Deck 31: Rank-Based Nonparametric Tests

Question 1

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).
Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the three diets.

Answer 1

H₀: The distributions of weight gain are identical for all three diets.
H_A: At least two of the distributions differ from one another.
T₁= 11,T₂ = 9,T₃ = 4
Test statistic: S = 6.50,P-value = 0.0388
Reject the null hypothesis.There is sufficient evidence to suggest at least two of diets differ in terms of their distribution of weight gain.

Question 2

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.
Conduct a Friedman test at the 0.05 level of significance to determine if there are differences in consumer ratings between the three formulas.

Answer 2

H₀: The distributions of ratings are identical for all three formulas.
H_A: At least two of the distributions differ from one another.
T₁= 9,T₂ = 13,T₃ = 8
Test statistic: S =2.80,P-value = 0.2466
Fail to reject the null hypothesis.There is insufficient evidence to suggest a difference in ratings between the three formulas.

Question 3

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.

Answer 3

H₀: The distributions of bacteria count are identical for all four methods.H_A: At least two of the distributions differ from one another.
T₁= 22.5,T₂ = 80.5,T₃ = 68
Test statistic: H = 10.9,P-value = 0.0043
Reject the null hypothesis.There is sufficient evidence to suggest at least two of the hand-washing methods differ in terms of their distribution of bacteria count.

Question 4

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?

Question 5

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?

Question 6

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.

Question 7

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.
Conduct a Friedman test at the 0.05 level of significance to determine if there are differences in consumer ratings between the three formulas.

Question 8

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.

Question 9

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?

Question 10

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?

Question 11

The table below shows the weights of seven subjects before and after following a particular diet for two months.
Do the data suggest that the diet is effective in reducing weight? Perform a Wilcoxon signed rank test at the 5% significance level.

Question 12

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?

Question 13

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.
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.

Question 14

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?

Question 15

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.

Question 16

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.

Question 17

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).
Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the three diets.

Question 18

Five students took a math test before and after tutoring.Their scores were as follows.
Do the data suggest that the tutoring improves math scores? Conduct a Wilcoxon signed rank test using a 0.05 level of significance.

Question 19

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.

Question 20

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?

Question 21

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

A)0.962
B)0.944
C)0.976
D)0.94
E)0.942

Question 22

Two different tests are designed to measure employee productivity and dexterity.Several employees are randomly selected and tested with these results.
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.

Question 23

Consider the following data from an experiment using a randomized block design.
Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the five treatments.

Question 24

Two different tests are designed to measure employee productivity and dexterity.Several employees are randomly selected and tested with these results.
36 75
Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.

A)0.159
B)0.471
C)-0.280
D)0.997
E)0.115

Question 25

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

A)0.017
B)-0.284
C)0.371
D)0.462
E)-0.381

Question 26

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test.
Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.

A)-0.678
B)-0.224
C)0.100
D)0.157
E)0.678

Question 27

Consider the following data from an experiment using a randomized block design.
Conduct a Friedman test at the 0.05 level of significance to determine if there are differences between the four treatments.

Question 28

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.
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.

Question 29

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

A)0.124
B)-0.982
C)-0.611
D)0.592
E)0.852