Chapter 4, Problem 18E

Suppose that $x_1~N\left(\mu ,{\sigma }_1^2\right)$ and $x_2~N\left({\mu }_2,{\sigma }_2^2\right),$ and that x₁ and x₂ are independent. Develop a procedure for constructing a confidence interval on μ₁ – μ_2, assuming that ${\sigma }_1^2$ and ${\sigma }_2^2$ are unknown and cannot be assumed equal.