Exam 31: Rank-Based Nonparametric Tests

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.

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.

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.

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.

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?

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 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.

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?

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.