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Unformatted text preview: STA5507 Section 8112 EXAM 2 Solutions 1. Comparison of peak expiratory flow rate (PEFR) before and after a walk on a cold winter’s day for a random sample of 9 asthmatics. Subject 1 2 3 4 5 6 7 8 9 Before 312 242 340 388 296 254 391 402 290 After 300 201 232 312 220 256 328 330 231 Determine whether or not there is a statistically significant difference of PEFR before and after a walk on a cold winter’s day. Use the all possible analysis you can think of, and be sure to be clearly stating HYPOTHESIS and what your assumptions are. (15 pts) • Pairedcomparison • Hypothesis H : F ( x ) = 1 − F ( − x ) H a : F ( x ) negationslash = 1 − F ( − x ) for at least one x • pairedcomparison permutation test Pairedcomparison permutation test number of permutations: R= 5000 D.bar_obs= 56.11 twosided pvalue=2*1/R sum{I(D.bar_b > D.bar_obs)}= 0.006 twosided pvalue=1/R sum{I(abs(D.bar_b) > abs(D.bar_obs))}= 0.006 S.plus_obs= 507 twosided pvalue=2*1/R sum{I(S.plus_b > S.plus_obs)}= 0.011 There are 512 possible ways that the pairs of observations could have occurred, but I tried randomly selected permutation methods. Exact pvalue calculation is OK. Based on the estimated pvalue, we reject H at significant level α = 0 . 05 for both test statistics. 1 • Wilcoxon signedrank test without ties in the data Exact Wilcoxon signed rank test data: bf and af V = 44, pvalue = 0.007812 alternative hypothesis: true mu is not equal to 0 Based on the pvalue of exact Wilcoxon signed rank test, we reject H at significant level α = 0 . 05, even at α = 0 . 01. • From a pairedcomparison permutation test and Wilcoxon signedrank test, we conclude that there is a statistically significant difference of PEFR before and after a walk on a cold winter’s day at significant level α = 0 . 05. • Large sample approximations can be tried. 2 2. An agronomist studied the effect of fertilizer on a certain grain. He postulated that the yield of grain would tend to be higher in plants that have been fertilized with more amount of fertilizer. None 58 29 37 40 44 37 50g 68 67 69 58 62 48 100g 96 90 90 92 99 86 Test if the given data support the conclusion that yield of grain would tend to be higher in plants that have been fertilized with more amount of fertilizer. (5 pts) • 3sample testing with ordered alternatives • Hypothesis H : μ = μ 50 = μ 100 H a : μ ≤ μ 50 ≤ μ 100 • JonckheereTerpstra Permutation Test Number of Permutation: 5000 JT_obs: 106 pvalue= 0 From the estimated p − value based on JT test stat, we observed that we reject H at significant level α = 0 . 01....
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This note was uploaded on 07/22/2011 for the course STA 4502 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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