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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. H0: H1: α = .05 Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the .05   level of significance that the standard deviation of the lengths of balance bars of scale sets has changed from 2.5 millimeters. σ = 2.5 σ ≠ 2.5

  4. Jaggia and Kelly (1stedition) Critical Value(s) Table 1 Group Flowchart * means coverage is different from text. yes Wald-Wolfowitz One-Sample Runs Test for Randomness pp. 634-638 Z using σ pp. 277-284 yes Z-table 2 1 Normal population ? yes no n > 30 ? Wilcoxon Signed-Ranks *pp. 610-614 (assumes population is symmetric) no WSR Table 3 no at least interval  known ? no Normal population ? no n > 30 ? mean or median level of data ? yes t with df = n-1 pp. 288-294 t-table 4 yes ordinal Sign Test *pp. 631-634 Sign Table 5 Z pp. 294-298 yes Z-table 6 np> 5 and n(1-p) > 5 ? proportion Parameter ? no Binomial Table Binomial/ Hypergeometric variance or standard deviation yes chi-square (df = n-1) pp. 336-344 Chi-square Table 7 Normal population ? no ? Default case

  5. H0: H1: α = .05 Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the .05   level of significance that the standard deviation of the lengths of balance bars of scale sets has changed from 2.5 millimeters. σ = 2.5 σ ≠ 2.5

  6. H0: H1: α = .05 Decision Rule: If then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the .05   level of significance that the standard deviation of the lengths of balance bars of scale sets has changed from 2.5 millimeters. σ = 2.5 σ ≠ 2.5 df = n - 1 = 12 - 1 = 11 1-.025 = .975 in the upper tail Χ2 = 3.8157 Χ2 = 21.9200

  7. H0: H1: α = .05 Decision Rule: If 3.8157 < Χ2computed < 21.9200 then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the .05   level of significance that the standard deviation of the lengths of balance bars of scale sets has changed from 2.5 millimeters. σ = 2.5 σ ≠ 2.5 df = n - 1 = 12 - 1 = 11 1-.025 = .975 in the upper tail Χ2 = 3.8157 Χ2 = 21.9200

  8. H0: H1: α = .05 Decision Rule: If 3.8157 < Χ2computed < 21.9200 then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the .05   level of significance that the standard deviation of the lengths of balance bars of scale sets has changed from 2.5 millimeters. σ = 2.5 σ ≠ 2.5 df = n - 1 = 12 - 1 = 11 1-.025 = .975 in the upper tail DonotrejectH0 Χ2 = 3.8157 Χ2 = 21.9200 Do not reject H0. insufficient

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