18. The m sample problem: Consider m independent random samples of respective sizes n1, . . . , nm from the respective population distributions F1, . . . , Fm; and consider the problem of testing H0 : F1 = F2 = · · · = Fm. To devise a test, let Ri denote the sum of the ranks of the ni elements of sample i, i = 1, . . . ,m. Show that when H0 is true

(b) Using the foregoing, and drawing insight from the goodness of fit test statistic, determine an appropriate test statistic for H0.

(c) Explain how an algorithm that generates a random permutation of the integers 1, 2, . . . ,N can be employed in a simulation study to determine the p-value when using the statistic in part

(b) to test H0.

n; (N + 1) (a) E[R]= where N = n 2