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Assume that, apart from any possible differences in central location, the two population distributions are identical. Suppose that n, observations are avail- able from the first population and n, observations from the second. The two samples are pooled, and the observations are ranked in ascending order with ties assigned the average of the next available ranks. Let R, denote the sum of the ranks of the observations trom the 1st population. The Mann-Whitney U test is based on the Mann-Whitney U statistic defined as follows: (n + 1) 2 U = #12 R v18 (14.21) It can be shown then that if the null hypothesis is true, the random variable U has mean and variance as defined in Equations 14.22 and 14.23. Mann-Whitney U Test: Normal Approximation Assuming as the null hypothesis that the central locations of the two popula- tion distributions are the same, the Mann-Whitney U has the following mean and variance: E(U) = HU 11,112 2 (14.22) 22,112 m + 12 + 1) Var(U) = = (14.23) 12 Then, for large sample sizes (both at least 10), the distribution of the random variable U-HU Z = (14.24) is approximated by the normal distribution. Example 14.13 Hours of Study (Mann-Whitney U Test) Table 14.17 shows the numbers of hours per week students claim to spend studying for introductory finance and accounting courses. The data are from independent random samples of 10 finance students and 12 accounting students. Do the data indicate a difference in the median number of hours per week that students spend studying for introductory finance and accounting courses? The name of the data file is Hours