Statistical Sampling for Testing Control Procedures MULTIPLE CHOICE 1. Auditors who prefer statistical sampling to non- statistical sampling may do so because statistical sampling hel ps the auditor a. Measure the sufficiency of the evidential matter obtained. b. Eliminate subjectivity in the evaluation of samp ling results. c. Reduce the level of tolerable error to a rel atively low amount. d. Minimize the failure to detect a material miss tatement 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 smal ler 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 de signed to estimate a numerical measurement of a population, s uch 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 f our percent, plus or minus two percent, of a firm's invoices contain errors. The plus or minus two percent is known a
Transcript
Statistical Sampling for Testing ControlProcedures
MULTIPLE CHOICE
1. Auditors who prefer statistical sampling to non-statisticalsampling may do so because statistical sampling helps theauditora. 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 a material 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 valuewould 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 toestimate a numerical measurement of a population, such as adollar 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 containerrors. The plus or minus two percent is known as theestimate's:a. Precision.b. Accuracy.c. Confidence level.d. Standard error.
ANSWER: A
142Chapter 9 Statistical Sampling for Testing Control Procedures 143
5. In order to quantify the risk that sample evidence leads toerroneous conclusions about the sampled populationa. 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 is not true regardingaudit risk assessment?a. The auditor studies the business and industry and
applies analytical procedures as a basis for assessinginherent risk.
b. When control risk and inherent risk are high, theauditor increases detection risk to maintain overallaudit risk at the desired level.
c. The auditor studies and evaluates internal controlpolicies and procedures for assessing control risk.
d. The auditor designs substantive audit procedures toreduce detection risk to an acceptable level.
ANSWER: B
7. Which of the following factors does an auditor generallyneed to consider in planning a particular audit sample for acontrol test?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 eachitem 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 isgenerally
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a. Lower than the expected occurrence rate in the relatedaccounting 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 isthat 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 orderto audit items of greatest value and highest risk.
ANSWER: A
11. An auditor samples cash disbursement records for significanterrors of $5 or more. Upon finding one such error, theserecords are scheduled for a complete review. Thisconclusion is most likely based on aa. Cluster sample.b. Discovery sample.c. Systematic sample.d. Stratified sample.
ANSWER: B
12. Of the following statements, which one best differentiatesstatistical sampling from nonstatistical sampling?a. Statistical sampling is a mathematical approach to
inference, whereas nonstatistical sampling is a moresubjective approach.
b. Nonstatistical sampling has greater applicability tolarge populations than does statistical sampling.
c. Nonstatistical sampling is more subjective, butproduces greater consistency in the application ofaudit judgment.
d. Nonstatistical sampling has greater applicability topopulations that lend themselves to random selection.
ANSWER: AChapter 9 Statistical Sampling for Testing Control Procedures 145
13. In examining cash disbursements, an auditor plans to choosea sample using systematic selection with a random start.The primary advantage of such a systematic selection is thatpopulation itemsa. Which include errors will not be overlooked when the
auditor exercises compatible reciprocal options.
b. May occur in a systematic pattern, thus making thesample 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.
ANSWER: D
14. When planning an attribute sampling application, thedifference between the expected occurrence rate and thetolerable occurrence rate is the planneda. Precision.b. Reliability.c. Dispersion.d. Skewness.
ANSWER: A
15. If certain forms are not consecutively numbereda. 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 factorsconstant, sample size will increase as which of thefollowing 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 toauditors when testing for internal control effectiveness?a. Stratified random sampling.b. Attribute sampling.c. Variables sampling.d. Unrestricted random sampling with replacement.
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ANSWER: B
18. Attribute sampling, as applied to control testing, canassist the auditor in several ways. Which of the followingtasks is not enhanced by sampling?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 would not be an attribute of interestto 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 tojustify lowering the assessed control risk level dependsprimarily on which of the following?a. The cause of the errors.b. The materiality of the attribute(s) to be tested.c. The amount of any substantive errors.d. The limit used in audits of similar clients.
ANSWER: B
22. Which of the following statements concerning sample size istrue?a. An increase in the tolerable occurrence rate, other
factors remaining unchanged, increases sample size.Chapter 9 Statistical Sampling for Testing Control Procedures 147
b. The higher the expected occurrence rate, other factorsremaining unchanged, the larger will be the samplesize.
c. The more critical the attribute being tested, thehigher will be the tolerable occurrence rate set by theauditor, and the larger will be the sample size.
d. The lower the acceptable risk of underassessment ofcontrol risk, the smaller will be the sample size.
ANSWER: B
23. In the examination of the financial statements of DeltaCompany, the auditor determines that in performing a test ofinternal control effectiveness, the rate of error in thesample does not support the auditor's preconceived notion ofa tolerable occurrence rate when, in fact, the actual errorrate in the population does meet the auditor's notion ofeffectiveness. This situation illustrates the risk of
a. Underassessment of control risk.b. Overassessment of control risk.c. Incorrect rejection.d. Incorrect acceptance.
ANSWER: B
24. If all other factors in a sampling plan are held constant,changing the risk of underassessment from five percent tothree 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 allmerchandise for which the client was billed was received.The population for this test consists of alla. Merchandise received.b. Vendors' invoices.c. Canceled checks.d. Receiving reports.
ANSWER: B
26. Although mathematically based, statistical sampling does notreplace audit judgment. In utilizing statistical samplingtechniques, the auditor must apply judgment in all but whichof the following tasks?
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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 samplingapplication, what must be specified?a. Population mean, expected error rate, precision.b. Precision, reliability, standard deviation.c. Precision, reliability, expected occurrence rate.d. Population mean, standard deviation, precision.
ANSWER: C
28. Which of the following statements regarding statisticalsampling in auditing is true?a. Inasmuch as audits are test-based, generally accepted
auditing standards require the use of statisticalsampling methods whenever the auditor decides toexamine only part of a population.
b. Although statistical sampling may be applied to controltesting, it is required for substantive testingpurposes.
c. Sampling methods are used by auditors in both controltesting and substantive testing.
d. Statistical sampling methods are more appropriate forcontrol testing when the auditor elects to reprocesstransactions, than when controls are tested by means ofdocument examination.
ANSWER: C
29. The application of statistical sampling techniques is leastrelated to which of the following generally acceptedauditing standards?a. The work is to be adequately planned and assistants, if
any, are to be properly supervised.b. In all matters relating to the assignment, an independ-
ence in mental attitude is to be maintained by theauditor or auditors.
c. A sufficient understanding of the internal controlsystem is to be obtained to plan the audit and todetermine the nature, timing, and extent of tests to beperformed.
d. Sufficient competent evidential matter is to beobtained through inspection, observation, inquiries,and confirmations to afford a reasonable basis for an
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opinion regarding the financial statements underexamination.
ANSWER: B
30. The major weakness of nonstatistical (judgmental) samplingis ita. 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 accurate point estimates of parameters than
statistical sampling.
ANSWER: B
31. An auditor is testing credit authorization procedures byexamining sales invoices for credit approval by the creditdepartment. The procedures will be considered to be workingadequately if 96% of all sales invoices either indicateapproval or are cash sales. The auditor selects a randomsample of 100 invoices. In this situation, which of thefollowing 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 populationdeviation rate is 5%.
c. The auditor finds no deviations and concludes that theprocedures work adequately. The true populationdeviation rate is 2%.
d. The auditor finds five deviations and concludes thatprocedures work inadequately. The true populationdeviation rate is 6%.
ANSWER: B
32. If an auditor, planning to use statistical sampling, isconcerned with the number of a client's sales invoices thatcontain mathematical errors, the auditor would most likelyutilizea. Random sampling with replacement.b. Sampling for attributes.c. Sampling for variables.d. Stratified random sampling.
ANSWER: B150 Chapter 9 Statistical Sampling for Testing Control Procedures
33. An advantage of using statistical over non-statisticalsampling methods in tests of controls is that thestatistical methodsa. 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 auditevidence which has been obtained through the use ofstatistical sampling. Which of the following risks is anexample 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 truebook value is not materially misstated.
ANSWER: C
35. As a result of tests of controls, an auditor underassessed
control risk and decreased substantive testing. Thisunderassessment occurred because the true occurrence rate inthe population wasa. 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 planremain constant, changing the specified precision from 6% to10%, and changing the specified reliability from 97% to 93%would cause the required sample size toa. Increase.b. Remain the same.
Chapter 9 Statistical Sampling for Testing Control Procedures 151
c. Decrease.d. Change by 4%.
ANSWER: C
37. Which of the following factors is generally not consideredin 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 billingerrors is 3%. The auditor has established a tolerable rateof 5%. In the review of client invoices the auditor shouldusea. Stratified sampling.b. Variable sampling.c. Discovery sampling.d. Attribute sampling.
ANSWER: D
39. An auditor desired to test credit approval on 10,000 salesinvoices processed during the year. The auditor designed astatistical sample that would provide a 1% risk of assessingcontrol risk too low (99% confidence) that not more than 7%of the sales invoices lacked approval. The auditor estimatedfrom previous experience that about 2 1/2% of the salesinvoices lacked approval. A sample of 200 invoices wasexamined and 7 of them were lacking approval. The auditorthen determined the upper occurrence limit to be 8%. In theevaluation of this sample, the auditor decided to increasethe level of the preliminary assessment of control risk
because thea. 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: A152 Chapter 9 Statistical Sampling for Testing Control Procedures
40. To evaluate the sample results for an attributes samplingapplication, a measure of precision is required. Which ofthe 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 oferror.
d. Precision is added to the sample occurrence rate andthe result is compared to the tolerable rate of error.
ANSWER: D
41. An auditor who uses statistical sampling for attributes intesting internal controls should increase the assessed levelof control risk when thea. 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 concerningstatistical sampling for control testing?a. The population size has little or no effect on
determining sample size except for very smallpopulations.
b. The expected population occurrence rate has little orno effect on determining sample size except for verysmall populations.
c. As the population size doubles, the sample size alsoshould double.
d. For a given tolerable rate, a larger sample size shouldbe selected as the expected population deviation ratedecreases.
ANSWER: A
43. An auditor wishes to determine if the error rate on travelreimbursement claims is within the five-percent tolerancelevel set by management. What sampling plan should theauditor use?
Chapter 9 Statistical Sampling for Testing Control Procedures 153
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 errorrate, which might be as high as 10%. The auditor is mostlikely to usea. Block sampling.b. Variables sampling.c. Attributes sampling.d. Discovery sampling.
ANSWER: C
45. An important difference between a statistical sample and anon-statistical (judgmental) sample is that with astatistical 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 insituations where a visible in the formof exists.
ANSWER: AUDIT TRAIL, DOCUMENTATION
48. As contrasted with statistical sampling, nonstatisticalsampling is a more approach to inference.
ANSWER: SUBJECTIVE
49. estimates the frequency of events,whereas is an estimate of amount.
ANSWER: ATTRIBUTE SAMPLING, VARIABLES SAMPLING
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50. The is the anticipatederror rate, whereas the isthe maximum rate of error acceptable to the auditor, whilestill warranting a lowering of assessed control risk belowthe maximum level.
____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 auditor’s conclusions about a populationwill be incorrect.
____7. A random selection method that involves choosing everynth item in the population until the requisite samplesize has been reached.
____8. The calculated maximum error rate based on the results ofsampling.
____9. Risk of overassessment.
____10. Range within the true answer most likely falls.
SOLUTION:
1. A2. C3. E4. D5. J6. H7. I8. K9. B10. F
PROBLEM/ESSAY:
58. Margaret Hopkins, CPA, wishes to test the effectiveness ofinternal controls over the customer billing function ofJack’s Wholesale Hardware, an audit client. Hopkins hasidentified the following attributes to be tested. For each
156 Chapter 9 Statistical Sampling for Testing Control Procedures
attribute, indicate the appropriate sampling unit andcarefully define what constitutes an error.
1. Does the customer order agree with the invoice as totype and quantity of goods?
2. Does the shipping order agree with the invoice as totype 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 invoiceERROR: Lack of agreement between invoice and order
as to:Type of goodsQuantity of goodsPrice of goodsCredit and discount terms
2. SAMPLING UNIT: Sales invoiceERROR: Lack of agreement between invoice and
shipping order as to:Type of goodsQuantity of goods
3. SAMPLING UNIT: Sales invoiceERROR: Lack of evidence of credit approval on face
of invoice
4. SAMPLING UNIT: Sales invoiceERROR: Invoice amount plus previous customer
balance exceeds prepared credit limit
5. SAMPLING UNIT: Sales invoiceERROR: Shipping order and/or bill of lading not
attached to customer invoice
6. SAMPLING UNIT: Bill of ladingERROR: Matching invoice not located
7. SAMPLING UNIT: Sales invoiceERROR: Price not in agreement with master price list
Chapter 9 Statistical Sampling for Testing Control Procedures 157
and no evidence of proper approval ofbilled price
8. SAMPLING UNIT: Sales invoiceERROR: Credit and/or discount terms at variance with
company policy, and no evidence of properapproval of quoted credit and discountterms.
9. SAMPLING UNIT: Sales invoiceERROR: Incorrect debits or credits appearing on face
of invoice and not corrected before postingaccounts.
59. Sampling can assist the auditor in various ways during theexamination of documentary evidence for tests of internalcontrols. Using a vouchering and vendor billing applicationas an example, assume that you are interested in evaluatinginternal controls relative to ordering goods, receivinggoods, and processing vendor invoices. Discuss howattribute sampling might assist you in the following phasesof 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.
SOLUTION:
a. In determining the number of vouchers to test, theauditor will need to set a tolerable occurrence rate and anacceptable risk of underassessment. These parameters,along with an estimated occurrence rate may then be used asinputs to determining sample size.
b. If vouchers are prenumbered, the auditor can elect to usea random selection approach to selecting vouchers testfor predefined attributes.
c. Having examined the sample for the attributes ofinterest, the auditor can calculate the observed errorrate and the upper occurrence limit.
d. The upper occurrence limit can be compared with thetolerable occurrence rate to support raising or loweringthe assessed level of control risk.
60. George Jones, CPA, wishes to test payroll controls forHopkins Manufacturing, an audit client. He has identifiedthe following attributes of interest for testing purposes:
1. Correctness of pay rates and hours used inpreparing the payroll summary;
158 Chapter 9 Statistical Sampling for Testing Control Procedures
2. Genuineness of listed employees;3. Correctness of gross pay, withholdings, and net
pay;4. Correctness of debits and credits.
A pilot test of forty payroll transactions revealed thefollowing errors: One transaction revealed an incorrectpay rate; two transactions resulted in incorrectcalculations of either gross pay or withholdings; and twotransactions resulted in erroneous debits or credits. Alllisted employees were found to be working for the companyduring the pay period being tested. Jones believes thatfour or more errors for each of the four attributes issignificant.
Required:a. Based on the pilot sample, calculate the expected
occurrence rate and the tolerable occurrence rate foreach attribute.
b. In determining sample size, Jones can select anexpected occurrence rate ranging from the low forattribute number 2 to the high for attributes 3 and 4.What impact will a low rate relative to a high ratehave on the calculated sample size?
c. What other factors must Jones consider beforedetermining the sample size?
c. Assuming that a sample of 100 payroll summary entriesproduced the following calculated upper occurrencelimits, what impact will these limits have onJones substantive audit program?
a. The tolerable occurrence rate is 10% (4/40) for eachof 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 largerwill be the sample size.
c. Jones must determine the acceptable risk ofunderassessing control risk.
d. Only attribute 3 produces an unacceptable upperChapter 9 Statistical Sampling for Testing Control Procedures 159
occurrence limit, exceeding the tolerable rate of 10%.Given incorrect calculation of gross pay, withholdings,and net pay, Jones should plan to focus more heavilyon inventory costing, inasmuch as inventory includesboth direct and indirect labor components. He shouldalso concentrate on payroll cost included in generaland administrative expense, as well as on accruedpayroll and payroll taxes payable at year end.Incorrect calculation of gross pay and withholdingswill also impact the calculation of employer’s payrolltax expense. Therefore, Jones must plan to audit theseaccounts more intensively than under conditions ofstrong internal control.
