a. Exercise 3—Mann-Whitney-Wilcoxon Test

Samples of starting annual salaries for individuals entering the public accounting and financial planning professions follow (Fortune, June 26, 1995). Annual salaries are shown in thousands of dollars.

1) Using a .05 level of significance, test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners. What is your conclusion?

2) What are the sample mean annual salaries for the two professions?

Solution to Exercise c.

1.-) We apply Mann-Whitney-Wilcoxon Test (also known as the Rank-Sum Test). Starting with the table provided, we need to make a “rank” table, ordering the observations in increasing order, taking into account from which sample each observation comes. We use the notation

PA = Public Accountant

FP = Financial Planner

The rank table would be:

Now, we obtain from the table the rank associated with PA:

With this , we find the following statistics:

We know from the table that Average(Rank) = 10.5, and SD(Rank) = 5.9139. Also, we know that

and

This allows us to compute:

and this leads to a one-sided p-value of 0.0087, which is less than . Or which is the same, the rejection region is Z>1.64485, which means that we reject the hypothesis that there is no difference in the salaries at the 0.05 level of significance.

2.-) From the table is straightforward to get that the sample mean salary for public accountants is 30.17 thousand dollars, and the sample mean salary for financial planners is 26.7 thousand dollars.