Week5 - Stat231 William Marshall Stat231 William Marshall...

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Stat231 William Marshall Stat231 William Marshall May 30, 2010
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Stat231 William Marshall Week 5 Goals: Define Estimors, Sampling distribution Introduce chi-squared distribution χ 2
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Stat231 William Marshall Measurement example revisited Object measured three times y 1 , y 2 , y 3 Model: Y i = μ + R i , R i G (0 , 0 . 03) ˆ μ = y 1 + y 2 + y 3 3 What attribute does μ represent? What can we say about the study error? What can we say about the sample error?
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Stat231 William Marshall Estimators Estimator is a random variable ˜ μ ˆ μ is a realization of the random variable ˜ μ To define the estimator, replace all occurances of realizations in the estimate formula with random variables ˜ μ = Y 1 + Y 2 + Y 3 3 The distribution of the estimator is called the sampling distribution
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Stat231 William Marshall Sampling Error Still can’t say anything about | μ - ˆ μ | What can we say about μ - ˜ μ ? Random variable with sampling distribution
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Week5 - Stat231 William Marshall Stat231 William Marshall...

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