Consider independent random samples from two normal distributions, $x_{1}N({}_1,{}_1^2)$ and

$Y_{j}N({}_2,{}_2^2)$ for $i=1,$dots,$n_1$ and $j=1,$dots,$n_2.$ Assuming ${}_1$ and ${}_2$ are known, derive a

$100(1-)\%$ confidence interval for $\frac{{}_2^2}{{}_1^2}$ based on sufficient statistics.