Let x be number of hours per week of studying and y be grade point average. Suppose we have one sample of (x, y) pairs for females and another for males. Then we might like to test the hypothesis H₀: ρ₁ − ρ₂ = 0 against the alternative that the two population correlation coefficients are different.

a. Use properties of the transformed variable V = .5ln[(1 + R)/(1 − R)] to propose an appropriate test statistic and rejection region (let R₁ and R₂ denote the two-sample correlation coefficients).

b. The paper “Relational Bonds and Customer’s Trust and Commitment: A Study on the Moderating Effects of Web Site Usage” (Serv. Ind. J. 2003: 103–124) reported that n₁ = 261, r₁ = .59, n₂ = 557, r₂ = .50, where the first sample consisted of corporate website users and the second of nonusers; here r is the correlation between an assessment of the strength of economic bonds and performance. Carry out the test for this data (as did the authors of the cited paper).