Statistical Sampling for Testing Control Procedures

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 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 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:

a. Precision. b. Accuracy. c. Confidence level. d. Standard error.

ANSWER: A

5. In order to quantify the risk that sample evidence leads to erroneous conclusions 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 is not true 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?

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

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 exercises compatible 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.

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 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 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?

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 is true?

a. An increase in the tolerable occurrence rate, other factors remaining unchanged, increases sample size.

b. The higher the expected occurrence rate, other factors remaining unchanged, the larger will be the sample size.

c. The more critical the attribute being tested, the higher will be the tolerable occurrence rate set by the auditor, and the larger will be the sample size.

d. The lower the acceptable risk of underassessment of control risk, the smaller will be the sample size.

ANSWER: B

23. In the examination of the financial statements of Delta Company, the auditor determines that in performing a test of internal control effectiveness, the rate of error in the sample does not support the auditor's preconceived notion of a tolerable occurrence rate when, in fact, the actual error rate in the population does meet the auditor's notion of effectiveness. 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 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?

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 statistical sampling in auditing is true?

a. Inasmuch as audits are test-based, generally accepted auditing standards require the use of statistical

sampling methods whenever the auditor decides to

examine only part of a population.

b. Although statistical sampling may be applied to control testing, it is required for substantive testing

purposes.

c. Sampling methods are used by auditors in both control testing and substantive testing.

d. Statistical sampling methods are more appropriate for control testing when the auditor elects to reprocess transactions, than when controls are tested by means of document examination.

ANSWER: C

29. The application of statistical sampling techniques is least related to which of the following generally accepted auditing 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 the auditor or auditors. c. A sufficient understanding of the internal control system is to be 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 accurate point 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 that procedures work inadequately. The true population deviation rate is 6%.

ANSWER: B

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 following risks 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

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%, and changing 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

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

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 occurrence rate 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.

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 visible in the form of exists.

ANSWER: AUDIT TRAIL, DOCUMENTATION

48. As contrasted with statistical sampling, nonstatistical sampling 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

50. The is the anticipated error rate, whereas the is 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. The the precision range, the larger the sample size.

ANSWER: NARROWER

52. The more critical an attribute to those control policies and procedures relevant to an audit, the the 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 a basis.

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 of detection 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

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 auditor’s 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

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

Jack’s Wholesale Hardware, an audit client. Hopkins has

identified the following attributes to be tested. For each

attribute, indicate the appropriate sampling unit and

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

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

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, and no 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.

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.

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?

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.

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 employer’s payroll

tax expense. Therefore, Jones must plan to audit these

accounts more intensively than under conditions of

strong internal control.