A study was conducted in which samples were selected independently from four populations. The sample size from each population was 20. The data were converted to ranks. The sum of the ranks for the data from each sample is as follows:

Sample 1 Sample 2 Sample 3 Sample 4 Sum of ranks 640 780 460 1,360

a. State the appropriate null and alternative hypotheses if we wish to determine whether the populations have equal medians.

b. Use the information in this exercise to perform a Kruskal–Wallis one-way ANOVA.