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Unformatted text preview: Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 14 (chap7) Donghyung Lee Chapter 7 Inferences Comparing Two Population means 1. Please read our text book from 7.1 to 7.10 Chapter 7 Inferences Comparing Two Population means 1 2 1 2 1 1 2 2 2 2 [ ] 1. , ,..., . 2. , ,..., . 3. . m n Basic Assumptions X X X is a random sample from a population with mean and variance Y Y Y is a random sample from a population with mean and variance The X and Y samples are independent of one another μ σ μ σ 2 2 2 1 2 1 2 [ ] ~ ( , ) Proposition X Y N m n σ σ μ μ + Chapter 7 Inferences Comparing Two Population means 2 2 1 1 1 2 1 2 2 2 2 2 1 2 1 2 1 2 [ : ] : : ( ) ( ) ( ) : ( ) : a Case I Normal populations with known variances and Null hypothesis H D x y D x y Test statistic value z m n m n Alternative Hypothesis Rejection region for level test a H σ σ μ μ μ μ σ σ σ σ α μ μ = = = + + 1 2 1 2 /2 /2 ( ) ( ) : ( ) ( ) : ( ) a a D z z upper tailed test b H D z z lower tailed test c H D either z z or z z two tailed test α α α α μ μ μ μ <π π ≡ Chapter 7 Inferences Comparing Two Population means 1 2 1 2 2 1 1 1 2 2 2 2 1 1 2 1 *** ( ) : : : *** ~ ( , ); ~ ( , ); ... : ... : ~ ( ,( ) ) ( , a m n X X Case I a H D H D X N is known Y N is known X X a random sample of size m from the normal population Y Y a random sample of size n from the normal population X N N μ μ...
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This note was uploaded on 03/28/2011 for the course AMS 110 taught by Professor N/a during the Spring '08 term at SUNY Stony Brook.
 Spring '08
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