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# Chapter+10 - Chapter 10 Two-Sample Tests Click to edit...

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Click to edit Master subtitle style 1Chap 10-1 Chapter 10 Two-Sample Tests

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2Chap 10-2 Two-Sample Tests Two-Sample Tests Population Means, Independent Samples Population Means, Related Samples Population Variances Group 1 vs. Group 2 Same group before vs. after treatment Variance 1 vs. Variance 2 Examples: Population Proportions Proportion 1 vs. Proportion 2
3Chap 10-3 Difference Between Two Means Population means, independent samples Goal: Test hypothesis or form a confidence interval for the difference between two population means, μ1 – μ2 The point estimate for the difference is X1 – X2 * σ1 and σ2 unknown, assumed equal σ1 and σ2 unknown, not assumed equal

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4Chap 10-4 Difference Between Two Means: Population means, independent samples * Use Sp to estimate unknown σ. Use a Pooled-Variance t test. σ1 and σ2 unknown, assumed equal σ1 and σ2 unknown, not assumed equal Use S1 and S2 to estimate unknown σ1 and σ2. Use a Separate-variance t test n Different data sources n Unrelated n Independent n Sample selected from one population has no effect on the sample selected from the other population
5Chap 10-5 Hypothesis Tests for Two Population Means Lower-tail test: H0: μ1 l μ2 H1: μ1 < μ2 i.e., H0: μ1 – μ2 l 0 H1: μ1 – μ2 < 0 Upper-tail test: H0: μ1 ≤ μ2 H1: μ1 > μ2 i.e., H0: μ1 – μ2 ≤ 0 H1: μ1 – μ2 > 0 Two-tail test: H0: μ1 = μ2 H1: μ1 ≠ μ2 i.e., H0: μ1 – μ2 = 0 H1: μ1 – μ2 ≠ 0 Two Population Means, Independent Samples

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6Chap 10-6 Two Population Means, Independent Samples Lower-tail test: H0: μ1 – μ2 l 0 H1: μ1 – μ2 < 0 Upper-tail test: H0: μ1 – μ2 ≤ 0 H1: μ1 – μ2 > 0 Two-tail test: H0: μ1 – μ2 = 0 H1: μ1 – μ2 ≠ 0 α α /2 α /2 α -t α -t α /2 t α t α /2 Reject H0 if tSTAT < - t α Reject H0 if tSTAT > t α Reject H0 if tSTAT < -t α /2 or tSTAT > t α /2 Hypothesis tests for μ1 – μ2
7Chap 10-7 Population means, independent samples Hypothesis tests for µ1 - µ2 with σ1 and σ2 unknown and assumed equal Assumptions: § Samples are randomly and independently drawn § Populations are normally distributed or both sample sizes are at least 30 § Population variances are unknown but assumed equal * σ1 and σ2 unknown, assumed equal σ1 and σ2 unknown, not assumed equal

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8Chap 10-8 Population means, independent samples The pooled variance is: The test statistic is: Where tSTAT has d.f. = (n1 + n2 – 2) (continued) ( 29 ( 29 1) n (n S 1 n S 1 n S 2 1 2 2 2 2 1 1 2 p - + - - + - = ( ) 1 * σ1 and σ2 unknown, assumed equal σ1 and σ2 unknown, not assumed equal Hypothesis tests for µ1 - µ2 with σ1 and σ2 unknown and assumed ( 29 ( 29 + - - - = 2 1 2 p 2 1 2 1 STAT n 1 n 1 S μ μ X X t
9Chap 10-9 Population means, independent samples Obj102 The confidence interval for μ1 – μ2 is: Where tα/2 has d.f. = n1 + n2 – 2 * Confidence interval for µ1 - µ2 with σ1 and σ2 unknown and assumed equal σ1 and σ2 unknown, assumed equal σ1 and σ2 unknown, not assumed equal

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## This note was uploaded on 05/31/2011 for the course MGT C06 taught by Professor A.stawinoga during the Fall '10 term at University of Toronto.

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Chapter+10 - Chapter 10 Two-Sample Tests Click to edit...

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