【正文】 2020 PrenticeHall, Inc. Chap 946 Chapter Summary ? Compared two independent samples ? Formed confidence intervals for the differences between two means ? Performed Z test for the differences in two means ? Performed t test for the differences in two means ? Compared two related samples (paired samples) ? Formed confidence intervals for the paired difference ? Performed paired sample t tests for the mean difference ? Compared two population proportions ? Formed confidence intervals for the difference between two population proportions ? Performed Ztest for two population proportions 。 2020 PrenticeHall, Inc. Chap 944 Two Sample Tests in PHStat Input Output Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 942 Two Sample Tests in EXCEL For independent samples: ? Independent sample Z test with variances known: ? Tools | data analysis | ztest: two sample for means ? Independent sample Z test with large sample ? Tools | data analysis | ztest: two sample for means ? If the population variances are unknown, use sample variances For paired samples (t test): ? Tools | data analysis… | t test: paired two sample for means Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 941 The test statistic for p1 – p2 is: Example: Two population Proportions (continued) .025 .025 Decision: Do not reject H0 Conclusion: There is not significant evidence of a difference in proportions who will vote yes between men and women. ? ? ? ?? ? ? ?1 . 3 1501721. 5 4 9 )(1. 5 4 90. 6 2. 5 0n1n1p)(1pppppz212121???????????????????????????Reject H0 Reject H0 Critical Values = 177。 2020 PrenticeHall, Inc. Chap 939 Example: Two population Proportions Is there a significant difference between the proportion of men and the proportion of women who will vote Yes on Proposition A? ? In a random sample, 36 of 72 men and 31 of 50 women indicated they would vote Yes ? Test at the .05 level of significance Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 937 Two Population Proportions Population proportions ? ? ? ???????????????212121n1n1)p1(pppppzThe test statistic for p1 – p2 is: (continued) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 935 Hypothesis Tests for Two Population Proportions Population proportions Lower tail test: H0: p1 ? p2 HA: p1 p2 ., H0: p1 – p2 ? 0 HA: p1 – p2 0 Upper tail test: H0: p1 ≤ p2 HA: p1 p2 ., H0: p1 – p2 ≤ 0 HA: p1 – p2 0 Twotailed test: H0: p1 = p2 HA: p1 ≠ p2 ., H0: p1 – p2 = 0 HA: p1 – p2 ≠ 0 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 933 Two Population Proportions Goal: Form a confidence interval for or test a hypothesis about the difference between two population proportions, p1 – p2 The point estimate for the difference is p1 – p2 Population proportions Assumptions: n1p1 ? 5 , n1(1p1) ? 5 n2p2 ? 5 , n2(1p2) ? 5 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 932 ? Has the training made a difference in the number of plaints (at the level)? d = 1 . 6 655 . 6 7 /04 . 2n/sμdtdd ???????H0: μd = 0 HA: μd ? 0 Test Statistic: Critical Value = 177。 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