【正文】 eject H0 if t t? Reject H0 if t t?/2 or t t?/2 Where t has n 1 . (continued) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 937 Two Population Proportions Population proportions ? ? ? ???????????????212121n1n1)p1(pppppzThe test statistic for p1 – p2 is: (continued) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 944 Two Sample Tests in PHStat Input Output Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 942 Two Sample Tests in EXCEL For independent samples: ? Independent sample Z test with variances known: ? Tools | data analysis | ztest: two sample for means ? Independent sample Z test with large sample ? Tools | data analysis | ztest: two sample for means ? If the population variances are unknown, use sample variances For paired samples (t test): ? Tools | data analysis… | t test: paired two sample for means Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 935 Hypothesis Tests for Two Population Proportions Population proportions Lower tail test: H0: p1 ? p2 HA: p1 p2 ., H0: p1 – p2 ? 0 HA: p1 – p2 0 Upper tail test: H0: p1 ≤ p2 HA: p1 p2 ., H0: p1 – p2 ≤ 0 HA: p1 – p2 0 Twotailed test: H0: p1 = p2 HA: p1 ≠ p2 ., H0: p1 – p2 = 0 HA: p1 – p2 ≠ 0 Business Statistics: A DecisionMaking Approach, 6e 169。 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 2512112 2 5 ????zBusiness 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 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 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 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 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 917 Paired Differences The ith paired difference is di , where Paired samples di = x1i x2i The point estimate for the population mean