# BUS152-Ch10 - BUS152 Statistics for Social Sciences Spring...

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Chapter 10: Hypothesis Testing – Two-Sample Tests Chap 10-1 BUS152 - Statistics for Social Sciences Spring 2011

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Two-Sample Tests Chap 10-2 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:
Difference Between Two Means Chap 10-3 Population means, independent samples Goal: Test hypothesis or form a confidence interval for the difference between two population means, μ 1 – μ 2 The point estimate for the difference is X 1 – X 2 * σ 1 and σ 2 unknown, assumed equal σ 1 and σ 2 unknown, not assumed equal

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Difference Between Two Means: Independent Samples Different data sources Unrelated Independent Sample selected from one population has no effect on the sample selected from the other population Chap 10-4 Population means, independent samples * Use S p to estimate unknown σ. Use a Pooled-Variance t test. σ 1 and σ 2 unknown, assumed equal σ 1 and σ 2 unknown, not assumed equal Use S 1 and S 2 to estimate unknown σ 1 and σ 2 . Use a Separate-variance t test
Hypothesis Tests for Two Population Means Chap 10-5 Lower-tail test: H 0 : μ 1 μ 2 H 1 : μ 1 < μ 2 i.e., H 0 : μ 1 – μ 2 0 H 1 : μ 1 – μ 2 < 0 Upper-tail test: H 0 : μ 1 ≤ μ 2 H 1 : μ 1 > μ 2 i.e., H 0 : μ 1 – μ 2 ≤ 0 H 1 : μ 1 – μ 2 > 0 Two-tail test: H 0 : μ 1 = μ 2 H 1 : μ 1 ≠ μ 2 i.e., H 0 : μ 1 – μ 2 = 0 H 1 : μ 1 – μ 2 ≠ 0 Two Population Means, Independent Samples

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Hypothesis tests for μ 1 – μ 2 Chap 10-6 Two Population Means, Independent Samples Lower-tail test: H 0 : μ 1 – μ 2 0 H 1 : μ 1 – μ 2 < 0 Upper-tail test: H 0 : μ 1 – μ 2 ≤ 0 H 1 : μ 1 – μ 2 > 0 Two-tail test: H 0 : μ 1 – μ 2 = 0 H 1 : μ 1 – μ 2 ≠ 0 α α /2 α /2 α -t α -t α /2 t α t α /2 Reject H 0 if t STAT < -t α Reject H 0 if t STAT > t α Reject H 0 if t STAT < -t α /2 or t STAT > t α /2
Hypothesis tests for µ 1 - µ 2 with σ 1 and σ 2 unknown and assumed equal Chap 10-7 Population means, independent samples 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 * σ 1 and σ 2 unknown, assumed equal σ 1 and σ 2 unknown, not assumed equal

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Hypothesis tests for µ 1 - µ 2 with σ 1 and σ
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BUS152-Ch10 - BUS152 Statistics for Social Sciences Spring...

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