Suppose that X1, , Xm form a random sample from the normal distribution with unknown mean 1 and unknown variance 2, and Y1, , Yn form an independent random sample from another normal distribution with unknown mean 2 and the same unknown variance 2 For each constant ( ), construct a t test of the following hypotheses with m n 2 degrees of freedom H0 1 2 , H1 1 2

Question: Suppose that X1, . . . , Xm form a random sample from the normal distribution with unknown mean 1 and unknown variance 2, and

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.

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