a&b

5. The set of artificial data shown in Table 6.32 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. Table 6.32 Data for Exercise 5 Treatment 1 2 3 4 11.6 10.0 10.5 10.6 10.7 8.5 9.7 6.7 7.5 6.7 14.5 14.5 13.3 14.8 14.4 12.3 12.9 11.4 12.4 11.6 13.9 16.1 14.3 13.7 14.9 (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 instruc- tors whose students have higher test scores. Do the sample results provide evidence to reward one or more of these instructors? (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 effects of the additives