Appendix 13 - Appendix 14 A14.1 One-way Analysis of...

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Appendix 14 A14.1 One-way Analysis of variance : H 0 3 2 1 μ = μ = μ : H 1 At least two means differ 10 11 12 13 14 15 A B C D E F G ANOVA Source of Variation SS df MS F P-value F crit Between Groups 91.43 2 45.72 1.09 0.3441 3.16 Within Groups 2397.5 57 42.06 Total 2488.9 59 F = 1.09, p-value = .3441. There is no evidence to infer that sales of candy differ according to placement. A14.2 t-test of D μ 0 : H D 0 = μ 0 : H D 1 < μ D D D D n / s x t μ - = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A B C t-Test: Paired Two Sample for Means Price shown Price not shown Mean 56.15 60.31 Variance 243.68 467.71 Observations 100 100 Pearson Correlation 0.79 Hypothesized Mean Difference 0 df 99 t Stat -3.12 P(T<=t) one-tail 0.0012 t Critical one-tail 1.6604 P(T<=t) two-tail 0.0024 t Critical two-tail 1.9842 t = –3.12, p-value = .0012. There is overwhelming evidence to conclude that ads with no price shown are more effective in generating interest than ads that show the price. A14.3 Unequal-variances t-test of 2 1 μ - μ 0 ) ( : H 2 1 0 = μ - μ 0 ) ( : H 2 1 1 < μ - μ 131
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2 2 2 1 2 1 2 1 2 1 n s n s ) ( ) x x ( t + μ - μ - - = 1 2 3 4 5 6 7 8 9 10 11 12 13 A B C t-Test: Two-Sample Assuming Unequal Variances Leftover Returned Mean 61.71 70.57 Variance 48.99 203.98 Observations 14 53 Hypothesized Mean Difference 0 df 44 t Stat -3.27 P(T<=t) one-tail 0.0011 t Critical one-tail 1.6802 P(T<=t) two-tail 0.0021 t Critical two-tail 2.0154 t = –3.27, p-value = .0011. There is enough evidence to support the professor's theory. A14.4 a z-test of 2 1 p p - (case 1) : H 0 2 1 p p - = 0 : H 1 2 1 p p - > 0 + - - = 2 1 2 1 n 1 n 1 ) p ˆ 1 ( p ˆ ) p ˆ p ˆ ( z 1 2 3 4 5 6 7 8 9 10 11 A B C D z-Test: Two Proportions Topiramate Placebo Sample Proportions 0.2364 0.1042 Observations 55 48 Hypothesized Difference 0 z Stat 1.76 P(Z<=z) one tail 0.0390 z Critical one-tail 1.6449 P(Z<=z) two-tail 0.0780 z Critical two-tail 1.96 z = 1.76, p-value = .0390. There is enough evidence to conclude that topiramate is effective in causing abstinence for the first month. b z-test of 2 1 p p - (case 1) : H 0 2 1 p p - = 0 132
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: H 1 2 1 p p - > 0 + - - = 2 1 2 1 n 1 n 1 ) p ˆ 1 ( p ˆ ) p ˆ p ˆ ( z 1 2 3 4 5 6 7 8 9 10 11 A B C D z-Test: Two Proportions Topiramate Placebo Sample Proportions 0.5091 0.1667 Observations 55 48 Hypothesized Difference 0 z Stat 3.64 P(Z<=z) one tail 0.0001 z Critical one-tail 1.6449 P(Z<=z) two-tail 0.0002 z Critical two-tail 1.96 z = 3.64, p-value = .0001. There is enough evidence to conclude that topiramate is effective in causing alcoholics to refrain from binge drinking in the final month. A14.5a Equal-variances t-test of 2 1 μ - μ 0 ) ( : H 2 1 0 = μ - μ 0 ) ( : H 2 1 1 < μ - μ + 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 Expenses MSA Expenses Regular Mean 347.24 479.25 Variance 21043 21128 Observations 63 141 Pooled Variance 21102 Hypothesized Mean Difference 0 df 202 t Stat -6.00 P(T<=t) one-tail 0.0000 t Critical one-tail 1.6524 P(T<=t) two-tail 0.0000 t Critical two-tail 1.9718 t = –6.00, p-value = 0. There is enough evidence to infer that medical expenses for those under the MSA plan are lower than those who are not.
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This note was uploaded on 09/28/2010 for the course FINOPMGT 250 taught by Professor Kumar during the Spring '10 term at University of Massachusetts Boston.

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Appendix 13 - Appendix 14 A14.1 One-way Analysis of...

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