inference3 - Inference Two Samples You have two samples:...

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1 - Mike Pore -Inference 3 - Oct 2005 You have two samples: one from process A, and one from process B. You have measured the process performances n times. Are the means of the two processes the same or different? Inference Inference Two Samples Two Samples
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2 - Mike Pore -Inference 3 - Oct 2005 This is a different kind of test. No given mean to compare to. If σ 1 = σ 2 , then how do we estimate σ ? What is the H 0 ? x 2 1 2 1 2 1 s s x x n n ( 29 ( 29 x x x x x x x x x x 1 2 1 2 1n 2n 1 n 1 1 - n 2 23 13 22 12 21 11 - Inference Inference Two Samples Two Samples
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3 - Mike Pore -Inference 3 - Oct 2005 2 1 2 1 2 1 s s x x n n ( 29 ( 29 x x x x x x x x x x 1 2 1 2 1n 2n 1 n 1 1 - n 2 23 13 22 12 21 11 - 2 1 2 1 σ σ μ μ distribution parameters the data statistics ( 29 ( 29 2 n n s 1 n s 1 n s 2 1 2 2 2 2 1 1 2 p - + - + - = The pooled sample variance Inference Inference Two Samples Two Samples and and σ σ 1 = = σ σ 2
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4 - Mike Pore -Inference 3 - Oct 2005 Statistics for Two Samples Statistics for Two Samples when when σ σ 1 = = σ σ 2 ( 29 ( 29 ( 29 ( 29 ( 29 2 n n s 1 n s 1 n s t ~ n 1 n 1 s μ - μ x - x 2 1 2 2 2 2 1 1 2 p 2 n n 2 1 p 2 1 2 1 2 1 - + - + - = + - - +
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5 - Mike Pore -Inference 3 - Oct 2005 Confidence Intervals Confidence Intervals Two Samples Two Samples ( 29 ( 29 ( 29 ( 29 ( 29 α - 1 n 1 n 1 s t x - x μ - μ n 1 n 1 s t x - x P α - 1 t n 1 n 1 s μ - μ x - x t P 2 1 p 2 α - 1 2 1 2 1 2 1 p 2 α 2 1 2 α - 1 2 1 p 2 1 2 1 2 α = + + + + = + - ( 29 ( 29 ( 29 ( 29 α - 1 n 1 n 1 s t x - x μ - μ P α - 1 μ - μ n 1 n 1 s t x - x P 2 1 p - 1 2 1 2 1 2 1 2 1 p 2 1 = + + = + + α α
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6 - Mike Pore -Inference 3 - Oct 2005 Prediction Intervals Prediction Intervals Two Samples Two Samples ( 29 ( 29 ( 29 ( 29 ( 29 α - 1 n 1 n 1 s t μ - μ x - x n 1 n 1 s t μ - μ P α - 1 t n 1 n 1 s μ - μ x - x t P 2 1 p 2 α - 1 2 1 2 1 2 1 p 2 α 2 1 2 α - 1 2 1 p 2 1 2 1 2 α = + + + + = + - ( 29 ( 29 ( 29 ( 29 α - 1 n 1 n 1 s t μ - μ x - x P α - 1 x - x n 1 n 1 s t μ - μ P 2 1 p - 1 2 1 2 1 2 1 2 1 p 2 1 = + + = + + α α
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7 - Mike Pore -Inference 3 - Oct 2005 H 0 : μ 1 = μ 2 or μ 1 - μ 2 = 0 H A : μ 1 μ 2 or μ 1 - μ 2 0 Hypothesis Testing Hypothesis Testing Test Statistics for Two Samples Test Statistics for Two Samples ( 29 ( 29 ( 29 ( 29 ( 29 2 n n s 1 n s 1 n s t ~ n 1 n 1 s μ - μ x - x 2 1 2 2 2 2 1 1 2 p 2 n n 2 1 p 2 1 2 1 2 1 - + - + - = + - - + s s x x n n 2 1 2 1 2 1
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8 - Mike Pore -Inference 3 - Oct 2005 53 53 41 46 54 59 57 59 43 58 51 62 45 57 55 56 49 54 55 49 54 55 56 52 54 52 55 51 60 56 60 52 48 60 56 63 63 54 53 64 57 55 51 56 56 58 62 56 56 47 60 61 38 53 47 46 53 55 55 50 53 52 51 54 53 60 49 52 52 59 54 55 The Data The Data Wafer Yield for 2 Etch Times Wafer Yield for 2 Etch Times 5.04 s 4.78 s 55.47 x 52.58 x 36 n 36 n 2 1 2 1 2 1 = = = = = = Yield at Standard Etch Time Yield at Longer Etch Time Can we even make this comparison?
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This note was uploaded on 04/26/2010 for the course ECO 329 taught by Professor K during the Spring '08 term at University of Texas at Austin.

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inference3 - Inference Two Samples You have two samples:...

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