Question

The internal auditing staff of a lical company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95% confidence interval for the proportion of all delinquent customer accounts at this company.

Answer 1

sample proportion, = 0.2
sample size, n = 400
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.2 * (1 - 0.2)/400) = 0.02

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.02
ME = 0.0392

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.2 - 1.96 * 0.02 , 0.2 + 1.96 * 0.02)
CI = (0.1608 , 0.2392)