Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Stat 312: Lecture 10Confidence intervals for varianceMoo K. Chung[email protected]August 13, 20041.Suppose the fat content of a hotdog follows nor-mal distribution. 10 measurements are given.> x<-c(25.2,21.3,22.8,17.0,29.8,21.0,25.5,16.0,20.9,19.5)We are interested in constructing interval estimateof the unknown population variance. To solve thisproblem, we need to know the following fact.2.LetX1,· · ·, XnbearandomsamplefromN(μ, σ2).(n-1)S2σ2=1σ2nXj=1(Xj-¯X)2χ2n-1Quiz. What is the expectation ofχ2n-1?> y<- 0:50> par(mfrow=c(2,2))> plot(y,dchisq(y,1),type=’l’)> plot(y,dchisq(y,5),type=’l’)> plot(y,dchisq(y,10),type=’l’)> plot(y,dchisq(y,20),type=’l’)3.Critical values forχ2ndistribution are defined asnumbers that givesP(χ21-α/2,n< χ2n< χ2α/2,n) = 1-αTo findχ20.975,9andχ20.025,9that is need to con-
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Term
Fall
Professor
Chung
Tags
Statistics, Normal Distribution, Variance, probability density function, 1 j, mchung stat wisc edu, Moo K Chung

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