estimationandhypothesistestingfortwopopulationparameters(编辑修改稿)

estimationandhypothesistestingfortwopopulationparameters(编辑修改稿)内容摘要：

ple sizes  30 or not  30 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 920 Hypothesis Tests for Two Population Proportions Lower tail test: H0: μ1  μ2 HA: μ1 μ2 ., H0: μ1 – μ2  0 HA: μ1 – μ2 0 Upper tail test: H0: μ1 ≤ μ2 HA: μ1 μ2 ., H0: μ1 – μ2 ≤ 0 HA: μ1 – μ2 0 Twotailed test: H0: μ1 = μ2 HA: μ1 ≠ μ2 ., H0: μ1 – μ2 = 0 HA: μ1 – μ2 ≠ 0 Two Population Means, Independent Samples Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 921 Hypothesis tests for μ1 – μ2 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2  30 σ1 and σ2 unknown, n1 or n2 30 Use a z test statistic Use s to estimate unknown σ , approximate with a z test statistic Use s to estimate unknown σ , use a t test statistic and pooled standard deviation 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 923 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 The test statistic for μ1 – μ2 is:    2221212121nsnsμμxxz* Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 924 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 Where t/2 has (n1 + n2 – 2) ., and    2nns1ns1ns21222211p    21p2121n1n1sμμxxzThe test statistic for μ1 – μ2 is: * Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 925 Two Population Means, Independent Samples Lower tail test: H0: μ1 – μ2  0 HA: μ1 – μ2 0 Upper tail test: H0: μ1 – μ2 ≤ 0 HA: μ1 – μ2 0 Twotailed test: H0: μ1 – μ2 = 0 HA: μ1 – μ2 ≠ 0  /2 /2  z z/2 z z/2 Reject H0 if z z Reject H0 if z z Reject H0 if z z/2 or z z/2 Hypothesis tests for μ1 – μ2 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。 NASDAQ? You collect the following data: NYSE NASDAQ Number 21 25 Sample mean Sample std dev Assuming equal variances, is there a difference in average yield ( = )? Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 927 Calculating the Test Statistic         1 . 2 2 5 6225211 . 1 61251 . 3 01212nns1ns1ns 2221222211p      2 . 0 4 02512111 . 2 2 5 602 . 5 33 . 2 7n1n1sμμxxz21p2121 The test statistic is: Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 928 Solution H0: μ1 μ2 = 0 . (μ1 = μ2) HA: μ1 μ2 ≠ 0 . (μ1 ≠ μ2)  = df = 21 + 25 2 = 44 Critical Values: t = 177。 Test Statistic: Decision: Conclusion: Reject H0 at  = There is evidence of a difference in means. t 0 .025 Reject H。