2. © Buddy Freeman, 2015 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

3. © Buddy Freeman, 2015 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.025

4. © Buddy Freeman, 2015 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 drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After H 0 :  1 =  2 H 1 :  1 >  2 After Before or

5. © Buddy Freeman, 2014 # of groups ? Parameter ? Can we make all f e > 5 ? Normal populations ? Hartley’s F max *(not in text) Resample and try again. yes no yes no chi-square df = (R-1)(C-1) pp. 368-374 yes no Kruskal-Wallis *pp. 621-625 1-way ANOVA pp. 386-395 ANOVA OK ? mean or median proportion variance or standard deviation more than 2 Parameter ? Related Samples ? mean or median proportion variance or standard deviation Normal populations ? yes no Levine-Brown-Forsythe F = S 1 2 /S 2 2 pp. 344-354 Z for proportions pp. 322-328 yes no unequal-variances t-test p. 307-315 pooled-variances t-test pp. 307-315 Wilcoxon Rank Sum *pp. 616-621 no yes Normal populations ? Normal populations ? yes no yes no n 1 > 30 and n 2 > 30 ? Z for means with σ 1 & σ 2 pp. 307-315 yes no σ 1 and σ 2 both known ? no Normal populations ? yes no yes at least interval level data ? yes no Sign Test *pp. 631-634. Wilcoxon Signed-Ranks *pp. 614-616 paired-difference t-test pp. 315-322 2 chi-square goodness-of-fit test pp. for the Multinomial Experiment 362-368 and the Normal Distribution 374-376 2 Groups and > 2 Groups Flowchart Spearman Rank Correlation test pp. 625-630 1 2 3 4 5 7 8 9 10 11 12 13 14 15 yes no n 1 > 30 and n 2 > 30 ? 6 σ 1 = σ 2 ? Levine-Brown-Forsythe Jaggia and Kelly (1 st edition) Default case * means coverage is different from text.

6. © Buddy Freeman, 2015 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 drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After

7. © Buddy Freeman, 2015 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 drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After Do not reject H 0 Reject H 0.025 t = -2.30600 df = n – 1 = 8

8. © Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If t computed > -2.3060 then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After Do not reject H 0 Reject H 0.025 t = -2.30600 df = n – 1 = 8

9. © Buddy Freeman, 2015 H 0 : H 1 : α = Decision Rule: If t computed > -2.3060 then do not reject H 0, otherwise reject H 0. Test Statistic: Decision: Conclusion: We have found ________________ evidence at the _____ level of significance that drinking coffee raises the body temperature..025 μ 1 < μ 2 μ 1 = μ 2 Before After Do not reject H 0. insufficient Do not reject H 0 Reject H 0.025 t = -2.30600 df = n – 1 = 8 Do not reject H 0