Confidence Interval for Variance
Let $X_1, X_2, \cdots , X_n$ be a random sample of size $n$ from $N(\mu, \sigma^2)$.
Formula
$100(1-\alpha)$% confidence interval estimate of population variance $\sigma^2$ is
$\bigg(\dfrac{(n-1)s^2}{\chi^2_{(\alpha/2,n-1)}}, \dfrac{(n-1)s^2}{\chi^2_{(1-\alpha/2,n-1)}}\bigg)$
where,
$\overline{X}=\frac{1}{n} \sum X_i$is the sample mean,$s^2= \frac{1}{n-1}\sum (X_i-\overline{X})^2$is the sample variance,$1-\alpha$is the confidence coefficient,$\chi^2_{(1-\alpha/2,n-1)}$and$\chi^2_{(1-\alpha/2,n-1)}$are the table values of$\chi^2$.
