Exercise 4.3.1 An experiment was conducted to see which of four brands of blue jeans were most resistant to wearing out as a result of students kneeling before their linear models instructor begging for additional test points. In a class of 32 students, 8 students were randomly assigned to each brand of jeans. Before being informed of their test score, each student was required to fall to his/her knees and crawl 3 meters to the instructor’s desk. This was done after each of 5 mid-quarter and 3 final exams.
(The jeans were distributed along with each of the 8 test forms and were collected again 36 hours after grades were posted.) A fabric wear score was determined for each pair of jeans. The scores are listed below.
Brand 1: 3.41 1.83 2.69 2.04 2.83 2.46 1.84 2.34 Brand 2: 3.58 3.83 2.64 3.00 3.19 3.57 3.04 3.09 Brand 3: 3.32 2.62 3.92 3.88 2.50 3.30 2.28 3.57 Brand 4: 3.22 2.61 2.07 2.58 2.80 2.98 2.30 1.66

(a) Give an ANOVA table for these data, and perform and interpret the F test for the differences between brands.

(b) Brands 2 and 3 were relatively inexpensive, while Brands 1 and 4 were very costly. Based on these facts, determine an appropriate set of orthogonal contrasts to consider in this problem. Find the sums of squares for the contrasts.

(c) What conclusions can be drawn from these data? Perform any additional computations that may be necessary