1. In a study, mosquitoes were divided into four groups of seven mosquitoes each:infected rhesus and sporozites present (Trt 1), infective rhesus and oocysts present (Trt2), infective rhesus and no infection developed (Trt 3), and non infective (Trt 4).Distances flown by the mosquitoes within 24 hours were recorded. The summary data are: \bar{x}_{1}=3.6453, \quad \bar{x}_{2}=4.8753, \quad \bar{x}_{3}=5.6572, \quad \bar{x}_{4}=4.9658 \sum_{i=1} \sum_{j=1}^{J} x_{i j}^{2}=668.3276 Use the ANOVA F test at level a = 0.10 to decide whether there are any significantdifferences between true average flight times for the four treatments. a. Show hand calculations for SST, SSTT, and SSE (Formulas 10B, C, D and that xi = xị * J) b. Follow the 4-step hypothesis test outline done in class (i.e. 1 - hypothesis/significance level, 2 - test statistic, 3 - rejection region, 4 - conclusion). You can also use the p-value approach in step 3 with R command 1 - pf(F, df1, df2) where F = test statistic, df1=treatment df, and df2 = MSE df.

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