A sales and marketing management magazine conducted a survey

A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a \"strip bar\" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer.

a) Construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report.

*Please show the formulas used and the steps.

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.58- 1.96*sqrt(0.58*(1-0.58)/200) =0.5115963

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.58+ 1.96*sqrt(0.58*(1-0.58)/200) =0.6484037