# Let x be number of hours per week of studying and y be grade point average. Suppose

## Question:

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 H_{0}: ρ_{1} − ρ_{2} = 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 R_{1} and R_{2} 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 n_{1} = 261, r_{1} = .59, n_{2 }= 557, r_{2} = .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).

## Step by Step Answer:

**Related Book For**

## Modern Mathematical Statistics With Applications

**ISBN:** 9783030551551

3rd Edition

**Authors:** Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton