## Example 103

hypothesis that the central locations of the distributions of study times in accounting and finance are the same. There is not very strong support for the conclusion that on the whole, students spend more time studying for one of these subjects than the other.

In a study designed to compare the performance of firms that give management forecasts of earnings with those that do not, independent random samples of eighty firms from each of the populations were taken.7 The variability of the growth rate of earnings over the previous ten periods was measured for each of the 160 firms, and these variabilities were ranked. The sum of the ranks for firms not disclosing management earnings forecasts was 7,287. Test against a two-sided alternative the null hypothesis that the central locations of the population distributions of earnings variabilities are the same for these two types of firms.

Since we have n, = 80, n2 - 80, and Ri = 7,287, the calculated value of the Mann-Whitney statistic is

«.(«i + 1) (80)(81 U = n,n2 + —-1 - /?, = (80X80) + 1

Under the null hypothesis, the Mann-Whitney statistic has mean n,n2 (80)(80)

fltj

and variance

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