the teacher why we got different confidence intervals she said it was because in this specific case we were talking of a sample, therefore, we had to multiply by standard error of the mean and not variance.
I thought this was super weird because I don't think i'd ever seen a formula of confidence intervals for the variance where they did this; of course AI is not the best source with these things but I asked Chat GPT about this and it agreed that it was NOT common to do that, in fact, rather weird that she did it that way.
I want to get a more experienced or detailed explanation on this to see if I'm just ignorant on the topic or if she did just do something weird.