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CHAPTER 5

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. . . . Density. . x 4. x 1. x 5. x 2. . x 3. … etc…. σ = 1.5.

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CHAPTER 5

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  1. CHAPTER 5 Sampling Distributions and the Central Limit Theorem

  2. Population Distribution of X Suppose X ~ N(μ, σ), then… X = Age of women in U.S. who have given birth    Density  x4 x1 x5 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 x μ= 25.4

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

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

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

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

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