problem 1)a) A farmer applies three kinds of fertilizers on 4 separate plots. The figures on yield per acre are tabulated below Perform the analysis of variance to test that:
(i) The three fertilizers make any material difference in yields.
(ii) The plots are materially different in fertility.
You must construct an suitable ANOVA table and state your conclusion clearly.
b) Professor Newton is interested in determining whether his brightest students (those making best grades) tend to turn in their tests earlier (as they can recall material faster) or later (as they take longer to prepare down all they know) than the others in the class. For a particular physics test, he observes that students make grades given below in order of turning their tests in:
Order Grades
1-10 94 70 85 89 92 98 63 88 74 85
11-20 69 90 57 86 79 72 80 93 66 74
21-30 50 55 47 59 68 63 89 51 90 88
If Professor Newton counts those making grade of 90 and above as his brightest students, then at a 5 percent level of significance, can he conclude that the brightest students turned their tests in randomly?
problem 2)a) Melisa’s Boutique has three small locations. Melisa keeps a daily record for each location of number of customers who actually make purchase. A sample of those data follows. Using Kruskal-Wallis, test at the 0.05 level of significance that her stores have same number of customers who buy.
Trianon 99 64 101 85 79 88 97 95 90 100
Caudan 83 102 125 61 91 96 94 89 93 75
Grand Baie 89 98 56 105 87 90 87 101 76 89
(b) A large hospital hires most of its nurses from universities in the area. Over the last year, they have been giving a test to newly graduated nurses entering hospital to find out which school, if either, seems to educate nurses better.
Based on following scores (out of 100 possible points), help personnel office of the hospital determine whether the schools differ in quality. Use the Mann-Whitney U test with a 10 percent level of significance.
Test Score
School A 97 69 73 84 76 92 90 88 84 87 93
School B 88 99 65 69 97 84 85 89 91 90 87 91 72