Exercise 4.3.2 After the final exam of spring quarter, 30 of the subjects of the previous experiment decided to test the sturdiness of 3 brands of sport coats and 2 brands of shirts. In this study, sturdiness was measured as the length of time before tearing when the instructor was hung by his collar out of his second-story office window. Each brand was randomly assigned to 6 students, but the instructor was occasionally dropped before his collar tore, resulting in some missing data. The data are listed below.

Coat 1: 2.34 2.46 2.83 2.04 2.69 Coat 2: 2.64 3.00 3.19 3.83 Coat 3: 2.61 2.07 2.80 2.58 2.98 2.30 Shirt 1: 1.32 1.62 1.92 0.88 1.50 1.30 Shirt 2: 0.41 0.83 0.53 0.32 1.62

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

(b) Test whether, on average, these brands of coats are sturdier than these brands of shirts.

(c) Give three contrasts that are mutually orthogonal and orthogonal to the contrast used in (b). Compute the sums of squares for all four contrasts.

(d) Give a 95% confidence interval for the difference in sturdiness between shirt Brands 1 and 2. Is one brand significantly sturdier than the other?