Probability and Statistics Homework help!!!!!?

Posted on 2014-04-15 06:17:00 in Statistics by MOM2DILLOND

The problem in the textbook is:



Let 0 ? ? ? ?. Then a 100(1 – ?)% CI for ? when n is large is



(x-bar – z? • s/(?n), x-bar + z?-? • s/(?n)



The choice ? = ?/2 yields the usual interval derived in Section 7.2; if ? ? ?/2, this interval is not symmetric about x-bar. 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. [Hint: (a) By definition of z?, ?(z?) = 1 – ?, so that z? = ?-1(1 – ?); (b) the relationship between he derivative of a function y = f(x) and the inverse function x = f-1(y) is (d/dy)f-1 (y) = 1/f’(x).]



Please help solve this problem.

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