STATISTICS 333 - Discussion 03Review1. One-Way ANOVA (H0: µ1= µ2= ... = µI)• Test statististic: F =MSbMSw=SSb/(I−1)SSw/(n−I)• ANOVA TableSource df SS MS F-statisticBetween groups I − 1 SSbSSb/dfbMSb/MSwWithin groups n − I SSwSSw/dfwTotal n − 1 SSt• sp=pMS(within)• p-va lue=Pr(FI−1,n−I> test statistic)• F distributionPractice Problems1. Investigators evaluated two new treatments for swine influenza with a control treat-ment in pigs. 30 sick pigs were randomly chosen to receive these treatments, 10 foreach. The data of their weight loss were recorded, and summarized in t he followingtable.Trt 1 Trt 2 Controlmean 11.79 10.32 17.01SD 3.31 5.70 5.39n 10 10 10Complete the ANOVA table below and answer the scientific question in the context.Source df SS MS F-statisticBetween 247.26WithinTotal 899.012. Show t hatˆb0=Pni=1yi2nis the maximizer of the following objective function:Q(b0) =nXi=1(yi− b0)b0.1Answers:1. The complete ANOVA table isSource df SS MS F-statisticBetween 2 247.26 123.63 5.12Within 27 651.75 24.14Total 29 899.01The p-value of the test is 0.013 which is smaller than 0.05. Thus, the data sug-gest that there is significant differences between the mean weight loss among 3treatments.2.
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