The director of graduate admissions at a local university is analyzing the relationship between scores on the

Question:

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 within the past five years, as shown in the accompanying table.

a. Calculate and interpret the Spearman rank correlation coefficient rs .
b. Specify the competing hypotheses to determine whether the Spearman rank correlation coefficient is greater than zero.
c. At the 5% significance level, specify the critical value and the decision rule.
d. Are GRE and GPA positively correlated? Explain.