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Unformatted text preview: MSOR221 1 / 5 Topic Four Inferences about Comparing Two Populations In Topics 2 and 3, we learned how to obtain confidence intervals and perform hypothesis tests for one population parameter ( μ , p , or σ 2 ). Frequently, however, inferential statistics is used to compare the parameters of two or more populations. In this topic we will study methods of making statistical inferences for two population parameters. The following methods require not only that the samples selected from the two populations be random but also that they be independent . Two samples are called independent samples if the sample selected from one of the populations has no effect or bearing on the sample selected from the other populations. Inferences about the Difference between Two Population Means μ 1 μ 2 using Independent Samples • Hypothesis Test for μ 1 μ 2 • Interval Estimate for μ 1 μ 2 – Population standard deviations σ 1 and σ 2 are known – Population standard deviations σ 1 and σ 2 are known Test statistic: 2 1 2 1 2 1 ) ( ) ( x x x x Z = σ μ μ Confidence interval = ± ) ( 2 1 x x 2 α Z 2 1 x x σ where 2 2 2 1 2 1 2 2 2 1 2 1 n n x x x x σ σ σ σ σ + = + = – Population standard deviations σ 1 and σ 2 are unknown – Population standard deviations σ 1 and σ 2 are unknown and unequal and unequal Test statistic: 2 1 2 1 2 1 ) ( ) ( x x x x t = ′ σ μ μ Confidence interval =...
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This note was uploaded on 03/30/2009 for the course MSOR MSOR221 taught by Professor Patrickchu during the Spring '09 term at University of Manchester.
 Spring '09
 patrickchu

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