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

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Stat 312: Lecture 09Confidence intervals from normal populationMoo K. Chung[email protected]September 30, 2004-1.5-1.0-0.50.00.51.01.51618202224262830Normal Q-Q PlotTheoretical QuantilesSample QuantilesFigure 1: Normal probability plot showing normalityof data.1.Fat content of 10 randomly selected hotdogs isgiven by> 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 a 95%CI for thepopulation mean fat content.Since the samplesize is small, we can not apply large sample sizeresults. Let us check the normality of data firstusingqqnorm(x).So we can assume our data to follow a normaldistribution but the variance is unknown.2.IfXiN(μ, σ2),T¯X-μS/ntn-1,a t distribution withn-1degrees of freedom. Asn→ ∞,tnN(0,1)so for large sample sizen,we can approximatetdistribution withN(0,1).Let us plottdistributions and compare them withN(0,1).-4-20240.000.150.30xdt(x, 1)-4-20240.00.20.4xdt(x, 100)-4
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Term
Fall
Professor
Chung
Tags
Statistics, Normal Distribution, 1 degrees, Student s t distribution, large sample size, 0 95 percent

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