71. Let 0 g

a. Then a 100(1  a)% CI for m when n is large is The choice g  a/2 yields the usual interval derived in Section 8.2; if g  a/2, this con dence interval is not symmetric about . The width of this interval is w  s(zg  zag)/ . Show that w is minimized for the choice g  a/2, so that the symmetric interval is the shortest. [Hints:

(a) By de nition of za, (za) 

1 

a, so that za1(1  a);

(b) the relationship between the derivative of a function yf (x) and the inverse function xf1(y) is (d/dy) f 1(y)1/f (x).]