Lect16_L6_L7_handout

# Lect16_L6_L7_handout - lecture 16 Sampling Distributions II...

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lecture 16, Sampling Distributions II Review Unbiased Estimates Finite Population Correction Sampling Distribution of the Sample Proportion lecture 16, Sampling Distributions II Outline 1 Review 2 Unbiased Estimates 3 Finite Population Correction 4 Sampling Distribution of the Sample Proportion

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lecture 16, Sampling Distributions II Review Unbiased Estimates Finite Population Correction Sampling Distribution of the Sample Proportion lecture 16, Sampling Distributions II Review CLT ( review) If the population of individual items is normal, then the population of all sample means is also normal Even if the population of individual items is not normal, as the sample size gets large, the population of all sample means is approximately normal (Central Limit Theorem (CLT)) The larger the sample size, the more nearly normally distributed is the population of all possible sample means Also, as the sample size increases, the spread of the sampling distribution decreases
lecture 16, Sampling Distributions II Review Unbiased Estimates Finite Population Correction Sampling Distribution of the Sample Proportion lecture 16, Sampling Distributions II Review CLT ( review, ctd)

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lecture 16, Sampling Distributions II Review Unbiased Estimates Finite Population Correction Sampling Distribution of the Sample Proportion lecture 16, Sampling Distributions II Review Properties of the Sampling Distribution of the Sample Mean ( review) The mean of all possible sample means equals the population mean, i.e., μ ¯ X = μ X For the standard deviation σ ¯ X of all sample means, if the population size N is infinity or is much larger than the sample size n (say, N / n 20), then σ ¯ X σ n .
lecture 16, Sampling Distributions II Review Unbiased Estimates Finite Population Correction Sampling Distribution of the Sample Proportion lecture 16, Sampling Distributions II Review The Empirical Rule for the Sample Mean When the sample size get large, the population of all sample means is approximately normal, hence the empirical rule holds for the sampling distribution of the sample mean about 68.26% of all possible sample means are within one standard deviation σ ¯ X of μ about 95.44% of all possible sample means are within two σ ¯ X of μ about 99.73% of all possible sample means are within three σ ¯ X of μ

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lecture 16, Sampling Distributions II Review Unbiased Estimates Finite Population Correction Sampling Distribution of the Sample Proportion lecture 16, Sampling Distributions II Unbiased Estimates Unbiased Estimates A sample statistic is an unbiased point estimate of a
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