Question: CHALLENG E Treatment and control groups. The two previous exercises illustrate a common setting for statistical inference. This exercise gives the general form of the

CHALLENG E Treatment and control groups. The two previous exercises illustrate a common setting for statistical inference. This exercise gives the general form of the sampling distribution needed in this setting. We have a sample of n observations from a treatment group and an independent sample of m observations from a control group. Suppose that the response to the treatment has the N(μX, σX)

distribution and that the response of control subjects has the N(μY, σY ) distribution. Inference about the difference μY − μX between the population means is based on the difference y − x between the sample means in the two groups.

(a) Under the assumptions given, what is the distribution of y? Of x?

(b) What is the distribution of y − x?

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