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CLT_Sp08_BB_nocolor - Sampling Distributions Z-distribution...

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1 Hypothesis Tests with Means of Samples Introducing the Central Limit Theorem (CLT) Sampling Distributions Z-distribution – A comparison distribution of individual scores . – We had the population and want to know how ONE score fits on that distribution. How does that ONE person fall WRT the mean in terms of standard deviations? Distribution of Means : – The distribution of the means of a very large number of samples of the same size taken from the same population of individuals The Central Limit Theorem (CLT) Given a population with mean μ and variance σ 2 , the sampling distribution of the mean (the distribution of sample means) will have 1. a mean equal to μ (i.e., μ X =μ) 2. a variance ( σ 2 X ) equal to σ 2 /n and 3. a standard deviation ( σ X ) equal to σ /(n) 1/2 The distribution will approach the normal distribution as n, the sample size, increases.” The Central Limit Theorem (CLT) The foundation for many statistical procedures. Backbone for parametric statistics: – Tests that require assumptions about the shape (including the variance) of the population distribution.
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2 The Central Limit Theorem (CLT) The Central Limit Theorem (CLT)
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CLT_Sp08_BB_nocolor - Sampling Distributions Z-distribution...

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