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15-1
Chapter 15
Audit Sampling for Tests of Controls and
Substantive Tests of Transactions
Concept Checks
P. 489
1. A representative sample is one in which the characteristics of interest for the
sample are approximately the same as for the population (that is, the sample
or she has a representative sample because the entire population is
ordinarily not tested, but certain things, such as the use of random
2. Statistical sampling is the use of mathematical measurement techniques to
calculate formal statistical results. The auditor therefore quantifies
sampling risk when statistical sampling is used. In nonstatistical sampling, the
P. 511
1. Analysis of exceptions is the investigation of individual exceptions to
effectiveness of internal control. The analysis attempts to tell the “why” and
types of exceptions have occurred.
2. The steps of the audit sampling process that differ across statistical and
nonstatistical sampling are as follows.
Specify acceptable risk of overreliance: the concepts are the same
evaluated.
15-2
Concept check, P. 511 (continued)
result.
Select the sample: The only difference in sample selection is the
requirement to use a probabilistic method when using statistical
sampling.
Generalize from the sample to the population: For statistical sampling,
Review Questions
15-1 Sampling risk is the risk that the auditor reaches the wrong conclusion
may perform procedures incorrectly or fail to correctly interpret the audit
of audit sampling are:
1. Plan the sample
2. Select the sample and perform the tests
3. Evaluate the results
15-3 In probabilistic sample selection, the auditor randomly selects items from
a population such that each item has a known probability of being included in
approach.
15-3
15-4 A block sample is the selection of several items in sequence. Once
the first item in the block is selected, the remainder of the block is chosen
procedure would be repeated 4 other times.
15-5 In replacement sampling, an element in the population can be included
in the sample more than once if the random number corresponding to that
element is selected more than once. In nonreplacement sampling, an element
15-6 A simple random sample is one in which every possible combination of
elements in the population has an equal chance of selection. Two methods of
15-7 In systematic sampling, the auditor calculates an interval and then
17. The next is 87, then 157, 227, and so on.
The advantage of systematic sampling is its ease of use. In most
populations a systematic sample can be drawn quickly, the approach automatically
puts the numbers in sequential order, and documentation is easy.
A major problem with the use of systematic sampling is the possibility
of bias. Because of the way systematic samples are selected, once the first
item in the sample is selected, other items are chosen automatically. This
15-4
15-8 Random (probabilistic) selection is a part of statistical sampling, but it is
not, by itself, statistical measurement. To have statistical measurement, it is
15-9 The purpose of using nonstatistical sampling for tests of controls and
substantive tests of transactions is to estimate the proportion of items in a
15-10 An attribute is the definition of the characteristic being tested and the
exception conditions whenever audit sampling is used. The attributes of interest
15-11 An attribute is the characteristic being tested for in a population. An
exception occurs when the attribute being tested for is absent. The exception
TERM
DEFINITION
a. Acceptable risk of
overreliance (ARO)
The risk the auditor is willing to take of accepting a control
as effective or a rate of monetary misstatements as
tolerable, when the true population exception rate is
greater than the tolerable exception rate.
b. Computed upper
exception rate (CUER)
The highest estimated exception rate in the population
at a given ARO.
c. Estimated population
exception rate (EPER)
The exception rate the auditor expects to find in the
population before testing begins. It is necessary to
plan the appropriate sample size.
d. Sample exception rate
(SER)
The actual rate of exception discovered in the sample.
It is calculated by dividing the actual number of
exceptions in the sample by the sample size.
e. Tolerable exception
rate (TER)
The exception rate the auditor will permit in the population
and still be willing to use the assessed control risk
and/or the amount of monetary misstatements in the
transactions established during planning.
15-5
Copyright © 2017 Pearson Education, Inc.
15-13 The sampling unit is the population item from which the auditor selects
sample items. The major consideration in defining the sampling unit is making
it consistent with the objectives of the audit tests. Thus, the definition of the
population and the planned audit procedures usually dictate the appropriate
sampling unit.
The sampling unit for verifying the occurrence of recorded sales would
be the entries in the sales journal since this is the record the auditor wishes to
15-14 The tolerable exception rate (TER) represents the exception rate that
the auditor will permit in the population and still be willing to use the assessed
15-15 Tolerable exception rate (TER) is the result of an auditor’s judgment.
The suitable TER is a question of materiality and is therefore affected by both
the definition and the importance of the attribute in the audit plan. It represents
acceptable.
The sample size for a TER of 7% would be smaller than that for a TER
of 4%, all other factors being equal.
15-16 The appropriate ARO is a decision the auditor must make using
auditor’s ARO.
The auditor will choose a smaller sample size for an ARO of 10% than
would be used if the risk were 5%, all other factors being equal.
15-17 The relationship between sample size and the four factors determining
sample size are as follows:
normally unchanged, or may increase slightly.
c. As the TER increases, the sample size decreases.
d. As the EPER increases, the required sample size increases.
15-6
Copyright © 2017 Pearson Education, Inc.
15-18 When the CUER exceeds the TER, the auditor may do one or more of
the following:
1. Revise the TER or the ARO. This alternative should be followed
risk associated with the higher specifications.
2. Expand the sample size. This alternative should be followed when
expected in the expanded sample.
3. Revise assessed control risk upward. This is likely to increase
are possible.
4. Write a letter to management. This action should be done in
conjunction with each of the three alternatives above. Management
should always be informed when its internal controls are not
operating effectively. If a deficiency in internal control is considered
to be a significant deficiency in the design or operation of internal
15-19 Attributes sampling is a statistical, probabilistic sampling method that
results in an estimate of the proportion of items in a population containing a
15-20 In this situation, the sample exception rate (SER) is 4%, the sample
size is 100 and the ARO is 10%. From the 10% ARO table (Table 15-9) then,
15-21 The decisions the auditor must make in using attributes sampling are:
What are the objectives of the audit test?
Does audit sampling apply?
15-7
15-21 (continued)
What should the TER be?
What should the ARO be?
What is the EPER?
What generalizations can be made from the sample to the population?
What are the causes of the individual exceptions?
Is the population acceptable?
In making the above decisions, the following should be considered:
The individual situation.
Multiple Choice Questions From CPA Examinations
15-22 a. (3) b. (1) c. (1)
Multiple Choice Questions From Becker CPA Review
15-25 a. (3) b. (3) c. (1)
Discussion Questions and Problems
guidance in the reorganized standards.
a. AS 2315, Audit Sampling, lists benefits and costs of statistical
sampling in section .46. Statistical sampling allows the auditor to
design an efficient sample, measure the sufficiency of evidence,
to use a statistical or nonstatistical approach.
15-8
15-26 (continued)
uncertainties unrelated to sampling (nonsampling risk).
c. According to AS 2315.32, sampling is not always appropriate for
tests of controls. For example, procedures performed during the
planning process to obtain an understanding of internal controls
observation) or the accounting system.
d. These risks are defined in AS 2315.12. The risk of assessing
control risk too low represents the risk that the level of control risk
assessed by the auditor based on the sample is lower than the
control warrants. This risk relates to the efficiency of the audit in
that it could result in the auditor increasing the level of substantive
testing unnecessarily.
a.
SAMPLING
UNIT
NUMBERING SYSTEM
FOR THE POPULATION
EXCEL SELECTION
FORMULA
1. Sales invoice
All invoices numbered
0001 to 8274
=RANDBETWEEN(1,8274)
2. Bill of lading
All bills of lading numbered
18221 through 29427
=RANDBETWEEN(18221,
29427)
3. Customer
A pair of random numbers,
where the first random
number is the page
number (1–20), and the
second random number
is the line number on the
page (1–50)
=RANDBETWEEN(1,20)
and
=RANDBETWEEN(1,50)
15-27 (continued)
copied down to select additional random numbers. When a pair of
random numbers is required, the formula for the first random
number can be entered in the first column, and the formula for the
second random number can be entered in the second column.
b. First five numbers using systematic selection:
SAMPLING UNIT
INTERVAL
RANDOM
STARTING
POINT
FIRST 5
SAMPLE
ITEMS
1. Sales invoice
110 (8274/75)
39
39
149
259
369
479
2. Bill of lading
149 [(29427-18221)
= 11206/75]
18259
18259
18408
18557
18706
18855
3. Customer
13 (979 lines/75)
Page 1, line #11
Page Line
1 11
1 24
1 37
1 50
2 13
the defined population.
15-10
15-28 (see text Web site for Excel solution for part c.- Filename P1528.xls)
be the warehouse removal slip.
b. Attributes sampling method: Assuming the auditor is willing to accept
Nonstatistical sampling method: There is no one right answer
to this question because the sample size is determined using
professional judgment. Due to the relatively small TER (4%), the
c. Systematic sample selection:
22946 = Population size of warehouse removal slips
(34687-11741).
removal slip after (12188, 12498, etc.)
Computer generation of random numbers using Excel (P1528.xls):
=RANDBETWEEN(11741,34687)
numbers.
d. Other audit procedures that could be performed are:
1. Test extensions on attached sales invoices for clerical
accuracy. (Accuracy)
