【正文】 nc. Chap 99 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 σ1 and σ2 unknown, large samples Assumptions: ? Samples are randomly and independently drawn ? both sample sizes are ? 30 ? Population standard deviations are unknown * Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 95 Independent Samples Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 ? Different data sources ? Unrelated ? Independent ? Sample selected from one population has no effect on the sample selected from the other population ? Use the difference between 2 sample means ? Use z test or pooled variance t test * Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 91 Business Statistics: A DecisionMaking Approach 6th Edition Chapter 9 Estimation and Hypothesis Testing for Two Population Parameters Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 92 Chapter Goals After pleting this chapter, you should be able to: ? Test hypotheses or form interval estimates for ? two independent population means ? Standard deviations known ? Standard deviations unknown ? two means from paired samples ? the difference between two population proportions Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 96 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 σ1 and σ2 known Assumptions: ? Samples are randomly and independently drawn ? population distributions are normal or both sample sizes are ? 30 ? Population standard deviations are known * Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 910 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 σ1 and σ2 unknown, large samples Forming interval estimates: ? use sample standard deviation s to estimate σ ? the test statistic is a z value (continued) * Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 914 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 σ1 and σ2 unknown, small samples The pooled standard deviation is (continued) ? ? ? ?2nns1ns1ns21222211p ??????* Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 918 Paired Differences The confidence interval for d is Paired samples 1n)d(dsn1i2id ?????nstd d/2??Where t?/2 has n 1 . and sd is: (continued) n is the number of pairs in the paired sample Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 922 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 ? ? ? ?2221212121nσnσμμxxz?????The test statistic for μ1 – μ2 is: σ1 and σ2 known * Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 926 Pooled sp t Test: Example You’re a financial analyst for a brokerage firm. Is there a difference in dividend yield between stocks listed on the NYSE amp。 Test Statistic: Decision: Conclusion: Reject H0 at ? = There is evidence of a difference in means. t 0 .025 Reject H0 Reject H0 .025 0 4 251