Stat 312: Lecture 08Large sample confidence intervalsMoo K. Chung[email protected]September 27, 20041.The sample size is inversely related to the widthof confidence interval. Example 7.4.2.Central Limit Theorem.LetX1,· · ·, Xnbe arandom sample with meanμand varianceσ2. Forsufficiently largen,Z=¯X-μσ/√n∼N(0,1).3.LetX1,· · ·, Xnbe a random sample with meanμ. For sufficiently largen,Z=¯X-μS/√n∼N(0,1)whereSis the sample standard deviation.Ifnis sufficiently large, approximate100(1-α)%confidence interval forμis¯x±zα/2s√n,wheresis the sample standard deviation.4.General large sample confidence interval.Sup-poseˆθis an unbiased estimator of some parame-terθ, Then100(1-α)%confidence interval isˆθ+zα/2pVˆθ.In many applications,Vˆθis a function ofθwhichmakes computation of CI complicated. In this sit-
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