Problem: Abusiness office has private information about its customers. A manager finds it necessary to check whether the workers inadvertently give away any private information over the phone. To estimate the percentage of times that a worker does give away such information, an experiment is proposed. At a randomly selected time, a call will be placed to the office and the caller will ask several routine questions. The caller will intersperse the routine questions with three questions (attempts) that ask for private information that should not be given out. The caller will note how many attempts were made and how many times private information was given away. The true proportion of the times that private information is given away during an attempt is guessed to be 7%. The cost of making a phone call, including the caller's wages, is $2.25. This cost is per call, or per three attempts. Thus the cost per attempt is $0.75. In addition, the fixed cost to design the experiment is $380.
Question: 1. What is the minimum sample size (of attempts) if the proportion is to be estimated within ±2% with 95% confidence? What is the associated total cost?
2. What is the minimum sample size if the proportion is to be estimated within ±1% with 95% confidence? What is the associated total cost?
3. Prepare a tabulation and a plot of the total cost as the desired accuracy varies from ±1% to ±3% and the population proportion varies from 5% to 10%.
4. If the caller can make as many as five attempts in one call, what is the total cost for ±2% accuracy with 95% confidence? Assume that cost per call and the fixed cost do not change.
5. If the caller can make as many as five attempts in one call, what is the total cost for ±1% accuracy with 95% confidence? Assume that the cost per call and the fixed cost do not change.
6. What are the problems with increasing the number of attempts in one call?