74. Let u1 and u2 denote the mean weights for animals of two different species. An investigator wishes to estimate the ratio u1/u2. Unfortunately the species are extremely rare, so the estimate will be based on nding a single animal of each species. Let Xi denote the weight of the species i animal (i  1, 2), assumed to be normally distributed with mean ui and standard deviation 1.

a. What is the distribution of the variable h(X1, X2;

u1, u2)  (u2X1  u1X2)/ ? Show that this variable depends on u1 and u2 only through u1/u2 (divide numerator and denominator by u2).

b. Consider Expression (8.6) from the rst section of this chapter with a  1.96 and b  1.96.

Now replace  by  and solve for u1/u2. Then show that a con dence interval results if

, whereas if this inequality is not satis ed, the resulting confidence set is the complement of an interval.