(In some of the exercises that follow, we must
Chapter 9, Problem 8E(choose chapter or problem)
Problem 8E
(In some of the exercises that follow, we must make assumptions of normal distributions with the usual notation.)
In sampling from a bivariate normal distribution, it is true that the sample correlation coefficient R has an approximate normal distribution N[ρ, (1 − ρ2)2/n] if the sample size n is large. Since, for large n, R is close to ρ, use two terms of the Taylor’s expansion of u(R) about ρ and determine that function u(R) such that it has a variance which is (essentially) free of p. (The solution of this exercise explains why the transformation (1/2) ln[(1+R)/ (1 − R)] was suggested.)
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