chapter 1

Chapter 14: The Analysis of Categorical Datab.p i 0.45883 0.18813 0.11032 0.24272exp 22.024 9.03 5.295 11.651222( 22 − 22.024) ( 10 − 9.03) ( 5 − 5.295) ( 11 11.651)χ =+++22.024 9.03 5.295 11.651= . 0000262 + .1041971+.0164353+ .0363746 = .1570332With the same rejection region as in a, we do not reject the null hypothesis. This modeldoes provide a good fit.2 −247.a. Our hypotheses are H 0 : no difference in proportion of concussions among the threegroups. Vs H a : there is a difference …Observed ConcussionNoConcussion TotalSoccer 45 46 91Non Soccer 28 68 96Control 8 45 53Total 81 159 240Expected ConcussionNoConcussion TotalSoccer 30.7125 60.2875 91Non Soccer 32.4 63.6 96Control 17.8875 37.1125 53Total 81 159 240222( 45 − 30.7125) ( 46 − 60.2875) ( 28 − 32.4) ( 68 63.6)χ =30.712528 −17.8875+17.8875++60.2875245 − 37.1125= 19.184237.11252 2χ > χ = 5.2 −( ) ( )32.4+63.6+ . The df for this test is (I – 1)(J –1) = 2, so we reject H o if 99 . 19.1842 > 5.99, so we reject H 0 . There.05,2is a difference in the proportion of concussions based on whether a person plays soccer.2b. We are testing the hypothesis H 0 : ρ = 0 vs H a : ρ ? 0. The test statistic isrt =n − 21−r2−.2289= = −2.1321−.22. At significance level α = .01, we would fail toreject and conclude that there is no evidence of non-zero correlation in the population. Ifwe were willing to accept a higher significance level, our decision could change. At best,there is evidence of only weak correlation.455