47. In the matched-pairs experiment for testing the effect of a treatment, suppose that only the differences Z, = Y; - X; are observable. The Z's are assumed to be a sample from an unknown continuous distribution, which under the hypothesis of no treatment effect is symmetric with respect to the origin. Under the alternatives it is symmetric with respect to a point f > o. Determine the test which among all unbiased tests maximizes the power against the alternatives that the Z's are a sample from N

(f, ( 2 ) with f > O. [Under the hypothesis, the set of statistics (I:7_1 zl,...,I:7_1 zln) is sufficient; that it is complete is shown as the corresponding result in Theorem 6. The remainder of the argument follows the lines of Section 11.]