11-44. Confidence Interval for the Coefficient of Variation:

We previously expressed the population coefficient of variation as CV =

σ

μ. Given a collection of sample random variables X1, . . . ,Xn, let us denote the realization of CV as cv = s

¯x . Then for n ≥ 25 and cv < 0.40, a 100(1 − α)% confidence interval for CV is

1 = cv 1 + zα/2

1 + 2cv2 2(n + 1)

≤ CV ≤ 2 = cv 1 − zα/2

1 + 2cv2 2(n + 1)

.

Suppose that from a random sample of size n = 75 it was found that

¯x = 127, s = 15.5, and cv = 0.122. Determine a 95% confidence interval for CV.