Exam 29: Rank-Based Nonparametric Tests

A researcher wishes to compare the GPAs at the Scarborough and Mississauga campuses at the University of Toronto are different.The sample data are listed below.At a 0.05 level of significance,does the Wilcoxon rank sum test provide evidence of a difference between the two campuses? Scarborough 3.2 4.0 2.4 2.6 2.0 1.8 1.3 0.0 0.5 1.4 2.9 Mississauga 2.4 1.9 0.3 0.8 2.8 3.0 3.1 3.1 3.1 3.5 3.5

A person who commutes to work is choosing between two different routes.He drives the first route 11 times and the second route 12 times and records the travel time of each trip.The results (in minutes)are shown in the table.Use a significance level of 0.01,does the Wilcoxon rank sum test provide evidence of a difference between the two routes? Route 1 Route 2 35 42 41 41 46 38 33 48 40 49 53 36 39 50 46 51 57 53 36 40 45 50 55

Below are bacteria count for four different hand-washing methods; alcohol spray,antibacterial soap,regular soap,and water alone.Conduct a Kruskal-Wallis test to determine if there are differences between the four methods in terms of their bacteria count.Use a 0.05 level of significance. Alcnhal AB Soap Soap Water 51 70 84 74 5 164 51 135 19 88 110 102 18 111 67 124 58 73 119 105

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course.The results are given below.Do the data suggest that the scores after the course differ from the scores before the course? Perform a Wilcoxon signed rank test at the 10% significance level. Before 74 83 75 88 84 63 93 84 91 77 After 73 77 70 77 74 67 95 83 84 75

A researcher was interested in comparing the GPAs of students at the three University of Toronto campuses: Scarborough,Mississauga,and St.George.Independent random samples of students were taken from each campus and their GPAs were recorded.At a significance level of 0.10,does the Kruskal-Wallis test provide evidence of any differences between the campuses in terms of the GPAs? Scarbarmugh Mississauga St. Gearge 3.7 3.8 3.9 3.2 3.2 2.8 3.0 3.1 3.5 2.5 3.9 3.4 2.7 3.8 2.9 3.6 2.5 3.7

The table below shows the weights of seven subjects before and after following a particular diet for two months. Subject A B C D E F G Befare 176 160 180 187 172 172 159 After 169 151 178 192 158 174 147 B-A 7 9 2 -5 14 -2 12 Do the data suggest that the diet is effective in reducing weight? Perform a Wilcoxon signed rank test at the 5% significance level.

The table below displays data showing weight gain,in grams,for 12 young rats,three from each of four litters.Three different diets (the treatments)were assigned at random to the three siblings in litter one (block 1).This was repeated for the other three litters (blocks 2,3,and 4). Treatment 1 Treatment 2 Treatment 3 Block 1 96 92 70 Block 2 97 90 72 Black 3 94 84 64 Block 4 88 94 69 Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the three diets.

Two different tests are designed to measure employee productivity and dexterity.Several employees are randomly selected and tested with these results. Productivity Dexterity 23 49 25 53 28 59 21 42 21 47 25 53 26 55 30 63 34 67 36 75 29 52 31 55 Using a 5% level of significance,perform a nonparametric test to determine if there is a monotonic association between an employee's productivity and their dexterity.Assume that rank ties will have little influence on your result.

11 female employees and 11 male employees were randomly selected from one company and their weekly salaries were recorded.The salaries (in dollars)are shown in the table.At a significance level of 0.10,does the Wilcoxon rank sum test provide evidence of a difference between the salaries of female and male employees? Female Male 350 420 470 410 460 650 385 675 520 545 720 810 540 400 550 660 500 880 450 640 700 750