Question: Suppose that X1, . . . , Xm form a random sample from the normal distribution with mean 1 and variance 21, and Y1, .

Suppose that X1, . . . , Xm form a random sample from the normal with mean μ1 and variance σ21, and Y1, . . . , Yn form an independent random sample from the normal with mean μ2 and variance σ22. Show that if μ1 = μ2 and σ22 = kσ21, then the random variable U defined by Eq. (9.6.13) has the t with m + n − 2 degrees of freedom.

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