Question

Student Evaluations of Professors Example 1 in this section used samples of course evaluations, and the table below lists student evaluations of female professors and male professors (from Data Set 17 “Course Evaluations” in Appendix B). Are the requirements for using the Wilcoxon rank-sum test satisfied? Why or why not?

Female	3.9	3.4	3.7	4.1	3.7	3.5	4.4	3.4	4.8	4.1	2.3	4.2	3.6	4.4
Male	3.8	3.4	4.9	4.1	3.2	4.2	3.9	4.9	4.7	4.4	4.3	4.1

Short answer

Yes, all the requirements of the Wilcoxon rank-sum test are fulfilled. They are:

• The two samples should be independent. They should consist of values from two different sets of people.
• Each of the two samples should have more than ten values. Here, both the samples corresponding to males and females have more than ten observations.

Step-by-step solution

Given information

Data are given on student evaluation of female and male professors.

Requirements of Wilcoxon rank-sum test

The following are the two requirements of the Wilcoxon rank-sum test:

• The two samples should be independent and simple random samples.
• The size of each sample should be more than 10.

Determine whether the requirements of the Wilcoxon rank-sum test are satisfied

Firstly, the student evaluations are given on two samples of professors that are different from each other. Hence, the observations are not matched pairs; they are random.

Thus, they are independent simple random samples.

Secondly, each of the two samples consists of more than ten values.

The sample size of course evaluation of students by female professors is 14.

The sample size of course evaluation of students by male professors is 12.

Therefore, both the requirements are satisfied for performing the Wilcoxon rank-sum test.