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Sampling Distributions and the Central Limit Theorem in Age Distribution of U.S. Women Giving Birth

Explore how the Central Limit Theorem applies to the age distribution of U.S. women who have given birth, understanding population distribution, standard error, and sample variability. Discover the impact of sample size on data distribution patterns.

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Sampling Distributions and the Central Limit Theorem in Age Distribution of U.S. Women Giving Birth

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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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