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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Common Information for Questions 1, 2, and 3 A. A research team studied Y, the protein production of a laboratory animal, and sought to set the dose of the medicine so that E (Y) is minimized. They used four doses of the medicine: 1, 2, 3, and 4 _u_n_it_s respectively. They randomly assigned 12 animals to dosage 1, 12 to dosage 2, 12 to dosage 3, and 12 to dosage 4. They observed that the average values of Yat each dosage were 311. = 525,312. 2 505, 313, = 380, and 314. = 338, where y, was the average of the observations taken with dosage i = 1,2,3,4, respectively. They also observed that 5'12 2 28,634, 3% = 34,537, 532,! = 36,491, and SE = 22,434, where 3,2 was the unbiased estimate of the variance for the observations taken with dosage i = 1,2,3,4_ respectively. 1. Complete the analysis of variance table for these results; that is, be sure to specify the degrees of freedom, sums of squares, mean squares, Ftest, and your conclusion. Test the null hypothesis that all treatment means are equal using signicance levels 0.10, 0.05, and 0.01. Also enter your F statistic and conclusion in the text box underneath this question. This question is worth 45 points. Find the estimated linear contrast, the sum of squares due to the linear contrast and the 99% Scheffe condence interval for the linear contrast. The coefcients of the linear contrast are 3, 1,1,3. Enter the left and right values of the Scheffe condence interval for the linear contrast in the text box underneath this question. This question is worth 30 points. What is the optimal setting of dosage, and how do you document it? This question is worth 10 points. End of Application of Common Information