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Lecture15 - April 16th Section 7.5 Two-sample tests...

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April 16 th Section 7.5 Two-sample tests Pooled-variance t-test - Pivotal Quantity method - Likelihood Ratio test Comparing two population means Example. There are 2 populations. The first population is about men and the second is about women. Paired sample approach Population 1 [Sample 1] Population 2 [Sample 2] Paired difference Pair 1 150 140 10 Pair 2 137 167 -30 Pair 3 172 155 17 There can be three cases. 0 0 : : 0( ) : : 0 M W d M W a M W a d H H H H μ μ μ μ μ μ μ μ = = = - 0 0 : : 0( ) : : 0 M W d M W a M W a d H H H H μ μ μ μ μ μ μ μ = = = - f f 0 0 : : 0( ) : : 0 M W d M W a M W a d H H H H μ μ μ μ μ μ μ μ = = = - p p Data for d μ is “paired difference” in the above example. The confidence Interval for d μ the confidence interval for ( ) M W μ μ - 1
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“unpaired data” [Independent Samples] Population 1 (Men) [Sample 1] Population 2 (Women) [Sample 2] 1 X 1 Y 2 X 2 Y 1 n X 2 n Y Assumptions for pooled-variance t-test for Independent Samples 1. Both populations are normal . . .
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