【正文】 t t? Reject 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。 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 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 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。 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 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 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 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 916 Paired Samples Tests Means of 2 Related Populations ? Paired or matched samples ? Repeated measures (before/after) ? Use difference between paired values: ? Eliminates Variation Among Subjects ? Assumptions: ? Both Populations Are Normally Distributed ? Or, if Not Normal, use large samples Paired samples d = x1 x2 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 912 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 Assumptions: ? populations are normally distributed ? the populations have equal variances ? samples are independent * Business Statistics: A DecisionMaking Approach, 6e 169。