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

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

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α-γ