chapter 1

Chapter 14: The Analysis of Categorical Data30. H o : the design configurations are homogeneous with respect to type of failure vs. H a : thedesign configurations are not homogeneous with respect to type of failure.χχ2Ê ij 1 2 3 41 16.11 43.58 18.00 12.32 902 7.16 19.37 8.00 5.47 403 10.74 29.05 12.00 8.21 602( 20 −16.11) ( 5 − 8.21)=+ ... +16.118.212= 12.592 < 13.253 < χ2. 05,6.025,6=34 92 38 26 1902= 13.25314.440. With 6 df,, so .025 < p-value < .05. Since the p-valueis < .05, we reject H o . (If a smaller significance level were chosen, a different conclusionwould be reached.) Configuration appears to have an effect on type of failure.31. With I denoting the I th type of car (I = 1, 2, 3, 4) and j the j th category of commuting distance,H o : p ij = p i. p .j (type of car and commuting distance are independent) will be rejected at level2 2.05 if χ ≥ χ = 12. 592 .χ2.05,6= 14.15 ≥ 12.592at level .025!)Ê ij 1 2 31 10.19 26.21 15.60 522 11.96 30.74 18.30 613 19.40 49.90 29.70 994 7.45 19.15 11.40 3849 126 75 250, so the independence hypothesis H o is rejected at level .05 (but not32.2222( 479 − 494.4) ( 173 − 151.5) ( 119 −125.2) ( 214 −177.0) ( 47 54.2)χ =++++494.4 151.5 125.2 177.0 54.22222( 15 − 44.8) ( 172 − 193.6) ( 45 − 59.3) ( 85 − 49.0)2= +++= 64.65 ≥ χ.01,4= 13.27744.8 193.6 59.3 49.0so the independence hypothesis is rejected in favor of the conclusion that political views andlevel of marijuana usage are related.2 −2450