Exercise 12.9.4. Lachenbruch (1975) presents information on four groups of junior technical college students from greater London. The information consists of summary statistics for the performance of the groups on arithmetic, English, and form relations tests that were given in the last year of secondary school. The four groups are Engineering, Building, Art, and Commerce students. The sample means are:

Engineering Building Art Commerce Arithmetic (y1) 27.88 20.65 15.01 24.38 English (y2) 98.36 85.43 80.31 94.94 Form Relations (y3) 33.60 31.51 32.01 26.69 Sample Size 404 400 258 286 The pooled estimate of the covariance matrix is Sp =

⎡

⎣

55.58 33.77 11.66 33.77 360.04 14.53 11.66 14.53 69.21

⎤

⎦.

What advice could you give to a student planning to go to a junior technical college who just achieved scores of (22,90,31)?

Exercise 12.9.5. Suppose the concern in Exercise 12.9.4 is minimizing the cost to society of allocating students to the various programs of study. The great bureaucrat in the sky, who works on the top floor of the tallest building in Whitehall, has determined that the costs of classification are as follows:

Cost Optimal Study Program Engineering Building Art Commerce Allocated Engineering 1 2 8 2 Study Building 4 2 7 3 Program Art 8 7 4 4 Commerce 4 3 5 2 Evaluate the program of study that the bureaucrat thinks is appropriate for the student from Exercise 12.9.4.