The director of graduate admissions at a local university is analyzing the relationship between scores on the Graduate Record Examination (GRE) and subsequent performance in graduate school, as measured by a student's grade point average (GPA). She uses a sample of 7 students who graduated with in the past five years. The data are in the accompanying table and on the text website, labeled GRE/GPA.
a. Calculate and interpret the Spearman rank correlation coefficient rs.
b. Specify the competing hypotheses in order to determine whether GRE and GPA are positively related.
c. At the 5% significance level, specify the critical value and the decision rule.
d. Are GRE and GPA positively related? Explain.