64. 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 H0: r1  r2  0 gxiyi g1yi  y22  465.34 gyi g1xi  x22  3756.96 gxi against the alternative that the two population correlation coef cients are different.

a. Use the results of the proposition concerning the transformed variable V  .5 ln[(1  R)/(1  R)]

to propose an appropriate test statistic and rejection region (let R1 and R2 denote the two sample correlation coef cients).

b. The paper Relational Bonds and Customer s Trust and Commitment: A Study on the Moderating Effects of Web Site Usage (Service Indust.

J., 2003: 103—124) reported that n1  261, r1 

.59, n2  557, r2  .50, where the rst 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).