## 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 $F$.