【正文】 2020 PrenticeHall, Inc. Chap 945 Two Sample Tests in PHStat Input Output Business Statistics: A DecisionMaking Approach, 6e 169。 For ? = .05 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 938 Hypothesis Tests for Two Population Proportions Population proportions Lower tail test: H0: p1 – p2 ? 0 HA: p1 – p2 0 Upper tail test: H0: p1 – p2 ≤ 0 HA: p1 – p2 0 Twotailed test: H0: p1 – p2 = 0 HA: p1 – p2 ≠ 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 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 934 Confidence Interval for Two Population Proportions Population proportions ? ?222111/221 n)p(1pn)p(1pzpp????? ?The confidence interval for p1 – p2 is: Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 931 ? Assume you send your salespeople to a “customer service” training workshop. Is the training effective? You collect the following data: Paired Samples Example Number of Complaints: (2) (1) Salesperson Before (1) After (2) Difference, di . 6 4 2 . 20 6 14 . 3 2 1 . 0 0 0 . 4 0 4 21 d = ? di n 5 . 6 71n)d(ds2id???? ? = 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。 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 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 917 Paired Differences The ith paired difference is di , where Paired samples di = x1i x2i The point estimate for the population mean paired difference is d : 1n)d(dsn1i2id ?????nddn1ii??? The sample standard deviation is n is the number of pairs in the paired sample Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 913 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 Forming interval estimates: ? The population variances are assumed equal, so use the two sample standard deviations and pool them to estimate σ ? the test statistic is a t value with (n1 + n2 – 2) degrees of freedom (continued) * Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, I