AMS 7, BiostatisticsWeek 7 Homework SolutionsChapter 7 (Glover & Mitchell)1. Big decrease in phosphate levels due to new laws?First determine if the variances are equal:H0:σ22=σ21, andHa:σ216=σ21.TheF-statistics22/s21= 2.7.Using theF- distribution withv1= 11 andv2= 9 degrees offreedom gives the critical valueF0.975= 3.96 leading the conclusion that there is not enoughevidence to rejectH0. So, treat the variances as equal (σ22=σ21) when testing the two-samplehypothesis for the means:H0:μ1≤μ2, andH0:μ1> μ2. Calculates2p= 1238.4 and teststatistict= 9.78, and use at-distribution with 20 degrees of freedom and obtain a criticalvalue oft0.95= 1.725 and thus rejectH0.3. Paired data for antibiotic effects.Subtract the amoxicillin column from the penicillin column and get (nd= 6) differencesd= 6,-10,4,5,-7,-2and calculate¯Xd=-2,¯s2d= 4.12. TestH0=μd= 0 againstHa:μd6= 0 using a two-sidedt-test on 5 degrees of freedom. The critical values are±to=±2.
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