This document contains 6 problems from a homework chapter on auditing sampling techniques:
1. It defines statistical and nonstatistical sampling and differentiates between them.
2. It describes the difference between sampling risk and nonsampling risk.
3. It explains the difference between an attributes sampling plan and a variables sampling plan in testing inventory extensions.
4. It lists advantages of statistical sampling and decisions requiring judgment when applying statistical sampling techniques to audit testing.
5. It provides true/false statements about unrestricted random sampling without replacement.
6. It identifies definitions that match sampling terminology.
1. Chapter 9 – Homework
1.
Problem 9-1
Define and differentiate between, nonstatistical (judgmental) sampling and statistical sampling.
Nonstatistical sampling is an audit sampling technique in which the risk of sampling error is estimated by the auditors
using professional judgment rather than by the laws of probability. Statistical sampling involves the quantification of the
risk of sampling error through the use of mathematics and laws of probability.
2.
Problem 9-2
Describe the difference between sampling risk and nonsampling risk.
Sampling risk is the possibility that the auditors will make an erroneous decision based on a sample result. To control
sampling risk the auditors increase the size of their samples. Nonsampling risk is the risk of erroneous conclusions by the
auditors based on any factor other then sampling. For example, the auditors may perform inappropriate tests, or they may
not recognize errors in the sample items examined. Nonsampling risk may be controlled by adequate planning and
supervision of engagements, and the establishment of effective quality control policies and procedures.
3.
Problem 9-17
What would be the difference between an attributes sampling plan and a variables sampling plan in a test of
inventory extensions?
Attributes sampling would estimate the percentage of extensions that are in error, and variables sampling would estimate
total dollar amount of misstatements in the schedule. In general, attributes sampling estimates the deviation rate
(occurrence rate) of a characteristic, and the variables sampling estimates the dollar value of a characteristic.
4.
Problem 9-29
CPAs may decide to apply nonstatistical or statistical techniques to audit testing.
a. List and explain the advantages or applying statistical sampling techniques to audit testing.
b. List and discuss the decisions involving professional judgment that must be made by the CPAs in applying
statistical sampling techniques to test of controls.
c. You have applied attributes sampling to the client's pricing to the inventory and discovered from your
sampling that the sample deviation rate exceeds your tolerable rate. Discuss the courses of action you take.
2. (a) Relative to nonstatistical sampling, statistical techniques may provide the auditors with the following
advantages:
(1) Designing efficient samples (that may avoid "overauditing").
(2) Measuring the sufficiency of the evidence obtained (this potentially could be helpful in a court
proceeding or to help justify work to a client who was critical of the extent of testing).
(3) Objectively evaluating sample results.
(b) Decisions requiring professional judgment in performing statistical tests of controls include:
(1) Identifying the controls to be tested. This involves consideration of the types of misstatements that
might occur, identifying the controls that should prevent these misstatements, and deciding whether
consideration of those controls to reduce the auditors' assessment of control risk would sufficiently
reduce the required amount of substantive procedures to justify the related tests of controls.
(2) Defining a "deviation." If the test results are to be meaningful, all exceptions included in the
definition of "deviation" must be similar in their potential audit significance.
(3) Determining the maximum tolerable deviation rate. This involves judgment because deviations do
not necessarily correspond directly with misstatements in the financial statements. A single
deviation may result in material misstatement, while numerous deviations may result in no
misstatement.
(4) Establishing an appropriate risk of assessing control risk too low.
(5) Defining the population to be tested. The auditor may want to consider stratifying the population
by time period if, for example, changes in internal control may have occurred or new personnel
may have been hired.
(6) Evaluating the results. In addition to drawing statistical conclusions, the CPAs should evaluate the
qualitative characteristics of the exceptions found in the sample. Also, if the sample results do not
support the planned assessed level of control risk, the CPA must determine the required
modification of substantive procedures.
(c) When the CPAs have applied attributes sampling techniques and discovered that the deviation rate
exceeds their stipulated maximum tolerable deviation rate, the following courses of action are available to
them:
(1) An investigation might be made to determine the reasons for the unexpectedly high deviation rate
and to ascertain its potential effect upon the financial statements.
(2) The CPAs might extend the size of their original sample to provide a more precise estimate of the
population deviation rate.
(3) In light of the higher than anticipated deviation rate, the auditors must increase their assessment of
control risk in the related area. This may necessitate expanding the planned substantive test
procedures for assertions that are potentially affected by the control weakness.
5.
Problem 9-38
3. The 10 following statements apply to unrestricted random sampling without replacement. Indicate whether each
statement is true or false.
A. True
B. False
1. When sampling from the population of accounts receivable for certain objectives, the auditor might sample
only active accounts with balances.
2. To be random, even item in the population must have an equal change of being selected for inclusion in the
sample.
3. In general, all items in excess of a material misstatement need to be examined and sampling of them is
appropriate.
4. It is likely that five different random samples from the sample population could produce five different
estimates of the true population mean.
5. A 100 percent sample would have to be taken to eliminate sampling risk.
6. The effect of the inclusion by chance of a very large or very small item in a random sample can be lessened
by increasing the size of the sample.
7. The standard deviation of a measure of the variability of items in a population.
8. The larger the standard deviation of a population, the smaller the required sample size.
9. Unrestricted random sampling with replacement may result in a larger sample size than unrestricted random
sampling without replacement.
10. Unrestricted random sampling normally results in a smaller sample size than does stratified sampling.
6.
Problem 9-40
4. For each term in the column below, identify the definition (or partial definition). Each definition may be used
once or not at all.
A. A classical variables sampling plan enabling the auditors to estimate the average dollar value (or other
variable) of items in a population by determining the average value of items in a sample.
B. A defined rate of departure from prescribed controls. Also referred to as occurrence rate or exception rate.
C. A sampling plan enabling auditors to estimate the rate of deviation (occurrence) in a population.
D. A sampling plan for locating at least 1 deviation, providing that the deviation occurs in the population with a
specified frequency.
E. A sampling plan in which the sample is selected in stages, with the need for each subsequent stage being
conditional on the results of the previous stage.
F. Also referred to as precision, an interval around the sample results in which the true population characteristic
is expected to lie.
G. An estimate of the most likely amount of monetary misstatement in a population.
H. The complement of the risk of incorrect acceptance.
I. The maximum population rate of deviations from a prescribed control that the auditors will accept without
modifying the planned assessment of control risk.
J. The possibility that the assessed level of control risk based on the sample is less than the true operating
effectiveness of the controls.
K. The possibility that the assessed level of control risk based on the sample is greater than the true operating
effectiveness of the control.
L. The risk that sample results will indicate that a population is materially misstated when, in fact, it is not.
M. The risk that sample results will indicate that a population is not materially misstated when, in fact, it is
materially misstated.
N. The risk that the auditors' conclusion based on a sample might be different from the conclusion they would
reach if the test were applied to the entire population.
Allowance for sampling risk
Deviation rate
Discovery sampling
Projected misstatement
Reliability
Risk of assessing control risk too low
Risk of incorrect acceptance
Sampling risk
Tolerable deviation rate
