Auditing & Assurance Services 6th Edition by Timothy Louwers

Exercise 211

Sample Evaluation. Gloria Bush has performed a sampling plan to estimate the number of children per household in her neighborhood. In doing so, she established a 10 percent acceptable level of sampling risk and found a sample estimate of 2.5 children per household. Based on the acceptable level of sampling risk, she calculated a precision of 0.7 children per household.
Required:
a. Define the terms precision and reliability. How are these terms related?
b. What is the precision interval in this example? What statement can Bush make based on her sample evidence?
c. Assume that she desires a lower sampling risk (5 percent). How will this affect the precision interval?
d. If she is interested in knowing whether the number of children per household exceeds
1.5 children, how would you advise her based on the following outcomes? In all cases, assume that the sample estimate is 2.5 children per household.
1. Reliability = 90 percent; precision = 0.7 children per household.
2. Reliability = 95 percent; precision = 1.4 children per household.
3. Reliability = 99 percent; precision = 1.8 children per household.
e. What causes the differences in the relationships noted in (d)?