Question

12. An actuary considers a portfolio of 40 policyholders which was taken as a random sam- ple from a block of business. She discovers that 11 of these policyholders were each compensated over $ 10,000 last year. Construct a 94% confidence interval for the proportion of policyholders who were com- pensated $ 10,000 or less last year from this block of business.

Answer 1

sample proportion, pcap = 11/40 = 0.275
sample size, n = 40
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.275 * (1 - 0.275)/40) = 0.0706

Given CI level is 94%, hence α = 1 - 0.94 = 0.06
α/2 = 0.06/2 = 0.03, Zc = Z(α/2) = 1.88

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.275 - 1.88 * 0.0706 , 0.275 + 1.88 * 0.0706)
CI = (0.1423 , 0.4077)