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The set of artificial data shown in artificial.jmp is used in several contexts to provide practice in implementing appropriate analyses for different situations. The use of the same numeric values for the different problems will save computational effort. (a) Assume that the data represent test scores of samples of students in each of five classes taught by five different instructors. We want to reward instructors whose students have higher test scores. Do the sample results provide evidence to reward one or more of these instructors? If yes, which of the instructors should be rewarded? Write out the fixed effects model, then perform the appropriate test. (b) Assume that the data represent gas mileage of automobiles resulting from using different gasoline additives. The treatments are: 1. additive type A, made by manufacturer I 2. no additive 3. additive type B, made by manufacturer I 4. additive type A. made by manufacturer II 5. additive type B, made by manufacturer II Construct three orthogonal contrasts to test meaningful hypotheses about the effect of the additives. Show that they are contrasts and that they are orthogonal, then test them for significance. artificial - JMP Pro File Edit Tables Rows Cols DOE Analyze Graph Tools View Window Q+=C artificial Source Columns (2/1) treatment y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 treatment 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 y 11.6 8.5 14.5 12.3 13.9 10 9.7 14.5 12.9 16.1 10.5 6.7 13.3 11.4 14.3 10.6 7.5 14.8 12.4 13.7 10.7 6.7 14.4 11.6 14.9 The set of artificial data shown in artificial.jmp is used in several contexts to provide practice in implementing appropriate analyses for different situations. The use of the same numeric values for the different problems will save computational effort. (a) Assume that the data represent test scores of samples of students in each of five classes taught by five different instructors. We want to reward instructors whose students have higher test scores. Do the sample results provide evidence to reward one or more of these instructors? If yes, which of the instructors should be rewarded? Write out the fixed effects model, then perform the appropriate test. (b) Assume that the data represent gas mileage of automobiles resulting from using different gasoline additives. The treatments are: 1. additive type A, made by manufacturer I 2. no additive 3. additive type B, made by manufacturer I 4. additive type A. made by manufacturer II 5. additive type B, made by manufacturer II Construct three orthogonal contrasts to test meaningful hypotheses about the effect of the additives. Show that they are contrasts and that they are orthogonal, then test them for significance. artificial - JMP Pro File Edit Tables Rows Cols DOE Analyze Graph Tools View Window Q+=C artificial Source Columns (2/1) treatment y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 treatment 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 y 11.6 8.5 14.5 12.3 13.9 10 9.7 14.5 12.9 16.1 10.5 6.7 13.3 11.4 14.3 10.6 7.5 14.8 12.4 13.7 10.7 6.7 14.4 11.6 14.9