Let 0 curren Icirc sup3 curren a Then a 100(1 Icirc plusmn ) CI for m when n is large is The choice Icirc sup3 Icirc plusmn 2 yields the usual interval derived in Section 7 2 if Icirc sup3 Icirc plusmn 2, this interval is not symmetric about x Igrave The width of this interval is w s(z Icirc sup3 z Icirc plusmn Icirc sup3 ) n Show that w is minimized for the choice Icirc sup3 Icirc plusmn 2, so that the symmetric interval is the shortest

Question: Let 0 ¤ Î³ ¤ a. Then a 100(1 - Î±)% CI for m when n is large is The choice Î³ = Î±/2 yields

Let 0 ‰¤ Î³ ‰¤ a. Then a 100(1 - Î±)% CI for m when n is large is

The choice Î³ = Î±/2 yields the usual interval derived in Section 7.2; if Î³ ‰ Î±/2, this interval is not symmetric about xÌ…. The width of this interval is w = s(zÎ³ - zÎ±-Î³)/ˆšn. Show that w is minimized for the choice Î³ = Î±/2, so that the symmetric interval is the shortest.

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