Suppose that X1, . . . , Xm form a random sample from the normal distribution with

Question:

Suppose that X1, . . . , Xm form a random sample from the normal with unknown mean μ1 and unknown variance σ2, and Y1, . . . , Yn form an independent random sample from another normal with unknown mean μ2 and the same unknown variance σ2. For each constant λ (−∞ < λ < ∞), construct a t test of the following hypotheses with m + n − 2 degrees of freedom:
H0: μ1 − μ2 = λ,
H1: μ1 − μ2 = λ. Distribution
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