【正文】 2020 PrenticeHall, Inc. Chap 943 Two Sample Tests in PHStat Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 936 Two Population Proportions Population proportions 2121212211nnxxnnpnpnp??????The pooled estimate for the overall proportion is: where x1 and x2 are the numbers from samples 1 and 2 with the characteristic of interest Since we begin by assuming the null hypothesis is true, we assume p1 = p2 and pool the two p estimates Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 929 The test statistic for d is Paired samples 1n)d(dsn1i2id ?????nsμdtdd??Where t?/2 has n 1 . and sd is: n is the number of pairs in the paired sample Hypothesis Testing for Paired Samples 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 915 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 ? ?21p/221 n1n1stxx ??? ?The confidence interval for μ1 – μ2 is: σ1 and σ2 unknown, small samples (continued) Where t?/2 has (n1 + n2 – 2) ., and ? ? ? ?2nns1ns1ns21222211p ??????* Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 97 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 …and the standard error of x1 – x2 is When σ1 and σ2 are known and both populations are normal or both sample sizes are at least 30, the test statistic is a zvalue… 222121xx nσnσσ21???(continued) σ1 and σ2 known * Business Statistics: A DecisionMaking Approach, 6e 169。Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 98 Population means, independent samples σ1 and σ2 known σ1 and σ2 unknown, n1 and n2 ? 30 σ1 and σ2 unknown, n1 or n2 30 ? ?222121/221 nσnσzxx ??? ?The confidence interval for μ1 – μ2 is: σ1 and σ2 known (continued) * 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 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 930 Lower tail test: H0: μd ? 0 HA: μd 0 Upper tail test: H0: μd ≤ 0 HA: μd 0 Twotailed test: H0: μd = 0 HA: μd ≠ 0 Paired Samples Hypothesis Testing for Paired Samples ? ?/2 ?/2 ? t? t?/2 t? t?/2 Reject H0 if t t? R