Given two normally distributed independent samples y1,1, …, y1,n1 and y2,1, …, y2,n2 with unknown means µ1 and µ2 and unknown variances σ21/ σ22, derive with all necessary steps a confidence interval

Given two normally distributed independent samples y1,1, …, y1,n1 and y2,1, …, y2,n2 with unknown means µ1 and µ2 and unknown variances σ21/ σ22, derive with all necessary steps a confidence interval for σ21/ σ22 from the appropriate pivotal value whose distribution must be specified. Let the confidence coefficient be 1 – α and denote the unbiased estimates of σ21 and σ22 by s21 and s22, respectively.