9.64.* A confidence interval for a population correlation requires a transformation of r, T = (1/2)

9.64.* A confidence interval for a population correlation

ρ requires a transformation of r, T = (1/2) loge[(1 +

r)/(1 − r)], for which the sampling distribution is approximately normal, with standard error 1/

√

n − 3. Once we get the endpoints of the interval for the population value of T, we substitute each endpoint in the inverse transformation

ρ = (e2T −1)/(e2T +1) to get the endpoints of the confidence interval for ρ. For r = 0.8338 for the data on house selling price and size of house (Table 9.5), show that T = 1.20 with standard error 0.1015, a 95% confidence interval for population T is (1.00, 1.40), and the corresponding confidence interval for ρ is (0.76, 0.89). (Unless r = 0, the confidence interval for ρ is not symmetric about r, because of the nonsymmetry of its sampling distribution.)