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17-1
Chapter 17
Audit Sampling for
Tests of Details of Balances
Concept Checks
P. 575
1. The steps in nonstatistical sampling for tests of details of balances
and for tests of controls are almost identical, as illustrated in the text.
objectives, tests of controls and substantives tests of transactions are
designed to measure the occurrence rate of an attribute. In contrast,
2. When a population is not considered acceptable, there are several
possible courses of action:
Perform expanded audit tests in specific areas. If an analysis of
the misstatements indicates that most of the misstatements are of
Increase the sample size. When the auditor increases the sample
size, sampling risk is reduced if the rate of misstatements in the
expanded sample, their dollar amount, and their direction are
Adjust the account balance. When the auditor concludes that an
Request the client to correct the population. In some cases the
Refuse to give an unmodified opinion. If the auditor believes the
recorded amount in accounts receivable or any other account is
17-2
P. 583
1. The sampling interval is the book value of the population being
2. The projected misstatement for the item sampled is the percentage
error multiplied by the sampling interval:
($300/$3000) = .10 x $15,000 = $1,500
P. 588
1. Difference estimation is a method for estimating the total
misstatement in a population by multiplying the average misstatement
(the audited value minus the recorded value) in a random sample by
the number of items in the entire population.
estimating the total audited value of the population by multiplying the
arithmetic average, or mean audited value of the sample times the
number of items in the population.
Stratified mean-per-unit estimation is similar to mean-per-unit
The following are examples where each method could be used:
a. Difference estimation can be used in computing the
balance in accounts receivable by using the misstatements
discovered during the confirmation process, where a significant
number of misstatements are found.
employed.
d. Stratified mean-per-unit estimation can be used to determine
17-3
Concept Check, P. 588 (continued)
2. Tolerable misstatement represents performance materiality for an
individual sampling application. It is the amount of misstatement
the auditor believes can be present in an account and the
account balance still be acceptable for audit purposes.
Perform expanded audit tests in specific areas.
Increase the sample size.
In addition, it may be possible to adjust tolerable misstatement
(upward) and remake the decision. The basis for this would be a
Review Questions
17-1 The most important difference between (a) tests of controls and
substantive tests of transactions and (b) tests of details of balances is in what the
auditor wants to measure. In tests of controls and substantive tests of transactions,
the primary concern is testing the effectiveness of internal controls and the rate
17-2 Stratified sampling is a method of sampling in which all the elements
in the total population are divided into two or more subpopulations. Each
In order for an auditor to obtain a stratified sample of 30 items from each
of three strata in the confirmation of accounts receivable, he or she must first
17-4
Copyright © 2017 Pearson Education, Inc.
17-3 ARIA for tests of details of balances is the equivalent of ARO for tests
of controls and substantive tests of transactions. There is an inverse relation
between ARO for tests of controls and ARIA for tests of details of balances. If
internal controls are considered to be effective, control risk can be reduced. A
lower control risk requires a lower ARO, which requires a larger sample size for
testing. If controls are determined to be effective after testing, control risk can
remain low, which permits the auditor to increase ARIA. An increased ARIA
allows the auditor to reduce sample sizes for tests of details of balances.
17-4 The point estimate is an estimate of the total amount of misstatement in
population book value.
The true value of misstatements in the population is the net sum of all
misstatements in the population and can only be determined by a 100% audit.
17-5 The statement illustrates how the misuse of statistical estimation can
appropriate levels of risk and sample size.
17-6 Monetary unit sampling is a method whereby the population is defined
as the individual dollars (or other currency) making up the account balance. A
attributes sampling yet still provides a statistical result expressed in dollars. It
does this by using attribute tables to estimate the total proportion of population
dollars misstated, based on the number of sample dollars misstated.
a. The risk of incorrect acceptance (ARIA) — this is the risk that the
sample supports the conclusion that the recorded account balance
is not materially misstated when it is materially misstated.
b. The risk of incorrect rejection (ARIR) — this is the risk that the sample
17-5
17-7 (continued)
17-8 The preliminary sample size is calculated as follows:
Confidence factor
(10% ARIA, no expected misstatements) 2.31
is in machine-readable form. As the cumulative total exceeds a successive
random number, the item causing this event is identified as containing the
random dollar unit.
When systematic sampling is used, the population total amount is
using the cumulative method described previously.
17-10 Acceptable risk of incorrect acceptance (ARIA) is the risk the auditor is
willing to take of accepting a balance as correct when the true misstatement in
the balance is greater than tolerable misstatement. ARIA is the equivalent term
substantive tests of transactions.
The primary factor affecting the auditor’s decision about ARIA is control
risk in the audit risk model, which is the extent to which the auditor relies on
internal controls. When internal controls are effective, control risk can be
reduced, which permits the auditor to increase ARIA, which in turn reduces the
and ARIA can be increased.
17-6
Copyright © 2017 Pearson Education, Inc.
17-11 The statement reflects a misunderstanding of the statistical inference
process. The process is based on the long-run probability that the process will
produce correct results in a predictable proportion of the times it is applied.
Thus, a random sampling process that produces a 90% confidence interval will
produce intervals that do, in fact, contain the true population value 90% of the
time. However, the confidence limits of each interval will not all be the same.
17-12 Basic precision is the upper limit when no misstatements are found in
the sample, and represents the minimum allowance for sampling risk inherent
in the sample. It is calculated by multiplying the sampling interval by the
17-13 Misstatement bounds
MISSTATEMENT
RECORDED
VALUE
AUDITED
VALUE
MISSTATEMENT
TAINTING
MISSTATEMENT/
RECORDED
AMOUNT
1
897.16
609.16
288.00
.321
2
47.02
0
47.02
1.000
3
1,621.68
1,522.68
99.00
.061
The calculation of the misstatement bound is given below:
(a)
TAINTING
(b)
SAMPLING
INTERVAL
( c = a x b)
PROJECTED
MISSTATEMENT
(d)
INCREMENTAL
CHANGE IN
CONFIDENCE
FACTOR
(e = c x d)
PROJECTED
MISSTATEMENT PLUS
INCREMENTAL
ALLOWANCE FOR
SAMPLING RISK
1.00
.321
.061
126,250
126,250
126,250
126,250
40,526
7,701
1.58
1.44
1.36
199,475
58,357
10.473
Totals
174,477
268,305
Add basic precisions
126,250 x 2.31
291,638
Upper misstatement bound
559,943
Based on this calculation method, the population is not acceptable as
17-7
17-14 The difficulty in determining sample size lies in estimating the number
and amount of misstatements that may be found in the sample. The upper
bound of a monetary unit sample is sensitive to these factors. Thus, sample
17-15 The population standard deviation is a measure of the difference between
the individual values and the mean of the population. It is calculated for all
variables sampling methods but not for monetary unit sampling. For the auditor,
values in the sample.
The required sample size is directly proportional to the square of the
population standard deviation.
1. No determination was made as to whether a random sample of
100 inventory items would be sufficient to generate an acceptable
net amount.
3. Although no misstatement by itself may be material, other material
4. Regardless of the size of individual or net amounts of misstatements
17-17 Difference estimation can be very effective and very efficient where (1)
an audited value and a book value is available for each population item, (2) a
relatively high frequency of misstatements is expected, and (3) a result in the
form of a confidence interval is desired. In those circumstances, difference
17-8
17-18 Examples of audit conclusions resulting from the use of attributes,
Use of attributes sampling in a test of sales transactions for internal
verification:
We have examined a random sample of 100 sales invoices for
indication of internal verification; two exceptions were noted. Based
does not exceed 6.2%.
Use of monetary unit sampling in a test of sales transactions for existence:
We have examined a random sample of 100 dollar units of sales
transactions for existence. All were supported by properly prepared
Use of variables sampling in confirmation of accounts receivable (in the
form of an interval estimate and a hypothesis test):
We have confirmed a random sample of 100 accounts receivable.
We obtained replies or examined satisfactory other evidence for
misstatement is between $20,000 understatement and $40,000
Multiple Choice Questions from CPA Examinations
17-19 a. (4) b. (2) c. (3)
17-22 a. (4) b. (2) c. (1)
17-9
Discussion Questions and Problems
(6,900,000 x 2) / 150,000
b. If poor results were obtained for tests of controls and substantive
tests of transactions for sales, sales returns and allowances, and
cash receipts, the required sample size for tests of details of
acceptable risk of incorrect acceptance (ARIA).
c. A systematic sample can be selected based on the number of
accounts, or the dollar value of the population. To select a systematic
sample based on the number of accounts, the total number of
into two or more samples.
To select a systematic sample based on the dollar value of
the population, the population value is divided by the required sample
size to obtain the appropriate interval. A random number is then
selected between one and the interval as the starting point. The
selected using this method.
d. The direct projection of error for the sample can be computed as
follows:
(1,500/230,000) x 6,900,000 = $45,000 overstatement
The projected error of $45,000 is well below tolerable misstatement
of $150,000 and provides an allowance for sampling risk of $105,000.
Accordingly, the population is deemed to be fairly stated.
17-10
17-24 (see text Web site for Excel solution for part b.- Filename P1724.xls)
a. The following summarizes the confirmation responses:
Recorded
Value
Confirmation
Response
Misstatement
Acct. 147
$ 24,692
$ 22,486
$ 2,206
Pricing error
Acct. 228
183,219
157,216
26,003
Cutoff error
Acct. 278
7,546
5,546
0
Timing difference
Acct. 497
15,319
0
0
Timing difference
Acct. 564
8,397
7,858
539
Error in quantity
shipped
Acct. 653
32,687
19,328
13,359
Cutoff error
Acct. 830
5,286
0
5,286
Cutoff error
Total misstatement
$47,393
b. Estimate of total misstatement (P1724.xls):
Sample
Value
Sample
Misstatements
Book
Value
Projected
Misstatement
Stratum 1
$1,287,643
$26,003
$1,287,643
$ 26,003
Stratum 2
1,349,678
15,565
4,348,268
50,146
Stratum 3
94,637
5,825
947,682
58,331
Totals
$2,731,958
$47,3935
$6,583,593
$134,480
of $134,480 exceeds tolerable misstatement of $100,000 even
before consideration of sampling risk. The auditor is likely to
propose an adjustment for the actual errors detected and increase
17-25 Addressing misstatements involves auditor judgment, and depends on
Sample
Response
Comment
1
b. Record an adjustment for
actual misstatements
The upper bound will be less than tolerable
misstatement after recording an
adjustment for $20,000.
2
c. Expand sample size
Expanding the sample will lower sampling
risk, which may allow the auditor to accept
the sample.
3
d. Request client to fix the
population
The large number of errors and large
projected misstatement suggests it would
be preferable to have the client fix the
population.
