You're applying to graduate school and have found a list of the top 50 PhD programs for your area of study. For each of the following scenarios, state which nonparametric hypothesis test is most appropriate: Spearman rank-order correlation coefficient, Wilcoxon signed-rank test, Mann-Whitney U test, or Kruskal- Wallis H test. Explain your answers.
a. You want to determine which institutions tend to be higher ranked: those that fund students primarily by offering fellowships, those that fund students primarily by offering teaching assistantships, or those that don't have full funding for most students.
b. You wonder whether rankings are related to the typical Graduate Record Examination (GRE) scores of incoming students.
c. You decide to compare the rankings of institutions within a three-hour drive of your current home and those beyond a three-hour drive.