4. A recruiter for a computer company would like to determine whether there are differences in sales ability between business, arts, and science graduates. The recruiter takes a random sample of 20 business graduates who have been working for the company for the past 2 years. Each is then matched with an arts graduate and a science graduate with similar educational and working experience. The commission earned by each (in $1,000s) in the last year was recorded. a. Is there sufficient evidence to allow the recruiter to conclude that there are differences in sales ability between the holders of the three types of degrees? b. Conduct a test to determine whether an independent samples design would have been a better choice. C. What are the required conditions for the test in part (a)? d. Are the required conditions satisfied? >>> A B D E 1 2 3 4 5 69 012345 Block Business Arts Science 42.8 42.4 44.4 2 25.9 28.0 31.0 33.1 34.9 30.0 33.5 36.2 32.9 51.7 50.9 44.7 7 6 30.2 25.3 29.8 8 9 10 11 1890 7 46.3 50.3 41.3 37.7 41.7 36.2 42.8 43.0 43.4 10 43.7 40.1 44.5 12 11 47.7 47.5 45.8 13 12 44.1 42.9 40.5 14 13 38.9 39.2 40.8 15 14 41.5 43.3 41.9 16 15 35.6 29.6 33.8 17 16 55.3 52.7 53.2 18 17 37.3 31.4 36.4 19 18 45.4 40.8 44.4 20 19 27.8 25.2 28.0 21 20 38.1 34.9 41.0 22 23 24 25 ANOVA MS F P-value F crit 0.00000 1.86733195 19 158.962903 26.6442951 5.1305 0.85993998 0.43125854 3.24481836 38 5.96611403 Source of Variation SS df Blocks 3020.295167 Treatments 10.261 2 Error 226.7123333 Total 3257.2685 59