8/10/2019 Statistical Sampling for Testing Control Procedures
1/25
Statistical Sampling for Testing ControlProcedures
Statistical Sampling for Testing Control Procedures
MULTIPLE CHOICE
1. Auditors who prefer statistical sampling to non-statistical sampling may
do so because statistical sampling helps the auditor
a. Measure the sufficiency of the evidential matter obtained. b. Eliminate
subjectivity in the evaluation of sampling results. c. Reduce the level of
tolerable error to a relatively low amount. d. Minimize the failure to detect amaterial misstatement due to non-sampling risk.
ANSWER: B
2. If all other factors in a sampling plan are held constant, changing the
measure of tolerable error to a smaller value would cause the sample size to
be:
a. Smaller. b. Larger. c. Unchanged. d. Indeterminate.
ANSWER: B
3. Which of the following sampling plans would be designed to estimate a
numerical measurement of a population, such as a dollar value?
a. Numerical sampling. b. Discovery sampling. c. Sampling for attributes. d.
Sampling for variables.
ANSWER: D
4. Based on a random sample, it is estimated that four percent, plus or
minus two percent, of a firm's invoices contain errors. The plus or minus two
percent is known as the estimate's:
8/10/2019 Statistical Sampling for Testing Control Procedures
2/25
a. Precision. b. Accuracy. c. Confidence level. d. Standard error.
ANSWER: A
5. In order to quantify the risk that sample evidence leads to erroneousconclusions about the sampled population
a. Each item in the sampled population must have an equal chance of
being selected. b. Each item in the sampled population must have a
chance of being selected proportional to its book value. c. Each item in
the sampled population must have an equal or known probability of
being selected. d. The precise number of items in the population must
be known.
ANSWER: C
6. Which of the following statements isnottrue regarding audit risk
assessment?
a. The auditor studies the business and industry and applies analytical
procedures as a basis for assessing inherent risk.
b. When control risk and inherent risk are high, the auditor increases
detection risk to maintain overall audit risk at the desired level.
c. The auditor studies and evaluates internal control policies and
procedures for assessing control risk.
d. The auditor designs substantive audit procedures to reduce
detection risk to an acceptable level.
ANSWER: B
7. Which of the following factors does an auditor generally need to consider
in planning a particular audit sample for a control test?
8/10/2019 Statistical Sampling for Testing Control Procedures
3/25
a. Number of items in the population. b. Total dollar amount of the items to
be sampled. c. Estimated standard deviation of the population. d. Tolerable
error.
ANSWER: D
8. Random numbers can be used to select a sample only when each item in
the population:
a. Can be assigned to a specific stratum. b. Is independent of outside
influence. c. Can be identified with a unique number. d. Is expected to be
within plus or minus three standard deviations of the population mean.
ANSWER: C
9. The tolerable occurrence rate for a control test is generally
a. Lower than the expected occurrence rate in the related accounting
records. b. Higher than the expected occurrence rate in the related
accounting records. c. Identical to the expected occurrence rate in the
related accounting records. d. Unrelated to the expected occurrence rate in
the related accounting records.
ANSWER: B
10. An advantage of statistical over non-statistical sampling is that statistical
sampling:
a. Enables auditors to objectively measure the reliability of their sample
results. b. Permits use of a smaller sample size than would be necessary
with non-statistical sampling. c. Is compatible with a wider variety of sample
selection methods than is non-statistical sampling. d. Allows auditors to
inject their subjective judgment in determining sample size and selection
process in order to audit items of greatest value and highest risk.
ANSWER: A
8/10/2019 Statistical Sampling for Testing Control Procedures
4/25
11. An auditor samples cash disbursement records for significant errors of
$5 or more. Upon finding one such error, these records are scheduled for a
complete review. This conclusion is most likely based on a
a. Cluster sample. b. Discovery sample. c. Systematic sample. d. Stratified
sample.
ANSWER: B
12. Of the following statements, which one best differentiates statistical
sampling from nonstatistical sampling?
a. Statistical sampling is a mathematical approach to inference,
whereas nonstatistical sampling is a more subjective approach.
b. Nonstatistical sampling has greater applicability to large populations
than does statistical sampling.
c. Nonstatistical sampling is more subjective, but produces greater
consistency in the application of audit judgment.
d. Nonstatistical sampling has greater applicability to populations that
lend themselves to random selection.
ANSWER: A
13. In examining cash disbursements, an auditor plans to choose a sample
using systematic selection with a random start. The primary advantage
of such a systematic selection is that population items
a. Which include errors will not be overlooked when the auditor exercisescompatible reciprocal options.
b. May occur in a systematic pattern, thus making the sample more
representative. c. May occur more than once in a sample. d. Do not have to
be prenumbered in order for the auditor to use the technique.
8/10/2019 Statistical Sampling for Testing Control Procedures
5/25
ANSWER: D
14. When planning an attribute sampling application, the difference between
the expected occurrence rate and the tolerable occurrence rate is the
planned
a. Precision. b. Reliability. c. Dispersion. d. Skewness.
ANSWER: A
15. If certain forms are not consecutively numbered
a. Selection of a random sample probably is not possible. b. Systematic
sampling may be appropriate. c. Stratified sampling should be used. d.
Random number tables cannot be used.
ANSWER: B
16. In an attribute sampling application, holding other factors constant,
sample size will increase as which of the following becomes smaller?
a. Reliability level. b. Population. c. Planned precision. d. Expected rate of
occurrence.
ANSWER: C
17. Which of the following sampling methods is most useful to auditors when
testing for internal control effectiveness?
a. Stratified random sampling. b. Attribute sampling. c. Variables sampling.
d. Unrestricted random sampling with replacement.
ANSWER: B
18. Attribute sampling, as applied to control testing, can assist the auditor in
several ways. Which of the following tasks isnotenhanced by
sampling?
8/10/2019 Statistical Sampling for Testing Control Procedures
6/25
a. Determining the number of documents to examine in testing for a
specific attribute.
b. Selecting the documents to be tested.
c. Examining the documents.
d. Evaluating the sample results.
ANSWER: C
19. Which of the following is an element of sampling risk?
a. Choosing an audit procedure that is inconsistent with the audit objective.b. Choosing a sample size that is too small to achieve the sampling
objective. c. Failing to detect an error on a document that has been
inspected by the auditor. d. Failing to perform audit procedures that are
required by the sampling plan.
ANSWER: B
20. Which of the following wouldnotbe an attribute of interest to an auditor
performing control tests?
a. Do selling prices agree with published price lists?
b. Do purchased parts meet established quality standards?
c. Are proper labor rates being used to compute payroll?
d. Are account distributions (debits and credits) correct?
ANSWER: B
21. The precision limit for control testing necessary to justify lowering the
assessed control risk level depends primarily on which of the following?
8/10/2019 Statistical Sampling for Testing Control Procedures
7/25
8/10/2019 Statistical Sampling for Testing Control Procedures
8/25
24. If all other factors in a sampling plan are held constant, changing the
risk of underassessment from five percent to
three percent would cause the sample size to be:
a. Smaller. b. Larger. c. Unchanged. d. Indeterminate.
ANSWER: B
25. An auditor performs a test to determine whether all merchandise for
which the client was billed was received. The population for this test consists
of all
a. Merchandise received. b. Vendors' invoices. c. Canceled checks. d.
Receiving reports.
ANSWER: B
26. Although mathematically based, statistical sampling does not replace
audit judgment. In utilizing statistical sampling techniques, the auditor
must apply judgment in all but which of the following tasks?
a. Selecting a tolerable rate of error.
b. Determining an acceptable risk of underassessing
control risk.
c. Calculating the actual error rate.
d. Assessing the materiality of control weaknesses.
ANSWER: C
27. To determine sample size in an attribute sampling application, what
must be specified?
8/10/2019 Statistical Sampling for Testing Control Procedures
9/25
8/10/2019 Statistical Sampling for Testing Control Procedures
10/25
obtained to plan the audit and to determine the nature, timing, and extent of
tests to be performed. d. Sufficient competent evidential matter is to be
obtained through inspection, observation, inquiries, and confirmations to
afford a reasonable basis for an opinion regarding the financial statements
under examination.
ANSWER: B
30. The major weakness of nonstatistical (judgmental) sampling is it
a. Usually requires larger sample sizes than statistical sampling. b. Does not
allow sampling risk to be objectively measured. c. Frequently results in
samples that are not representative of the population. d. Gives less accuratepoint estimates of parameters than statistical sampling.
ANSWER: B
31. An auditor is testing credit authorization procedures by examining sales
invoices for credit approval by the credit department. The procedures will be
considered to be working adequately if 96% of all sales invoices either
indicate approval or are cash sales. The auditor selects a random sample of
100 invoices. In this situation, which of the following outcomes illustrates
underassessment?
a. The auditor finds five deviations and concludes that procedures work
inadequately. The actual population deviation rate is 2%. b. The auditor
finds no deviations and concludes that procedures work adequately. The true
population deviation rate is 5%. c. The auditor finds no deviations and
concludes that the procedures work adequately. The true population
deviation rate is 2%. d. The auditor finds five deviations and concludes thatprocedures work inadequately. The true population deviation rate is 6%.
ANSWER: B
8/10/2019 Statistical Sampling for Testing Control Procedures
11/25
32. If an auditor, planning to use statistical sampling, is concerned with the
number of a client's sales invoices that contain mathematical errors, the
auditor would most likely utilize
a. Random sampling with replacement. b. Sampling for attributes. c.
Sampling for variables. d. Stratified random sampling.
ANSWER: B
33. An advantage of using statistical over non-statistical sampling methods
in tests of controls is that the statistical methods
a. Afford greater assurance than a non-statistical sample of equal size. b.
Provide an objective basis for quantitatively evaluating sample risks. c. Can
more easily convert the sample into a dual-purpose test useful for
substantive testing. d. Eliminate the need to use judgment in determining
appropriate sample sizes.
ANSWER: B
34. Several risks are inherent in the evaluation of audit evidence which has
been obtained through the use of statistical sampling. Which of the followingrisks is an example of the risk of underassessment of control risk?
a. Failure to properly define the population to be sampled.
b. Failure to draw a random sample from the population. c. Failure to
accept the statistical hypothesis that
internal control is unreliable when, in fact, it is. d. Failure to
accept the statistical hypothesis that a book value is not materially
misstated when the true book value is not materially misstated.
ANSWER: C
8/10/2019 Statistical Sampling for Testing Control Procedures
12/25
35. As a result of tests of controls, an auditor underassessed control risk and
decreased substantive testing. This underassessment occurred because the
true occurrence rate in the population was
a. Less than the risk of underassessment in the auditor's sample. b. Less
than the occurrence rate in the auditor's sample. c. More than the risk of
underassessment in the auditor's sample. d. More than the occurrence rate
in the auditor's sample.
ANSWER: D
36. If all other factors specified in an attribute sampling plan remain
constant, changing the specified precision from 6% to 10%, andchanging the specified reliability from 97% to 93% would cause the
required sample size to
a. Increase. b. Remain the same. c. Decrease. d. Change by 4%.
ANSWER: C
37. Which of the following factors is generally not considered in determining
the sample size for a test of controls?
a. Population size. b. Tolerable rate. c. Risk of underassessment. d. Expected
population occurrence rate.
ANSWER: A
38. The expected population occurrence rate of client billing errors is 3%.
The auditor has established a tolerable rate of 5%. In the review of client
invoices the auditor should use
a. Stratified sampling. b. Variable sampling. c. Discovery sampling. d.
Attribute sampling.
ANSWER: D
8/10/2019 Statistical Sampling for Testing Control Procedures
13/25
39. An auditor desired to test credit approval on 10,000 sales invoices
processed during the year. The auditor designed a statistical sample that
would provide a 1% risk of assessing control risk too low (99% confidence)
that not more than 7% of the sales invoices lacked approval. The auditor
estimated from previous experience that about 2 1/2% of the sales invoices
lacked approval. A sample of 200 invoices was examined and 7 of them were
lacking approval. The auditor then determined the upper occurrence limit to
be 8%. In the evaluation of this sample, the auditor decided to increase the
level of the preliminary assessment of control risk because the
a. Tolerable rate (7%) was less than the achieved upper occurrence limit
(8%). b. Expected occurrence rate (7%) was more than the percentage of
errors in the sample (3 1/2%). c. Achieved upper occurrence limit (8%) was
more than the percentage of errors in the sample (3 1/2%). d. Expected
occurrence rate (2 1/2%) was less than the tolerable rate (7%).
ANSWER: A
40. To evaluate the sample results for an attributes sampling application, a
measure of precision is required. Which of the following statements is true
regarding precision?
a. Precision is subtracted from the tolerable rate of error to determine
the acceptability of sample results. b. Precision is added to the
tolerable rate of error to determine the acceptability of sample results.
c. Precision is subtracted from the sample occurrence rate and the
result is compared to the tolerable rate of error. d. Precision is added
to the sample occurrence rate and the result is compared to the
tolerable rate of error.
ANSWER: D
41. An auditor who uses statistical sampling for attributes in testing internal
controls should increase the assessed level of control risk when the
8/10/2019 Statistical Sampling for Testing Control Procedures
14/25
a. Sample occurrence rate is less than the expected occurrence rate used in
planning the sample. b. Tolerable rate less the allowance for sampling risk
exceeds the sample occurrence rate. c. Sample occurrence rate plus the
allowance for sampling risk exceeds the tolerable rate. d. Sample occurrence
rate plus the allowance for sampling risk equals the tolerable rate.
ANSWER: C
42. Which of the following statements is correct concerning statistical
sampling for control testing?
a. The population size has little or no effect on determining sample size
except for very small populations. b. The expected population occurrencerate has little or no effect on determining sample size except for very small
populations. c. As the population size doubles, the sample size also should
double. d. For a given tolerable rate, a larger sample size should be selected
as the expected population deviation rate decreases.
ANSWER: A
43. An auditor wishes to determine if the error rate on travel reimbursement
claims is within the five-percent tolerance level set by management.
What sampling plan should the auditor use?
a. Variables sampling. b. Attribute sampling. c. Judgment sampling. d. PPS
sampling.
ANSWER: B
44. The auditor samples cash disbursements for minor errors of $5 or less.
The parameter to be estimated is the error rate, which might be as high as
10%. The auditor is most likely to use
a. Block sampling. b. Variables sampling. c. Attributes sampling. d.
Discovery sampling.
8/10/2019 Statistical Sampling for Testing Control Procedures
15/25
ANSWER: C
45. An important difference between a statistical sample and a non-
statistical (judgmental) sample is that with a statistical sample:
a. No judgment is required, everything is by formula. b. A smaller sample
size can be used. c. More accurate results are obtained. d. Population
estimates with measurable reliability can be made.
ANSWER: D
COMPLETION:
47. Statistical sampling for attributes is most applicable in situations where a
visiblein the form ofexists.
ANSWER: AUDIT TRAIL, DOCUMENTATION
48. As contrasted with statistical sampling, nonstatistical sampling is a
moreapproach to inference.
ANSWER: SUBJECTIVE
49.estimates the frequency of events, whereasis an estimate of amount.
ANSWER: ATTRIBUTE SAMPLING, VARIABLES SAMPLING
50. Theis the anticipated error rate, whereas theis the maximum rate of
error acceptable to the auditor, while still warranting a lowering of
assessed control risk below the maximum level.
ANSWER: EXPECTED OCCURRENCE RATE, TOLERABLE OCCURRENCE RATE
51. Thethe precision range, the larger the sample size.
ANSWER: NARROWER
8/10/2019 Statistical Sampling for Testing Control Procedures
16/25
52. The more critical an attribute to those control policies and procedures
relevant to an audit, thethe tolerable occurrence rate.
ANSWER: LOWER
53.Another term for "risk of underassessment" is____________
` risk.
ANSWER: BETA
54. Random selection requires that items to be included in the sample must
be drawn on abasis.
ANSWER: PROBABILITY
55. When documents are not prenumbered, an acceptable alternative to the
use of random number tables or computer-generated numbers is.
ANSWER: SYSTEMATIC SAMPLING
56. Under conditions ofdetection risk, a minimal quantity of audit evidence
is needed.
ANSWER: HIGH
MATCHING:
57. Indicate by letter the term matching the definition given.
A. Attribute sampling
B. Alpha risk
C. Discovery sampling
D. Beta risk
8/10/2019 Statistical Sampling for Testing Control Procedures
17/25
E. Expected occurrence rate
F. Precision
G. Discovery sampling
H. Sampling risk
I. Systematic sampling
J. Tolerable occurrence rate
K. Upper occurrence limit
L. Variables sampling
____1. An estimate of frequency of events.
____2. An orderly approach to locating a particular event.
____3. The anticipated error rate.
____4. Risk of underassessment.
____5. Maximum rate of error acceptable to the auditor.
____6. Risk that the auditors conclusions about a population
will be incorrect.
____7. A random selection method that involves choosing every
nth item in the population until the requisite sample
size has been reached.
____8. The calculated maximum error rate based on the results of
8/10/2019 Statistical Sampling for Testing Control Procedures
18/25
sampling.
____9. Risk of overassessment.
____10. Range within the true answer most likely falls.
SOLUTION:
1. A
2. C
3. E
4. D
5. J
6. H
7. I
8. K
9. B
10. F
PROBLEM/ESSAY:
58. Margaret Hopkins, CPA, wishes to test the effectiveness of internal
controls over the customer billing function of
Jacks Wholesale Hardware, an audit client. Hopkins has
identified the following attributes to be tested. For each
attribute, indicate the appropriate sampling unit and
8/10/2019 Statistical Sampling for Testing Control Procedures
19/25
carefully define what constitutes an error.
1. Does the customer order agree with the invoice as to
type and quantity of goods?
2. Does the shipping order agree with the invoice as to
type and quantity of goods?
3. Has customer credit been approved?
4. Does the invoice amount cause the customer to exceed
the prepared credit limit?
5. Have goods been billed but not shipped?
6. Have goods been shipped but not billed?
7. Do invoiced prices agree with official price lists?
8. Do credit and discount terms appearing on face of customer invoice
accord with company policy?
9. Are proper accounts debited and credited?
SOLUTION:
1. SAMPLING UNIT: Sales invoice
ERROR: Lack of agreement between invoice and order
as to:
Type of goods
Quantity of goods
8/10/2019 Statistical Sampling for Testing Control Procedures
20/25
Price of goods
Credit and discount terms
2. SAMPLING UNIT: Sales invoice
ERROR: Lack of agreement between invoice and
shipping order as to:
Type of goods
Quantity of goods
3. SAMPLING UNIT: Sales invoice
ERROR: Lack of evidence of credit approval on face
of invoice
4. SAMPLING UNIT: Sales invoice
ERROR: Invoice amount plus previous customer balance exceeds prepared
credit limit
5. SAMPLING UNIT: Sales invoice
ERROR: Shipping order and/or bill of lading not
attached to customer invoice
6. SAMPLING UNIT: Bill of lading
ERROR: Matching invoice not located
7. SAMPLING UNIT: Sales invoice
ERROR: Price not in agreement with master price list
8/10/2019 Statistical Sampling for Testing Control Procedures
21/25
and no evidence of proper approval of billed price
8. SAMPLING UNIT: Sales invoice
ERROR: Credit and/or discount terms at variance with company policy, andno evidence of proper approval of quoted credit and discount terms.
9. SAMPLING UNIT: Sales invoice
ERROR: Incorrect debits or credits appearing on face
of invoice and not corrected before posting
accounts.
59. Sampling can assist the auditor in various ways during the examination
of documentary evidence for tests of internal
controls. Using a vouchering and vendor billing application
as an example, assume that you are interested in evaluating
internal controls relative to ordering goods, receiving
goods, and processing vendor invoices. Discuss how attribute sampling
might assist you in the following phases
of your tests of controls:
a. Determining the number of vouchers to test;
b. Selecting the vouchers for testing;
c. Evaluating the results of the voucher test;
d. Assessing audit risk associated with the
expenditure cycle.
8/10/2019 Statistical Sampling for Testing Control Procedures
22/25
SOLUTION:
a. In determining the number of vouchers to test, the auditor will need to
set a tolerable occurrence rate and an acceptable risk of underassessment.
These parameters, along with an estimated occurrence rate may then be
used as inputs to determining sample size.
b. If vouchers are prenumbered, the auditor can elect to use a random
selection approach to selecting vouchers test
for predefined attributes.
c. Having examined the sample for the attributes of interest, the auditor can
calculate the observed error
rate and the upper occurrence limit.
d. The upper occurrence limit can be compared with the tolerable occurrence
rate to support raising or lowering the assessed level of control risk.
60. George Jones, CPA, wishes to test payroll controls for
Hopkins Manufacturing, an audit client. He has identified
the following attributes of interest for testing purposes:
1. Correctness of pay rates and hours used in
preparing the payroll summary;
2. Genuineness of listed employees;
3. Correctness of gross pay, withholdings, and net
pay;
4. Correctness of debits and credits.
8/10/2019 Statistical Sampling for Testing Control Procedures
23/25
A pilot test of forty payroll transactions revealed the following errors: One
transaction revealed an incorrect
pay rate; two transactions resulted in incorrect
calculations of either gross pay or withholdings; and two
transactions resulted in erroneous debits or credits. All
listed employees were found to be working for the company
during the pay period being tested. Jones believes that
four or more errors for each of the four attributes is
significant.
Required:
a. Based on the pilot sample, calculate the expected
occurrence rate and the tolerable occurrence rate for
each attribute.
b. In determining sample size, Jones can select an
expected occurrence rate ranging from the low for
attribute number 2 to the high for attributes 3 and 4.
What impact will a low rate relative to a high rate
have on the calculated sample size?
c. What other factors must Jones consider before
determining the sample size?
8/10/2019 Statistical Sampling for Testing Control Procedures
24/25
c. Assuming that a sample of 100 payroll summary entries
produced the following calculated upper occurrence
limits, what impact will these limits have on
Jones substantive audit program?
Attribute 1: 7.0%
Attribute 2: 4.0%
Attribute 3: 12.0%
Attribute 4: 6.0%
SOLUTION:
a. The tolerable occurrence rate is 10% (4/40) for each
of the attributes. The expected occurrence rates are:
Attribute No. 1: 2.5%
Attribute No. 2: 0.0%
Attribute No. 3: 5.0%
Attribute No. 4: 5.0%
b. The higher the expected occurrence rate, the larger
will be the sample size.
c. Jones must determine the acceptable risk of
underassessing control risk.
8/10/2019 Statistical Sampling for Testing Control Procedures
25/25
d. Only attribute 3 produces an unacceptable upper
occurrence limit, exceeding the tolerable rate of 10%.
Given incorrect calculation of gross pay, withholdings,
and net pay, Jones should plan to focus more heavily
on inventory costing, inasmuch as inventory includes
both direct and indirect labor components. He should
also concentrate on payroll cost included in general
and administrative expense, as well as on accrued
payroll and payroll taxes payable at year end.
Incorrect calculation of gross pay and withholdings
will also impact the calculation of employers payroll
tax expense. Therefore, Jones must plan to audit these
accounts more intensively than under conditions of
strong internal control.