chapter 1

Chapter 14: The Analysis of Categorical Data25. Let P ij = the proportion of white clover in area of type i which has a type j mark (i = 1, 2; j =1, 2, 3, 4, 5). The hypothesis H o : p 1j = p 2j for j = 1, …, 5 will be rejected at level .01 if2 22χ ≥ χ = χ = 13.277 ..01,(2−1)(5−1).01,4Ê ij 1 2 3 4 51 449.66 7.32 17.58 8.79 242.65 726 χ2 = 23. 182 471.34 7.68 18.42 9.21 254.35 761Since .18 13. 277921 15 36 18 497 148723 ≥ , H o is rejected.26. Let p i1 = the probability that a fruit given treatment i matures and p i2 = the probability that afruit given treatment i aborts. Then H o : p i1 = p i2 for i = 1, 2, 3, 4, 5 will be rejected if2 2χ ≥ χ = 13.277 ..01,4ObservedEstimated ExpectedThusMatured Aborted Matured Aborted n i141 206 110.7 236.3 34728 69 30.9 66.1 9725 73 31.3 66.7 9824 78 32.5 69.5 10220 82 32.5 69.5 102238 508 7462( 141 −110.7) ( 82 − 69.5)2χ =+ ... += 24.82 , which is ≥ 13. 277110.769.5rejected at level .01.2, so H o is27. With i = 1 identified with men and i = 2 identified with women, and j = 1, 2, 3 denoting the 3categories L>R, L=R, L χ , p-value < .005, which strongly suggests that H o. 005,2=448