Question

An audit firm surveyed salespeople cheating on their expense reports and other unethical conduct. In the survey of 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 “bars” as a “restaurants” on an expense report, and 19% have caught salespeople giving a kickback to a customer. What is the estimated upper limit for the proportion of managers who caught salespeople working a second job on company time with a 96% confidence?

Answer 1

sample size          n=		200
sample proportion p̂ =x/n=		0.5000
std error se= √(p*(1-p)/n) =		0.0354
for 96 % CI value of z=		2.054
margin of error E=z*std error   =		0.0726
lower bound=p̂ -E                       =		0.4274
Upper bound=p̂ +E                     =		0.5726

from above:

upper limit for the proportion of managers who caught salespeople working a second job on company time with a 96% confidence =0.5726  

(please try 0.572 if z is required to 2 decimals)