Sampling Distributions and the Central Limit Theorem

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Sampling Distributions and the Central Limit Theorem CHAPTER 5 Sampling Distributions and the Central Limit Theorem

Population Distribution of X Suppose X ~ N(μ, σ), then… X = Age of women in U.S. who have given birth X Density     x4 x5 x1 x2  x3 … etc…. σ = 1.5 Most individual ages are in the neighborhood of μ, but there are occasional outliers in the tails of the distribution. x x x x x μ = 25.4

Population Distribution of X Suppose X ~ N(μ, σ), then… Sample, n = 400 Sample, n = 400 X = Age of women in U.S. who have given birth Sample, n = 400 Sample, n = 400 X Density Sample, n = 400 … etc…. How are these values distributed? σ = 1.5 μ = 25.4

Population Distribution of X Sampling Distribution of for any sample size n. Suppose X ~ N(μ, σ), then… Suppose X ~ N(μ, σ), then… X = Age of women in U.S. who have given birth Density μ = X Density μ = σ = 1.5 “standard error” … etc…. How are these values distributed? The vast majority of sample mean ages are extremely close to μ, i.e., extremely small variability. μ = 25.4

Population Distribution of X Sampling Distribution of Suppose X ~ N(μ, σ), then… Suppose X ~ N(μ, σ), then…   for large sample size n. for any sample size n. X = Age of women in U.S. who have given birth Density μ = X Density μ = σ = 2.4 Suppose X ~ N(μ, σ), then… “standard error” … etc…. How are these values distributed? The vast majority of sample mean ages are extremely close to μ, i.e., extremely small variability. μ = 25.4

Population Distribution of X Sampling Distribution of X ~ Anything with finite μ and σ Suppose X  N(μ, σ), then…  for large sample size n. for any sample size n. X = Age of women in U.S. who have given birth Density μ = X Density μ = σ = 2.4 Suppose X ~ N(μ, σ), then… “standard error” … etc…. How are these values distributed? The vast majority of sample mean ages are extremely close to μ, i.e., extremely small variability. μ = 25.4