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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 = 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 true average diameter of the ball bearings produced differs from .25 inches. μ = .25 μ ≠ .25 .05 .05

  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 = 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 true average diameter of the ball bearings produced differs from .25 inches. μ = .25 μ ≠ .25 .05 .05

  6. 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 true average diameter of the ball bearings produced differs from .25 inches. μ = .25 μ ≠ .25 .05 df = n – 1 = 60 Do not reject H0 Reject H0 Reject H0 .025 .025 t = -2.0003 0 t = 2.0003 .05

  7. H0: H1: α = Decision Rule: If -2.0003 < tcomputed < 2.0003 then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the true average diameter of the ball bearings produced differs from .25 inches. μ = .25 μ ≠ .25 .05 df = n – 1 = 60 Do not reject H0 Reject H0 Reject H0 .025 .025 t = -2.0003 0 t = 2.0003 .05

  8. 3 Steps to standard deviation 1. Calculate the variation of the sample, SS. 2. Calculate the variance of the sample, S2. 3. Calculate the standard deviation of the sample, S.

  9. H0: H1: α = Decision Rule: If -2.0003 < tcomputed < 2.0003 then do not reject H0, otherwise reject H0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that the true average diameter of the ball bearings produced differs from .25 inches. μ = .25 µ ≠ .25 .05 df = n – 1 = 60 Do not reject H0 Do not reject H0 Reject H0 Reject H0 .025 .025 t = -2.0003 0 t = 2.0003 Do not reject H0. .05 insufficient

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