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mat2378-Chapter7-9-1

mat2378-Chapter7-9-1 - MAT2378 Rafal Kulik Version...

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MAT2378 Rafal Kulik Version 2009/Nov/9 Rafal Kulik

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MAT2378 Probability and Statistics for the Natural Sciences Chapter 7,9 Comments These notes cover material from Chapter 7, Sections 7.1-7.4, 7.6 and Chapter 9, 91.-9.4. They are not complete . I will do a lot of calculations on blackboard. I’m planning to spend two lectures on this material. Rafal Kulik 1
MAT2378 Probability and Statistics for the Natural Sciences Chapter 7,9 Comparison of Two Independent Samples Example 7.1, 7.2 We want to do inference for the population differences. Assumptions: Y 11 , . . . , Y 1 n 1 is a random sample from population 1. Y 21 , . . . , Y 2 n 2 is a random sample from population 2. Two populations are independent and normal with means μ 1 and μ 2 , respectively. Population variances are unknown. Rafal Kulik 2

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MAT2378 Probability and Statistics for the Natural Sciences Chapter 7,9 Standard Error If data Y 1 , . . . , Y n come from a population with mean μ and variance σ 2 , then Var( Y ) = σ 2 /n . If data Y 11 , . . . , Y 1 n 1 come from a pop. with mean μ 1 and variance σ 2 1 , then Var( Y 1 ) = σ 2 1 /n 1 . If data Y 21 , . . . , Y 2 n 2 come from a pop. with mean μ 2 and variance σ 2 2 , then Var( Y 2 ) = σ 2 2 /n 2 . Since populations are independent Var( Y 1 - Y 2 ) = σ 2 1 /n 1 + σ 2 2 /n 2 Standard error of the Mean: σ Y = σ n . Standard error of the Difference between Means σ Y 1 - Y 2 = σ 2 1 n 1 + σ 2 2 n 2 . Rafal Kulik 3
MAT2378 Probability and Statistics for the Natural Sciences Chapter 7,9 If the variance is unknown , then Estimated Standard error of the Mean SE Y = s n , where s 2 is the

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mat2378-Chapter7-9-1 - MAT2378 Rafal Kulik Version...

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