【正文】 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。 2020 PrenticeHall, Inc. Chap 911 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 nsnszxx ??? ?The confidence interval for μ1 – μ2 is: σ1 and σ2 unknown, large samples (continued) * 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 919 Hypothesis Tests for the Difference Between Two Means ? Testing Hypotheses about μ1 – μ2 ? Use the same situations discussed already: ? Standard deviations known or unknown ? Sample sizes ? 30 or not ? 30 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。 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 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。 . = n 1 = 4 Reject ?/2 Decision: Do not reject H0 (t stat is not in the reject region) Conclusion: There is not a significant change in the number of plaints. Paired Samples: Solution Reject ?/2 ? = .01 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 940 ? The hypothesis test is: H0: p1 – p2 = 0 (the two proportions are equal) HA: p1 – p2 ≠ 0 (there is a significant difference between proportions) ? The sample proportions are: ? Men: p1 = 36/72 = .50 ? Women: p2 = 31/50 = .62 . 5 4 91 2 2675072 3136nn xxp2121 ????????? The pooled estimate for the overall proportion is: Example: Two population Proportions (continued) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 943 Two Sample Tests in PHStat Business Statistics: A DecisionMaking Approach, 6e 169