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CH7 Notes

CH7 Notes - Statistical Inference for Two Populations...

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Statistical Inference for Two Populations Chapter 7 deals with the methods of statistical inference for comparing parameters of two populations or processes with respect to their means or their proportions. We must determine the best statistic for the desired comparison and the sampling distribution of that statistic. Two basic plans available for this purpose are : Independent Samples and Paired Samples Independent samples design Sample 1 Sample 2 Property Appraiser 1 Property Appraiser 2 4 x 7 x 10 x 2 x 1 x 9 x 8 x 6 x 5 x 3 x __ __ X 1 X 2 __ __ Interested in X 1 – X 2 where sampling distribution is _ _ _ _ E(X 1 –X 2 ) = E(X 1 ) – E(X 2 ) = μ 1 - μ 2 __ __ __ __ Var (X 1 – X 2 ) = Var (X 1 ) + Var (X 2 ) = σ 1 2 /n 1 + σ 2 2 /n 2 SE (X 1 – X 2 ) = √ σ 1 2 /n 1 + σ 2 2 /n 2

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Paired Samples Design Appraiser Property 1 2 Difference 1 x 11 x 21 D 1 2 x 12 x 22 D 2 3 x 13 x 23 D 3 4 x 14 x 24 D 4 5 x 15 x 25 D 5 The paired comparisons analysis reduces to a one-sample analysis of the mean of the differences between appraisals. __ So we are interested in D = ∑ D i / n _ _ where E( D) = μ d and Var (D) = σ d 2 _ Since we would not k now the value σ d 2 we would estimate σ 2 with S 2 and hence the standard error of D is estimated to be SE(D) ≈ S d / √n Comparison of Independent vs. Paired Samples
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CH7 Notes - Statistical Inference for Two Populations...

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