Question: Let . Then a % CI for m when n is large is The choice yields the usual interval derived in Section 7.2; if ,

Let . Then a % CI for m when n is large is The choice yields the usual interval derived in Section 7.2; if , this interval is not symmetric about

. The width of this interval is . Show that w is minimized for the choice , so that the symmetric interval is the shortest. [Hints:

(a) By definition of

, so that ;

(b) the relationship between the derivative of a function and the inverse function is .]

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