mat2378-Chapter7-9-1

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

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Unformatted text preview: MAT2378 Rafal Kulik Version 2009/Nov/9 Rafal Kulik 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. Im 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 1 and 2 , respectively. Population variances are unknown. Rafal Kulik 2 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 and variance 2 , then Var( Y ) = 2 /n . If data Y 11 ,...,Y 1 n 1 come from a pop. with mean 1 and variance 2 1 , then Var( Y 1 ) = 2 1 /n 1 . If data Y 21 ,...,Y 2 n 2 come from a pop. with mean 2 and variance 2 2 , then Var( Y 2 ) = 2 2 /n 2 . Since populations are independent Var( Y 1- Y 2 ) = 2 1 /n 1 + 2 2 /n 2 Standard error of the Mean: Y = n . Standard error of the Difference between Means Y 1- Y 2 = s 2 1 n 1 + 2 2 n 2 ....
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This note was uploaded on 01/13/2010 for the course MAT MAT2378 taught by Professor Kulik during the Spring '09 term at University of Ottawa.

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

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