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H 0 : H 1 : α = Decision Rule: If then do not reject H 0 , otherwise reject H 0 . Test Statistic:

H 0 : H 1 : α = Decision Rule: If then do not reject H 0 , otherwise reject H 0 . Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that. H 0 : H 1 : α = Decision Rule: If

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H 0 : H 1 : α = Decision Rule: If then do not reject H 0 , otherwise reject H 0 . Test Statistic:

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  1. H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that

  2. H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that .05 .05

  3. μ1 = μ2 μ1 > μ2 With Without H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the additive increases the number of miles per gallon. .05 .05

  4. * means coverage is different from text. 2 Groups and > 2 Groups Flowchart 3 4 6 5 7 8 9 10 11 12 13 14 15 paired-difference t-test pp. 315-322 Spearman Rank Correlation test pp. 625-630 yes 1 yes yes Normal populations ? Wilcoxon Signed-Ranks *pp. 614-616 chi-square goodness-of-fit test pp. for the Multinomial Experiment 362-368 and the Normal Distribution 374-376 at least interval level data ? no no 2 Sign Test *pp. 631-634. mean or median yes Z for means with σ1 & σ2 pp. 307-315 yes n1> 30 and n2> 30 ? Related Samples ? yes Normal populations ? Jaggia and Kelly (1stedition) no no Wilcoxon Rank Sum *pp. 616-621 no no σ1 and σ2 both known ? n1> 30 and n2> 30 ? no yes pooled-variances t-test pp. 307-315 yes Normal populations ? no yes σ1 = σ2 ? no unequal-variances t-test p. 307-315 proportion 2 Z for proportions pp. 322-328 Parameter ? variance or standard deviation yes # of groups ? F = S12/S22 pp. 344-354 Normal populations ? no Levine-Brown-Forsythe mean or median yes 1-way ANOVA pp. 386-395 ANOVA OK ? no Kruskal-Wallis *pp. 621-625 more than 2 chi-square df = (R-1)(C-1) pp. 368-374 yes Can we make all fe> 5 ? proportion Parameter ? no Resample and try again. variance or standard deviation yes Hartley’s Fmax *(not in text) Normal populations ? no Default case Levine-Brown-Forsythe

  5. μ1 = μ2 μ1 > μ2 With Without H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the additive increases the number of miles per gallon. .05 .05

  6. where

  7. μ1 = μ2 μ1 > μ2 With Without H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the additive increases the number of miles per gallon. .05 .05

  8. μ1 = μ2 μ1 > μ2 With Without H0: H1: α = Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the additive increases the number of miles per gallon. .05 df = n1 +n2 – 2 = 16 0 t = 1.7459 .05

  9. μ1 = μ2 μ1 > μ2 With Without H0: H1: α = Decision Rule: If tcomputed < 1.7459 then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the additive increases the number of miles per gallon. .05 df = n1 +n2 – 2 = 16 0 t = 1.7459 .05

  10. μ1 = μ2 μ1 > μ2 With Without H0: H1: α = Decision Rule: If tcomputed < 1.7459 then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the additive increases the number of miles per gallon. .05 df = n1 +n2 – 2 = 16 Reject H0 0 t = 1.7459 Reject H0. sufficient .05

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