Exam 29: Rank-Based Nonparametric Tests

A study was conducted to compare the average time spent in the lab each week versus course grade for computer students.The results are recorded in the table below. Number of hours spent in lab Grade (percent) 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.

A person who commutes to work is choosing between three different routes.He drives each route 5 times and records the travel time of each trip.The results (in minutes)are shown in the table.At a significance level of 0.10,does the Kruskal-Wallis test provide evidence of any differences between the routes? Route 1 Route 2 Route 3 35 41 50 48 49 45 42 51 46 40 49 47 46 45 52

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Hours Score 5 64 10 86 4 69 6 86 10 59 9 87 Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.

A soft drink company is introducing a new drink and wishes to evaluate which of three different formulas will be most popular.Five people taste each of the three formulas in a random order and rate each formula's taste on a scale from 1 to 10.The results are given below. Formula 1 Formula 2 Formula 3 Persen 1 6 9 4 Persan 2 7 8 2 Persan 3 3 6 5 Persan 4 2 5 7 Persan 5 8 7 2 Conduct a Friedman test at the 0.05 level of significance to determine if there are differences in consumer ratings between the three formulas.

Five students took a math test before and after tutoring.Their scores were as follows. Subject A B C D E F Before 69 68 73 69 65 78 After 73 77 71 72 77 82 B - A -4 -9 2 -3 -12 -4 Do the data suggest that the tutoring improves math scores? Conduct a Wilcoxon signed rank test using a 0.05 level of significance.

A scientist collects data to predict the wheat yield (in bushels per acre)based on rainfall (in millimetres).The results are recorded in the table below. Rainfall () Wheat Yield (bushels per acre) 11.5 61.2 7.6 25.8 11.2 50.6 18 78.5 8.6 40.9 10.5 42.3 14.7 70.4 13.1 54 Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.

A group of persons filled in a questionnaire their age and the number of countries they had visited in their lifetime.The results are recorded in the table below. Age Countries Visited 42 4 43 21 42 16 59 4 50 6 75 36 70 13 76 31 60 21 Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.

A study was conducted to compare the average time spent in the lab each week versus course grade for computer students.The results are recorded in the table below. Haurs Grade 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 8 65 8 69 12 94 10 90 Using a 5% level of significance,perform a nonparametric test to determine if there is a monotonic association between the number of hours spent in the lab each week and the grade a student receives.Assume that rank ties will have little influence on your result.

Consider the following data from an experiment using a randomized block design. Treatment 1 Treatment 2 Treatment 3 Treatment 4 Block 1 17 19 21 28 Black 2 31 12 74 25 Black 3 25 23 23 17 Black 4 41 32 45 38 Black 5 64 72 69 70 Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the four treatments.

Fifty (50)students took a math test before and after tutoring.Of the 50 students,34 showed an improvement and 2 showed no change.After ranking the remaining 48 differences (before - after),it is found that T- = 873 and T+ = 303.Do the data suggest that the tutoring improves math scores? Conduct a Wilcoxon signed rank test using a 0.01 level of significance.

Below are bacteria count for three different hand-washing methods; alcohol spray,antibacterial soap,and regular soap.Conduct a Kruskal-Wallis test to determine if there are differences between the three methods in terms of their bacteria count.Use a 0.05 level of significance. Alcuhal AB Sarp Sanp 51 70 84 5 164 51 19 88 110 18 111 67 58 73 119 50 119 108

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 Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.

The table below displays data showing weight gain,in grams,for nine young rats,three from each of three 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 two litters (blocks 2 and 3). Treatment 1 Treatment 2 Treatment 3 Block 1 96 92 80 Black 2 97 90 72 Block 3 94 84 64 Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the three diets.

A soft drink company is introducing a new drink and wishes to evaluate which of three different formulas will be most popular.Five people taste each of the three formulas in a random order and rate each formula's taste on a scale from 1 to 10.The results are given below. Farmula 1 Farmula 2 Farmula 3 Person 1 9 6 4 Person 2 7 8 2 Persan 3 5 6 3 Persan 4 7 5 2 Persan 5 8 7 2 Conduct a Friedman test at the 0.05 level of significance to determine if there are differences in consumer ratings between the three formulas.

Consider the following data from an experiment using a randomized block design. Treatment 1 Treatment 2 Treatment 3 Treatment4 Treatment 5 Block 1 88 96 91 95 97 Block 2 71 73 72 76 79 Block 3 51 58 54 57 62 Block 4 64 72 69 70 81 Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the five treatments.

A teacher uses two different programs to remediate students.Results for each group on a standardized test are listed in the table.At the 0.05 level of significance,does the Wilcoxon rank sum test provide evidence of a difference between the two programs in terms of the scores that students obtain? Program I Program II 60 75 61 63 66 89 68 77 86 69 64 70 84 80 81 87 72 82 59 78 73 91 93 94 95

SAT scores for students selected randomly from two different schools are shown in the table.At a significance level of 0.05,does the Wilcoxon rank sum test provide evidence of a difference between the two schools? School A School B 550 480 670 460 580 620 400 700 520 380 680 570 540 740 560 660 500 480 360 560 650 600 550

Ten different families are tested for the number of litres of water a week they use before and after viewing a conservation video.Do the data suggest that the amount after the viewing differs from the amount before the viewing? Perform a Wilcoxon signed rank test at the 5% significance level. Before 33 33 38 33 35 35 40 40 40 31 After 34 28 25 28 35 33 31 28 35 33 - -1 5 13 5 0 2 9 12 5 -2

A coach uses a new technique in training middle distance runners.The times for 8 different athletes to run 800 metres before and after this training are shown below. Athlete Time before trairing (seconds) 109.2 110.6 109.3 108 114.3 118.1 111.9 110.1 Time after training (seconds) 109.8 109.3 106.9 108.8 112.5 118.2 108.3 106.2 Before - After -0.6 1.3 2.4 -0.8 1.8 -0.1 3.6 3.9 Do the data suggest that the training helps to improve the athletes' times for the 800 metres? Perform a Wilcoxon signed-rank test at the 5% significance level.

To see how much of a difference time of day made on the speed at which he could download files,a university student performed an experiment.He place a file on a remote server and then proceeded to download it during three different time periods.For each time period,he downloaded the file 6 times and recorded the time,in seconds,it took to complete the download.Conduct a Kruskal-Wallis test to determine if there are differences between the three time periods in terms of the downloading speed.Use a 0.01 level of significance. Maming Afternann Evening 68 299 216 138 367 175 75 331 274 186 257 171 69 260 187 217 269 213