Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6CHAPTER 5Sampling Distributions and the Central Limit TheoremXDensityX = Age of women in U.S. who have given birthPopulation Distribution of X Population Distribution of X Suppose X ~ N(μ, σ), then…… etc….μ = 25.4σ = 1.5x1xxx3xx4 x2xx5 xMost individual ages are in the neighborhood of μ, but there are occasional outliers in the tails of the distribution.X = Age of women in U.S. who have given birthSample,n = 400XDensitySample,n = 400Sample,n = 400Sample,n = 4001x2x3x4x5x… etc….Sample,n = 400Population Distribution of X Population Distribution of X How are these values distributed?σ = 1.5Suppose X ~ N(μ, σ), then…μ = 25.4XDensityμ =σ = 2.4XDensityμ =Suppose X ~ N(μ, σ), then…Suppose X ~ N(μ, σ), then…X = Age of women in U.S. who have given birthSampling Distribution ofSampling Distribution ofXfor any sample size n.,nsm� �� �� �X ~ N ,… etc….Population Distribution of X Population Distribution of X How are these values distributed?The vast majority of sample mean ages are extremely close to μ, i.e., extremely small variability. 1x2x3x4x5xμ = 25.4“standard error”1.5 yrs.075 yrs400ns= =Suppose X ~ N(μ, σ), then…Suppose X ~ N(μ, σ), then…Suppose X ~ N(μ, σ), then…XDensityμ =σ = 2.4XDensityμ =X = Age of women in U.S. who have given birthSampling Distribution ofSampling Distribution ofXfor any sample size n.,nsm� �� �� �X ~ N ,… etc….Population Distribution of X Population Distribution of X How are these values distributed?The vast majority of sample mean ages are extremely close to μ, i.e., extremely small variability. 1x2x3x4x5xfor large sample size n.μ = 25.4“standard error”1.5 yrs.075 yrs400ns= =X ~ Anything with finite μ and σ Suppose X N(μ, σ), then…Suppose X ~ N(μ, σ), then…XDensityμ =σ = 2.4XDensityμ =X = Age of women in U.S. who have given birthSampling Distribution ofSampling Distribution ofXfor any sample size n.,nsm� �� �� �X ~ N ,… etc….Population Distribution of X Population Distribution of X How are these values distributed?The vast majority of sample mean ages are extremely close to μ, i.e., extremely small variability. 1x2x3x4x5xfor large sample size n.μ = 25.4“standard error”1.5 yrs.075 yrs400ns=
View Full Document
Unlocking...