Question: Suppose that \({{x}_{1}}\tilde{\ }N\left( {{\mu }_{1}},\sigma _{1}^{2} \right)\), and \({{x}_{2}}\tilde{\ }N\left( {{\mu }_{2}},\sigma _{2}^{2} \right)\) that x1 and x2 are independent. Develop a procedure for constructing a 100(1 — \(\alpha \) )% confidence interval on \(\sigma _{1}^{2}\) and \(\sigma _{2}^{2}\), assuming that of and are unknown and cannot be assumed equal.

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