Matstat - confidence interval for estimating variance - what is u and Xi^2?

Question

Mathematics

Task: determine the confidence interval for estimating the variance of the population.
Here is the whole solution.

I have one question: where did u come from?
It seems like it should be from Pearson, but how did you find it?

Answer 1

In short - from the table of quantiles of the chi-squared distribution.
Longer: we know that the estimate of the population variance (which is obviously a random variable and depends on the sample) is chi-squared distributed with known parameters. For this theoretical distribution, the formula P(X>x) is known; from it you can build tables like the one above, and from them it is easy to find quantiles.