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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 7.17.4, 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.
 Spring '09
 Kulik
 Statistics, Probability

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