Stat 371 Spring 2005 Discussion 5: Sampling Distribution and Confidence Intervals, Study notes of Statistics

Download Stat 371 Spring 2005 Discussion 5: Sampling Distribution and Confidence Intervals and more Study notes Statistics in PDF only on Docsity! Stat 371 Spring 2005 Feb. 21, 2005 Discussion 5 1 Sampling Distribution of Ȳ The mean of the sampling distribution of Ȳ is equal to the population mean. µȲ = µ The standard deviation of the sampling distribution of Ȳ is equal to the population standard deviation divided by the square root of the sample size. σȲ = σ√ n 2 Central Limit Theorem If sample size is large, then the sampling distribution of Ȳ is approximately normal, even if the population distribution of Ȳ is not normal. 2.1 Example (Illustration of the central limit theorem using R) > yvalues = c(1,3,11,23,33) > yprobs = c(0.3,0.2,0.1,0.2,0.2) > clt20 = matrix(sample(yvalues,20*100,replace=T,prob=yprobs),nrow=100,ncol=20) > ybar20 = apply(clt20,1,mean) > hist(ybar20) Histogram of ybar20 ybar20 F re qu en cy 5 10 15 20 0 5 10 15 20 25 1250D MSC ting-li@stat.wisc.edu Ting-Li Lin