1. In a oneway ANOVA model with k = 3 groups and 4 observations per group: (a) Use die F-statistic in Model Reduction Method 2 to derive a statistic for testing whether the average of the means of the first two groups is the same for the mean of the third group. That is, create the Fstatistic for testing Ho : (p1 + 21.2)}? = #3. (Hint: Don't fit a model with a vintercept . It makes everything easier .) (b) Where :11 2 5.6.11; = 7.9.213 = 6.1. and SSE = 12.8. test your hypothesis . Use a = 0.05. 2. {Old Qualifying Exam Question )A randomized trial was conducted to investigate the relationship between a continuous response y and four treatments A, B. C, and D. The sample size was n = 200 . with 50 observations in each of the four treatment groups . Let y be the 200 x] vector of response values. ordered so that the first 50 entries are for treatment group A. the next 50 for B. then C. and nally D. The regression model 3 = X6 + e was fit, where X is the 290 x 4 design matrix given by: l__I i-Ii-Ii-ti-t QQHQ can-lac: 9 and where each entry is a column vector of length 50. The estimated regression coefcients were r = [3? .5. ]1.5. 1.0. 2Tr'.?]. with standard errors 2.?5. 3.89. 3.89. 3.89. and residual standard deviation Er = 19 .45 . Also : [0.02 0.02 0.02 0.02 [X'Xl'l _ .-0.02 0.04 0.02 0.02 I T [0.02 0.02 0.04 0.02 J 0.02 0.02 0.02 0.04 (a) Interpret each of the four regression parameters. (b) What is an approximate 95% confidence interval for the mean difference in response between treatment groups B and A (so. the difference #3 21\")? [c] What is an approximate 95% confidence interval for the mean response in treatment group B