Confidence Interval for ratio of variances
Let $X_1, X_2, \cdots , X_{n_1}$ be a random sample of size $n_1$ from $N(\mu_1, \sigma_1^2)$ and $Y_1, Y_2, \cdots , Y_{n_2}$ be a random sample of size $n_2$ from $N(\mu_2, \sigma_2^2)$. Moreover, $X$ and $Y$ are independently distributed.
Formula
$100(1-\alpha)$% confidence interval estimate for the ratio of variances is
$\bigg(\dfrac{s_1^2}{s_2^2}\dfrac{1}{F_{(\alpha/2,n_1-1,n_2-1)}}, \dfrac{s_1^2}{s_2^2}\dfrac{1}{F_{(1-\alpha/2,n_1-1,n_2-1)}}\bigg)$
where,
$s_1^2$and$s_2^2$are the sample variances for the first and second sample respectively,$1-\alpha$is the confidence coefficient,$F_{(\alpha/2,n_1-1,n_2-1)}$and$F_{(1-\alpha/2,n_1-1,n_2-1)}$are the table values of $F$.
