Appendix 16 - Appendix 16 A16.1 t-test of H0 : = 0 H1 : 0 A...

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Appendix 16 A16.1 t-test of ρ 0 : H 0 = ρ 0 : H 1 ρ 1 2 3 4 5 6 7 8 9 10 A B Correlation Weight and B/A Level Pearson Coefficient of Correlation 0.4177 t Stat 3.19 df 48 P(T<=t) one tail 0.0013 t Critical one tail 1.6772 P(T<=t) two tail 0.0026 t Critical two tail 2.0106 r = .4177, t = 3.19, p–value = .0026. There is sufficient evidence to infer that weight and blood–alcohol level are related. A16.2 Two-way analysis of variance : H 0 4 3 2 1 μ = μ = μ = μ : H 1 At least two means differ 40 41 42 43 44 45 46 A B C D E F G ANOVA Source of Variation SS df MS F P-value F crit Rows 3708.8 28 132.46 8.63 6.52E-15 1.61 Columns 997.0 3 332.33 21.64 1.77E-10 2.71 Error 1289.8 84 15.35 Total 5995.5 115 F = 21.64; p-value = 0. There is enough evidence to conclude that there are differences in the decrease in test scores between the four types of breakfast meals. A16.3a Chi-squared goodness-of-fit test (the percentages must be converted to actual and expected values and we must include those who did not have cancer) 000 , 420 / 634 . 419 p , 000 , 420 / 13 p , 000 , 420 / 12 p , 000 , 420 / 57 p , 000 , 420 / 52 p , 000 , 420 / 80 p , 000 , 420 / 9 p , 000 , 420 / 143 p : H 8 7 6 5 4 3 2 1 0 = = = = = = = = : H 1 At least one i p is not equal to its specified value. 235
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= - = χ 8 1 i i 2 i i 2 e ) e f ( 1 2 3 4 5 6 7 8 9 A B C D Actual Expected 135 143 7 9 77 80 32 52 42 57 8 12 13 13 419686 419634 p-value = 0.0515 p-value = .0515. There is not enough evidence to conclude that there is a relationship between cell phone use and cancer. b The data are observational. Even if we regard the statistical result as significant we cannot automatically infer that cell phone use causes cancer. Additionally, an examination of the actual and expected values reveals that in all 7 types of cancers the actual values are less than or equal to the expected values, indicating that (if anything) cell phone use prevents cancer. A16.4 t-test of ρ or t-test of β 1 0 : H 0 = ρ 0 : H 1 ρ 2 r 1 2 n r t - - = 1 2 3 4 5 6 7 8 9 10 A B C D Correlation Age and Duration Pearson Coefficient of Correlation 0.558 t Stat 7.90 df 138 P(T<=t) one tail 0 t Critical one tail 1.6560 P(T<=t) two tail 0 t Critical two tail 1.9773 t = 7.90; p-value = 0. There is overwhelming evidence to infer that the older the patient the longer it takes for the symptoms to disappear? 236
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A16.5a Equal-variances t-test of 2 1 μ - μ 0 ) ( : H 2 1 0 = μ - μ ) ( : H 2 1 1 μ - μ > 0 + μ - μ - - = 2 1 2 p 2 1 2 1 n 1 n 1 s ) ( ) x x ( t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A B C t-Test: Two-Sample Assuming Equal Variances Home Outside Mean 59.21 54.91 Variance 102.03 88.28 Observations 196 152 Pooled Variance 96.03 Hypothesized Mean Difference 0 df 346 t Stat 4.06 P(T<=t) one-tail 0.0000 t Critical one-tail 1.6493 P(T<=t) two-tail 0.0001 t Critical two-tail 1.9668 t = 4.06, p-value = 0. There is enough evidence to infer that men whose wives stay at home earn more than men whose wives work outside the home. b It may be that men whose wives stay at home work harder, and thus earn more.
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Appendix 16 - Appendix 16 A16.1 t-test of H0 : = 0 H1 : 0 A...

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