Let 0 . Then a 100(1 )% CI for when n is large is x z s n

Chapter 7, Problem 7.60

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Let 0 . Then a 100(1 )% CI for when n is large is x z s n , x z s n The choice /2 yields the usual interval derived in Section 7.2; if /2, this interval is not symmetric about x . The width of this interval is w s(z z )/n. Show that w is minimized for the choice /2, so that the symmetric interval is the shortest. [Hints: (a) By definition of z, (z) 1 , so that z 1 (1 ); 282 CHAPTE (b) the relationship between the derivative of a functiony f(x) and the inverse function x f 1(y) is (d/dy)f 1(y) 1/f(x).]

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