Solutions to Exam 3, Math 382,Spr04

Statistics for Science and Engineering

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Unformatted text preview: 1. In Morton eta]. (1982)1 fathers who worked in a battery manufacturing plant and, consequently, were exposed to lead, were classiﬁed as having good, moderately good, or poor hygienic practices as follows: Good Hygiene: Usually showered and shampooed, and changed his clothes and shoes before leaving work (this was recommended by the company). Mgderatglx Qood Hygiene: Changed clothes before leaving work, but did not shower. Poor Hygiene: Did not practice any of the above lead containment procedures. Blood lead levels were taken of children aged 12-83 months with at least one year of potential exposure to the lead from their fathers and the results were tabulated: Hygiene Blood Lead Sample Sample Sample Standard Level Size Mean Deviation (micrograms per deciliter) Moderately 16, 18, 29, 41 ,49 Good 10,15,17,20,21, 22,23,23,24,27, 31,34,34,35,35, 36,37,38,39,43, 44,45,48,62,73 a. (5 pts.) To conduct a oneway ANOVA F-test we must assume that we have independent samples. We must also assume what (choose one)? i. All of the sample sizes are not “small” iii. Samples are normal wi . common . .. e s ndard deviation b. (5 pts.) The Kruskal-Wallis z: approximation relies on certain sample size conditions being met. Are these conditions satisﬁed (choose one)? ' Yes, the sample size conditions are satisﬁed w W3 WM) Lem lot on 1 - ons are not satis Unknown, more information is nee-ue l"Lead absorption in children of employees in a lead-related industry", American Journal of Epidemiology, vol. 115, no. 4. 402.7; +5 , 3 c. (20 pts.) Conduct a oneway ANOVA F -test of Ho=A=ﬂz=Ie HﬁNmHo Use the critical-region approach and include the following: 0 A sketch of the relevant F curve 0 The value along the horizontal axis for which the area to the right of it under the F curve is a = 0.05 Label the regions along the axiaﬂir which you accept and reject the null hmthesis 0 The computed value of the Fmtmic 0 A conclusion - which hypom do you believe? fk'Un-‘K : F21)! ’/ r nan 50.6.5 W W Wm- Ho 345 (water H, 4,, (3-1) (12.11)‘ 4 (tax/433’? ( U- I)( 1M4): 0" 2 3:“ ”L5 . , P Q‘f'i) 4- (1.5-!) 4- _ (2.5—! ) 195 Palm-rm (0.70/13 a? fur "ﬂaErr n. 72'7”», WM” m d. (15 pts.) Conduct the Kmskal-Wallis test of H, : The three blood-level densities are identical H 4 : Not H 0 Use the critical-region approach and include the following: o A sketch of the relevant 1’ curve 0 The value along the horizontal axis for which the area to the right of it under the 1' curve is a = 0.05 0 Label the regions along the axis for which you accept and reject the null hypothesis 0 The computed value of the 12 statistic ‘ 0 A conclusion - which hypothesis do you believe? x: ((4: #:2‘) pm 2 0.05 1/ . .? 5W W M5097 "9 “W K' K _. / z _ ku’shmm c .13; ’7: m( 13- "3—5) —- I-‘H ”(A-H) in ﬁg 4)» kLJr'SM is 1:. he 'MWHQ. ram?” MW m, to» A 2. (20 psogeel plate girders are measured for their shear strength, each girder by two diﬂ’erent sruh methods: the arl e and Lehigh procedlnes. The data2 appear below. Strength Predictions for Nine Steel Plate Girders Girder . Method Lehi II Method Difference Sl/l ‘ ‘ ‘ 1.186 - 1.061 0.125 52/] 1.151 0.992 0.159 83/] 1.322 1.063 0.259 ' 84/] 1.339 1.062 0.277 85/ 1 1.200 1.065 0.135 52/1 1.402 1.178 0.224 82/2 1.365 1.037 0.328 82/3 1.537 1.086 0.451 82/4 1.559 1.052 0.507 Sunmy Statistics W , Karlﬂ'lhe Method Lehigh Method Diﬂ'erenee . - Sample Average 1.340 1.066 0.274 Sample 0.1460 0.0494 0.1351 Standard Deviation Is there any difference in the two methods? Conduct the appropriate critical region test. In particular, be sure State null and alternatiiie hypotheses Sketch the relewnt density curve to: 0 Label the regions along the axis for which you accept and reject the null hypothesis along with the appropriate cutoﬁ"value(s) along the horizontal axis Compute the tube of the relevant test statistic State a conclusion - which hypothesis do you believe? I: ._, .27+— ~ 40¢ 8 5%; .I35l/ﬁ ’12—: 05 47‘ 4.4%)»: 35. mail MMJMKp Muisé” MJZ’WMD. 2 from Journal of Strain Analysis, 1983, vol. 18, no 2. / .oﬁmm 3. 'A controlled study involved 9,541 patients 55 years of age and older which were at high risk3 for "cardiovascular even ". A total of 287 of the 4,761 patients who were assigned to receive vitamin E died from coronary heart disease over a 4-5 year period, while 277 of the 4,780 Who were assigned the placebo died from coronary heart disease over this time. Does vitamin E help reduce deaths from coronary heart disease? H? .‘ p4 : F1. a. (20 pts.) Conduct the appropriate test. In particular, be sure to: M _ ’0 - It ' (— > Pr State null and alternative hypotheses . Sketch the relevant density curve Label the regions along the axis for which you accept and reject the null hypothesis along with the appropriate cutoﬂ'value(s) along the horizontal axis 0 Compute the value of the relevant test statistic 0 State a conclusion - which hypothesis do you believe? pMD W , 76’ (’1': 2774' 7 ) #Jh.ﬂ a - \$730 + f 75/ MR 2 b. (5 pts.) The validity of the above test rests on (choose one): i ’ o‘- K’MUSI a...) z ﬂees/r [49 6 H 4. (10 pts.) a. The string of equalities in the null hypothesis of the test Ho=M=#2=---=M. H‘nqouar0 is equivalent to how my pairwise comparisons p, = p] (i at j)? Give me a formula. L5) = a?" b. To conductatest of Ho=M=ﬂz=ﬂs=ﬂ4=ﬂs=ﬂs (Keé) leNotHo with an error of at most a = 0.05, the “Bonferonni Meth " says that each pairwise test H0:ﬂl=#j HA ”it‘ll; (i 1! j) should be conducted with what error? Give me a numeric value. i l g 05 ‘ as ‘ 0.5 e 00; } as) a) - ,5 / ...
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