chapter 1

Chapter 9: Inferences Based on Two Samples31.a.Comparative Box Plot for High Range and Mid Range470460mid range450440430420m id rangehigh rangeThe mo st notable feature of these boxplots is the larger amount of variation present in themid-range data compared to the high-range data. Otherwise, both look reasonablysymmetric with no outliers present.b. Using df = 23, a 95% confidence interval for µmid−range− µhigh−rangeis( .3 437.45) 2.06915.1 226.83− ± + = .85 ± 8.69 = ( − 7.84,9.54)43817 11mid−range− µhigh−plausible values forrange. Sinceµ are both positive and negative (i.e., theinterval spans zero) we would conclude that there is not sufficient evidence to suggestthat the average value for mid-range and the average value for high-range differ.32. Let =1µ the true average proportional stress limit for red oak and let µ2= the true averageH0: µ1− µ2= vs.a: µ1− µ2> 1( 8.48−6.65)−11.83t == 1.818 . With degrees of freedom22.79 1.28+ .2084proportional stress limit for Douglas fir. We test 1The test statistic is(.2084)2 22.79 1.28( ) ( )1410ν == 13.85 ≈ 14 , the p-value ≈ P ( t > 1.8) = . 0461413+21092H .. This p-valueindicates strong support for the alternative hypothesis since we would reject H o at significancelevels greater than .046. There is sufficient evidence to claim that true average proportionalstress limit for red oak exceeds that of Douglas fir by more than 1 MPa.272