Mann-whitney u test with a 10 percent level of significance

Question

Question 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 write 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?

Question 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