Exam3_sol - STA4502/5507 EXAM 3 Solutions Name UFID 1...

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Unformatted text preview: STA4502/5507 EXAM 3 Solutions Name : UFID #: 1. Featherston (1971) was interested in the relationship between the weight of tapeworms fed to dogs and the weight of the scoleces recovered from the dogs after 20 days. The cysticerci used in the experiment were collected from wheep carcasses and force-fed to 10 dogs via gelatine capsules. The scoleces were recovered from each dog at autopsy, 20 days after the introduction of the tapeworms. The mean weight of the initial cysticerci and the mean weight of the recovered worms for each of the 10 dogs are given below. Dog 1 2 3 4 5 6 7 8 9 10 Cysticerci 28.9 32.8 12.0 9.9 15.0 38.0 12.5 36.5 8.6 26.8 Worms Recovered 1.0 7.7 7.3 7.9 1.1 3.5 18.9 33.9 28.6 25.0 Do Pearsons’s correlation test (with t-distribution) , permutation test for the correlation and slope, Spearman’s rank correlation test (with normal approximation), permutation test for the Spearman rank correlation, Kendall’s tau test (with normal approximation) and permutation test for the Kendall’s tau between “Cysticerci” and “Worms Recovered”. Clarify Hypothesis and assumptions for each methods. Interprete p-values with full sentences. (20 pts) Pearson’s correlation H : ρ = 0 H a : ρ negationslash = 0 Spearman’s rank correlation H : ρ s = 0 H a : ρ s negationslash = 0 Kendall’s tau H : τ = 0 H a : τ negationslash = 0---------------------------------------------------------- Pearsons’ Correlation Test with t-distribution: Pearson’s product-moment correlation data: CY and WR t = 0.0112, df = 8, p-value = 0.9913 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval:-0.6272209 0.6320196 sample estimates: cor 0.003975228 1---------------------------------------------------------- Spearman Rank Correlation Test with normal distribution: Spearman’s rank correlation rho data: CY and WR S = 198, p-value = 0.5835 alternative hypothesis: true rho is not equal to 0 sample estimates: rho-0.2---------------------------------------------------------- Kendall’s Tau Test with normal distribution: Kendall’s rank correlation tau data: CY and WR T = 19, p-value = 0.6007 alternative hypothesis: true tau is not equal to 0 sample estimates: tau-0.1555556-------------------------------------------------------------------------------------------------------------------- Number of the random permutations: R= 10000---------------------------------------------------------- Testing H0:rho=0 vs. Ha:rho=/=0: Pearson’s correlation of original data: 0.003975228 estimated p-value for Pearson correlation= 0.9898---------------------------------------------------------- Testing H0:beta_1=0 vs. Ha:beta_1=/=0: Slope of original data: 0.00413569 estimated p-value for Slope= 0.9898---------------------------------------------------------- Testing H0:rho_s=0 vs. Ha:rho_s=/=0: Spearman’s correlation of original data: -0.2 estimated p-value for Spearman correlation= 0.5806---------------------------------------------------------- 2 Testing H0:tau=0 vs. Ha:tau=/=0:Testing H0:tau=0 vs....
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Exam3_sol - STA4502/5507 EXAM 3 Solutions Name UFID 1...

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