Question

What Are We Testing? Refer to the sample data in Exercise 1. Assuming that we use the Wilcoxon rank-sum test with those data, identify the null hypothesis and all possible alternative hypotheses.

Short answer

The null hypothesis and the three possible alternative hypotheses are:

\({H_0}:\)The evaluations of female and male professors have the same median.

\({H_1}:\)The evaluations of female and male professors do not have the same median.

\({H_1}:\)The median of the evaluations of female professors is greater than the median of the evaluations of male professors.

\({H_1}:\)The median of the evaluations of female professors is less than the median of the evaluations of male professors.

Step-by-step solution

Given information

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

Identify the null hypothesis and all possible alternative hypothesis

TheWilcoxon rank-sum test is used to test the difference in the medians of the populations from which the two samples are obtained.

Here, the two samples show the evaluations of female and male professors.

So, the null hypothesis or the “no difference hypothesis”\(\left( {{H_0}} \right)\)becomes

“The evaluations of female and male professors have the same median.”

The alternative hypothesis can be of three types based on whether the medians are unequal, or one median is greater (or smaller) than the other.

The three alternative hypotheses\(\left( {{H_1}} \right)\)are given below:

• The evaluations of female and male professors do not have the same median.
• The median of the evaluations of female professors is greater than the median of the evaluations of male professors.
• The median of the evaluations of female professors is less than the median of the evaluations of male professors.