Chapter 15 Auditing Solutions
CHAPTER 15
Multiple-Choice Questions
1. easy A sample in which the characteristics of the sample are the same as those of the population is a(n): b a. variables sample. b. representative sample. c. attributes sample. d. random sample. 2. easy When the auditor decides to select less than 100 percent of the population for testing, the auditor is said to use: a a. audit sampling. b. representative sampling. c. poor judgment. d. none of the above. 3. In practice, auditors _________ know if a sample is truly a representative one. easy a. sometimes d b. often c. routinely d. never 4. To determine if a sample is truly representative, an auditor must: easy a. conduct multiple samples of the same population. c b. never use sampling because of the expense involved. c. audit the entire population. d. perform none of the above. 5. One of the ways to eliminate nonsampling risk is through: easy a. proper supervision and instruction of the client’s employees. b b. proper supervision and instruction of the audit team. c. the use of attributes sampling rather than variables sampling. d. controls which ensure that the sample drawn is random and representative. 6. One cause of nonsampling risk is: easy a. ineffective use of audit procedures. a b. testing less than the entire population. c. use of extensive tests of controls. d. any of the above. 7. An auditor can increase the likelihood that a sample is representative by using care in: easy a. designing the sampling process. d b. designing the sample selection. c. evaluating the sample results. d. performing all of the above.
8. easy When the auditor goes through a population and selects items for the sample without regard to their size, source, or other distinguishing characteristics, it is called: b a. block sample selection. b. haphazard selection. c. stratfieselection. d. statistical selection. 9. When auditors wish to evaluate a sample statistically, the only acceptable selection method is: easy a. probabilistic selection. a b. judgmental selection. c. haphazard selection. d. block sample selection. 10. easy A sample in which every possible combination of items in the population has an equal chance of constituting the sample is a: a a. random sample. b. statistical sample. c. judgment sample. d. representative sample. 11. easy The process which requires the calculation of an interval and then selects the items based on the size of the interval is: c a. statistical sampling. b. random sample selection. c. systematic sample selection. d. computerized sample selection. 12. ________ is the risk that audit tests will not uncover existing exceptions in a sample. easy a. Sampling risk. b b. Nonsampling risk. c. Audit risk. d. Detection risk. 13. easy ________ is the risk that an auditor will reach an incorrect conclusion because a sample is not representative of the population. a a. Sampling risk b. Nonsampling risk c. Audit risk d. Detection risk 14. easy In systematic sample selection, the population size is divided by the number of sample items desired in order to determine the: a a. sampling interval. b. tolerable exception rate. c. computed upper exceptions rate. d. mean. 15. Sampling risk may be controlled by: easy a. adjusting the sample size. d b. always using random sampling . c. using whatever sample selection technique is appropriate for the population. d. both a and c.
16. Which of the following occurrences would be least likely to attract the auditor’s attention? easy a. Deviations from client’s established control procedures. b b. Deviations from client’s budgeted values. c. Monetary errors in populations of transaction data. d. Monetary errors in populations of account balance details. 17. Which of the following statements is correct? easy d a. A sample of all items of a population will eliminate sampling risk, but increase nonsampling risk. b. The use of an appropriate sample selection technique ensures a representative sample. c. The auditor’s failure to recognize an exception is a significant cause of sampling risk. d. The use of inappropriate audit procedures is a significant cause of nonsampling risk. 18. easy The risk which the auditor is willing to take in accepting a control as being effective when the true population exception rate is greater than a tolerable rate is the: c a. finite correction factor. b. tolerable exception rate. c. acceptable risk of assessing control risk too low. d. estimated population exception rate. 19. easy The exception rate the auditor will permit in the population and still be willing to reduce the assessed level of control risk is called the: a a. tolerable exception rate. b. estimated population exception rate. c. acceptable risk of overreliance. d. sample exception rate. 20. easy If the auditor decides to assess control risk at the maximum level in a private company audit, tests of controls are: c a. increased in number. b. reduced in number. c. not performed. d. unchanged from prior planned settings. 21. Which of the following is not one of the basic phases in audit sampling? easy a. Planning the sample d b. Evaluating the results of the sample c. Selecting the sample and performing the tests d. Each of the above is a phase in audit sampling. 22. easy Attributes sampling would be an appropriate method to use on which one of the following procedures in an audit program? c a. Review sales transactions for large and unreasonable amounts. b. Observe whether the duties of the accounts receivable clerk are separate from handling cash. c. Examine a sample of duplicate sales invoices for credit approval by the credit manager. d. Review the aged schedule of accounts receivable to determine if receivables from officers are included.
23. easy a When the computed upper exception rate is greater than the tolerable exception rate, it is necessary for the auditor to take specific action. Which of the following courses of action would be most difficult to defend if the auditor is ever subject to review by a court? a. Reduce the tolerable exception rate so as to accept the sample results. b. Expand the sample size and perform more tests. c. Revise the assessed control risk. d. Write a letter to management which outlines the control deficiencies. 24. easy Which of the following is not generally considered in determining sample size for tests of controls? d a. Expected population exception rate. b. Risk of assessing control risk too low. c. Tolerable exception rate. d. Population size. 25. Which of the following statement is correct with respect to the quantification of sampling risk? easy a. Sampling risk cannot be quantified. c b. Sampling risk can be quantified only when non-probabilistic selection techniques are used to select the sample. c. Sampling risk can be quantified only when probabilistic selection techniques are used to select the sample. d. None of the above. 26. easy The auditor may use which of the following criteria when using the directed sample selection technique? d a. Items most likely to contain misstatements. b. Items containing selected population characteristics. c. Large dollar coverage. d. Any of the above. 27. Non-sampling errors occur when audit tests do not uncover existing exceptions in the: medium a. population. b b. sample. c. planning stage. d. financial statements. 28. Which of the following statements is correct with respect to the evaluation of sample results? medium c a. It is acceptable to make non-probabilistic evaluations only when probabilistic sample selection is used. b. It is acceptable to make non-probabilistic evaluations only if the auditor cannot quantify sampling risk. c. It is never acceptable to evaluate a non-probabilistic sample as if it were a statistical one. d. All of the above are correct. 29. Which of the following statements is a valid criticism of non-statistical sampling? medium d a. Many audit tests, such as footing of journals, must be performed outside a statistical sampling context. b. The cost of performing random selection or testing often exceeds the benefits. c. Non-statistical sampling does not differ substantially from statistical sampling methods. d. Conclusions may be drawn in more precise ways when using statistical sampling methods.
30. medium Which of the following methods of sample selection is appropriately used when selecting a random sample? d a. Use of random number tables. b. Use of computer generated random numbers. c. Auditor’s random selection of items. d. Both a and b, but not c. 31. Correspondence is established between the random number table and the population by: medium a. identifying each item in the population with a unique number. b b. deciding the number of digits to use in the random number table and their association with the population numbering system. c. defining which digits the auditor uses in a column and the method of reading the table. d. selecting a random starting point on the table. 32. (Public) medium The acceptable risk of assessing control risk to low will normally be assessed at a ____ level when auditing a public company. c a. higher b. compensating c. lower d. nominal 33. Which of the following statements is not correct? medium b a. It is acceptable to pick a starting point on a random number table by using a “blind stab” method. b. It is impossible to draw a six-digit random number from a table that is separated into columns of five digits. c. The only reason for selecting a random starting point on a random number table is to eliminate the predictability of the sample. d. When selecting a three-digit number from a table that is separated into columns of five digits, it is permissible to use the first three digits, the middle three digits, or the last three digits. 34. medium Which of the following is not one of the types of computer tools used to generate random samples? d a. Electronic spreadsheet programs. b. Random number generators. c. Generalized audit software. d. Random application search software. 35. Auditors are concerned with which type of exceptions? medium a. Deviations from a client’s established internal control processes. d b. Monetary misstatements in transaction data. c. Monetary misstatements in account balance details. d. Auditors are concerned with all of these exceptions. 36. medium In using audit sampling for exception rates, the auditor is primarily interested in determining the _____ the exception rate might be. b a. lowest b. most c. average range in which d. none of the above
37. medium The highest estimated exception rate in the population at a particular acceptable risk of assessing control risk too low is: c a. the upper exception rate. b. estimated population exception rate. c. the computed upper exception rate. d. the tolerable exception rate. 38. The advantage of systematic sample selection is that: medium a. it is easy to use. a b. there is limited possibility of it being biased. c. it is unnecessary to determine if the population is arranged randomly. d. all three of the above. 39. medium A statistical method used to estimate the proportion of items in a population containing an attribute of interest is: a a. attributes sampling. b. variables sampling. c. estimation sampling. d. population-proportional-to-size sampling. 40. medium The exception rate that the auditor will permit in the population and still be willing to use the preliminary control risk assessment is called the: d a. acceptable exception rate. b. estimated population exception rate. c. sample exception rate. d. tolerable exception rate. 41. The auditor’s best estimate of the population exception rate is the: medium a. current year’s sample exception rate. a b. tolerable exception rate. c. prior year’s sample exception rate. d. computed upper exception rate. 42. medium c Place the following steps in their proper order:
1. Analyze exceptions
2. Select the sample
3. Define attributes and exception conditions
4. State the objectives of the audit test
5. Specify the tolerable exception rate a. 1,3,2,4,5. b. 4,3,1,2,5. c. 4,3,5,2,1. d. 1,2,3,4,5. 43. medium If an auditor judgmentally selects a sample of one hundred items from a population and finds two exceptions, the auditor: a a. can conclude that the sample exception rate is 2%. b. can conclude that the population exception rate is 2%. c. can calculate the highest exception rate expected in the population. d. cannot make any conclusions about either the sample or the population.
44. _________ represents the auditor’s measure of sampling risk. medium a. TER b b. ARACR c. SER d. EPER 45. For which of the following audit procedures is audit sampling not appropriate? medium a. Review sales transactions for large and unusual amounts. a b. Examine a sample of duplicate sales invoices for credit approval. c. Compare the quantity on duplicate sales invoices with the quantity on related shipping documents. d. Audit sampling is appropriate for each of the above procedures. 46. Which of the following statements about the process of defining the population is not correct? medium a. The auditor can define the population to include the desired data. d b. The auditor may generalize only about that population that has been sampled. c. The population represents the body of data about which the auditor wishes to generalize. d. The auditor can randomly sample from any part of the population that she chooses. 47. Which of the following is the exception rate that the auditor expects to find before testing? medium a. Sample exception rate. b b. Estimated population exception rate. c. Computed exception rate. d. Tolerable exception rate. 48. Which of the following is not determined until after a sample is tested and evaluated? medium a. Sample exception rate. c b. Estimated population exception rate. c. Computed exception rate. d. Tolerable exception rate. 49. The relationship of tolerable exception rate (TER) to sample size is: medium a. direct (larger TER = larger sample). b b. inverse (larger TER = smaller sample). c. variable (sometimes larger, sometimes smaller). d. not determinable. 50. Which of the following must be set prior to testing a sample? medium a. Sample exception rate. d b. Achieved upper precision limit. c. Computed exception rate. d. Tolerable exception rate. 51. The relationship of acceptable risk of accessing control risk too low (ARACR) to sample size is: medium a. variable (sometimes larger, sometimes smaller). c b. direct (larger ARACR = larger sample). c. inverse (larger ARACR = smaller sample). d. nonexistent.
52. medium In attributes sampling, an estimate of the expected population exception rate is necessary to plan the sample size. The relationship of expected population exception rate (EPER) to sample size is: a a. direct (small EPER = small sample). b. inverse (small EPER = large sample). c. a variable (sometimes small, sometimes large) dependent on other factors present. d. indeterminate. 53. The initial sample size is so called because: medium a. there is always another sample to be done. d b. an auditor must take several samples to ensure randomness. c. an auditor must take several samples to ensure that the final sample is representative. d. exceptions must be evaluated before deciding whether the sample is sufficiently large to achieve the objectives. 54. The sample exception rate equals: medium a. the number of exceptions in the population divided by the sample size. c b. the number of items in the population multiplied by the number of exceptions in the sample. c. the number of exceptions in the sample divided by the sample size. d. the number of exceptions in the population divided by the population size. 55. medium Before the population can be considered acceptable based on the acceptable risk of assessing control risk too low, the computed upper exception rate must be: c a. greater than or equal to the tolerable exception rate. b. greater than the tolerable exception rate. c. less than or equal to the tolerable exception rate. d. less than the tolerable exception rate. 56. Which of the following combinations of attributes and exception conditions is not appropriate? medium d a. Existence of sales invoice number in the sales journal – No record of sales invoice number in the sales journal. b. Credit is approved – Lack of initials indicating credit approval. c. Quantity on customer order agrees with duplicate sales invoice – Quantity on customer order does not agree with quantity on duplicate sales invoice. d. Evidence that pricing is checked – Lack of initials on duplicate sales invoice indicating that extensions were checked. 57. Which of the following statements is not true? medium a. Random selection is statistical measurement. a b. It is acceptable to use random selection procedures without drawing statistical conclusions. c. It would be inappropriate to draw a statistical conclusion unless the sample were randomly selected. d. Random selection is a part of statistical sampling. 58. medium An auditor selects a sample from the file of shipping documents to determine whether invoices were prepared. This test is performed to satisfy the audit objective of: d a. accuracy. b. existence. c. control. d. completeness.
59. The acceptable risk of assessing control risk too low is: medium d a. the risk that the auditor is willing to take of accepting a control as ineffective when it is effective. b. the risk that the auditor is willing to take of accepting a control as effective when it is ineffective. c. the auditor’s measure of sampling risk. d. both b and c, but not a. 60. When using statistical sampling, the auditor would probably require a smaller sample if the: medium a. population increases. b b. desired reliability decreases. c. desired precision interval narrows. d. expected exception rate increases. 61. medium A principal advantage of statistical methods of attributes sampling over nonstatistical methods is that they provide a scientific basis for establishing the: d a. risk of assessing control risk too low. b. tolerable exception rate. c. expected population exception rate. d. sample size. 62. medium In performing a review of a client’s cash disbursements, an auditor uses systematic sample selection with a random start. The primary disadvantage of this technique is population items: c a. may occur twice in the sample. b. must be reordered in a systematic pattern before the sample can be drawn. c. may occur in a systematic pattern, thus negating the randomness of the sample. d. must be replaced in the population after sampling to permit valid statistical inference. 63. medium In estimation sampling for attributes, which one of the following must be known to evaluate the sample results? d a. Estimated dollar value of the population. b. Standard exception of the values in the population. c. Actual exception rate of the attribute in the population. d. Sample size. 64. challenging Which of the following statements is not correct regarding probabilistic and non-probabilistic sample selection? b a. In probabilistic selection, every population item has a known chance of being selected. b. It is not acceptable to make non-probabilistic evaluations using probabilistic selection. c. Probabilistic selection is required for all statistical sampling methods. d. Both methods are acceptable and commonly used. 65. Non-probabilistic selection methods are not based on mathematical probabilities; therefore: challenging a. the extent to which a sample is representative may be difficult to determine. a b. they are discouraged by the AICPA. c. they are forbidden by the Statements on Auditing Standards. d. they are not as good as statistical sampling.
66. Which of the following statements regarding block sampling is not true? challenging a. Block sampling is the selection of several items in sequence. c b. It is acceptable to use block sampling for tests of transactions only if a reasonable number of blocks is used. c. A “reasonable number” for most situations is probably at least six blocks from six different periods, locations, divisions, and so forth. d. Once the first item in the block is selected, the remainder of the block is chosen automatically. 67. A means of reducing the potential bias in systematic sample selection is to: challenging a. use multiple starts. a b. use a random number table. c. include a large block of the population. d. include only the high-dollar-value items. 68. When deciding on the acceptable risk of assessing control risk too low, the auditor should: challenging a. rely on his/her professional judgment. a b. err on the side of being conservative. c. consult the professional standards. d. do any of the above. 69. Which of the following statements is true? challenging d a. The audit procedures will vary as a result of using either statistical or nonstatistical sampling. b. The audit procedures will be the same for either statistical or nonstatistical sampling but they must be performed differently for each. c. Statistical sampling requires quantitative audit procedures whereas nonstatistical sampling requires judgmental audit procedures. d. The same audit procedures are performed in the same manner for either statistical or nonstatistical sampling. 70. challenging b When audit procedures have been completed for an attributes sampling application, the auditor must generalize from the sample to the population. Which of the following statements would be incorrect regarding this process? a. The auditor would use an attributes sampling table to determine the computed upper exception rate. b. The computed upper exception rate is the highest exception rate in the population that the auditor is willing to accept. c. It would be wrong for the auditor to conclude that the population exception rate is exactly the same as the sample exception rate. d. In selecting the table corresponding to the risk of overreliance, it should be the same as the ARACR used for determining the initial sample size. 71. challenging When performing tests of controls and tests of transactions for sales, the auditor generally defines the population as: b a. all accounts receivable transactions for the year. b. all sales invoices for the year. c. all cash receipts transactions for the year. d. all of the above.
72. challenging The difference between the tolerable exception rate and the estimated population exception rate is called: c a. accuracy of the initial sample estimate. b. inflation factor of the initial sample estimate. c. precision of the initial sample estimate. d. none of the above. 73. challenging 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: b a. random sampling with replacement. b. sampling for attributes. c. sampling for variables. d. stratified random sampling. 74. challenging If the result obtained from a particular sample is critical to the formation of an audit opinion, which of the following is the most important to the auditor? a a. Acceptable risk of assessing control risk too low. b. Estimated population exception rate. c. Tolerable exception rate. d. Size of the population. 75. The tolerable rate of exceptions for tests of controls is generally: challenging a. lower than the expected rate of errors in the related accounting records. b b. higher than the expected rate of errors in the related accounting records. c. identical to the expected rate of errors in the related accounting records. d. unrelated to the expected rate of errors in the related accounting records. 76. An advantage of using statistical sampling techniques is that such techniques: challenging a. mathematically measure risk. a b. eliminate the need for judgmental decisions. c. define the values of precision and reliability required to provide audit satisfaction. d. have been established in the courts to be superior to judgmental sampling. 77. challenging Auditors who prefer statistical to nonstatistical sampling believe that the principal advantage of statistical sampling flows from its unique ability to: a a. provide a mathematical measurement of uncertainty. b. promote a more legally defensible procedural approach. c. define the precision required to provide audit satisfaction. d. establish conclusive audit evidence with decreased audit effort. 78. challenging Which of the following is an advantage of systematic sample selection over random number sampling? d a. It provides a stronger basis for statistical conclusions. b. It enables the auditor to use the more efficient “sampling with replacement” tables. c. There may be correlation between the location of items in the population, the feature of sampling interest, and the sampling interval. d. It does not require establishment of correspondence between random numbers and items in the population.
79. challenging b What is an auditor’s evaluation of a statistical sample for attributes when a test of 100 documents results in four exceptions if the tolerable exception rate is 5%, the expected population exception rate is 3%, and the allowance for sampling risk is 2%? a. Accept the sample results as support for planned reliance on the control because the tolerable rate less the allowance for sampling risk equals the expected population exception rate. b. Modify planned reliance on the control because the sample exception rate plus the allowance for sampling risk exceeds the tolerable rate. c. Modify planned reliance on the control because the tolerable rate plus the allowance for sampling risk exceeds the expected population exception rate. d. Accept the sample results as support for planned reliance on the control because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate. 80. challenging a In the evaluation of the results of an attributes sample, the fact that the exception rate in the sample was 2% rather than the estimated population exception rate of 4% would cause the computed upper exception rate to: a. be less than the tolerable exception rate. b. equal the tolerable exception rate. c. exceed the tolerable exception rate. d. cannot be determined from the information given. 81. challenging If the size of the sample to be used in a test of attributes is not determined by using statistical concepts, but the sample is chosen in accordance with random selection procedures: c a. no inferences can be drawn from the sample. b. the auditor has committed a nonsampling error. c. the auditor may or may not achieve the tolerable exception rate at the acceptable risk of assessing control risk too low. d. the auditor will have to evaluate results using the principles of discovery sampling.
Essay Questions
82. easy Briefly explain why auditors utilize audit sampling.
Answer: Auditors use sampling techniques primarily because it is generally impractical to audit all transactions or balances. Consequently, auditors must design strategies to select items from the population that are likely to be representative of the remaining unaudited population items. In addition, auditors often use sampling techniques because of economic realities. That is, clients generally do not want to incur the substantial fees associated with auditing every transaction or balance.
83. easy Discuss what is meant by “sampling risk.”
Answer: Sampling risk occurs when the sample is not representative of the population; that is, the characteristics of interest in the sample are not the same as those in the population.
84. easy Discuss what is meant by “nonsampling risk.”
Answer: Nonsampling risk occurs when audit tests do not uncover existing exceptions in the sample.
85. easy Explain the difference between sampling with replacement and without replacement. Which method is more common in audit practice?
Answer: In replacement sampling, an element in the population can be included in the sample more than once, whereas in nonreplacement sampling, an element can be included only once. Nonreplacement sampling is more common in audit practice.
86. medium Discuss two causes of nonsampling risk. Also discuss ways the auditor can control nonsampling risk.
Answer: The two causes of nonsampling risk are (1) the auditor’s failure to recognize exceptions and (2) inappropriate or ineffective audit procedures. The auditor can control nonsampling risk through careful design of audit procedures and through proper instruction, supervision, and review.
87. medium What is the key advantage and disadvantage associated with systematic sample selection? How must auditors address this disadvantage?
Answer: The key advantage is its ease of use. Generally, systematic samples are easily drawn from the population and supporting documentation is easily developed. The key disadvantage is the potential for bias. Once the first item in the sample is selected, all other items are chosen automatically. Auditors should be careful to consider any potential pattern in the data prior to selecting their sample to ensure that their selection considers the possible bias.
88. medium Describe the differences between statistical and nonstatistical sampling in terms of (1) the sample selection methods used, and (2) quantification of sampling risk.
Answer: Nonstatistical sampling differs from statistical sampling in that non-probabilistic sampling can be used for the former but not the latter. In addition, sampling risk can be quantified when using statistical sampling but not when using nonstatistical sampling.
89. medium Describe each of the three types of sample selection methods commonly associated with nonstatistical audit sampling.
Answer: Three types of sample selection methods commonly associated with nonstatistical audit sampling are:
• Directed sample selection. Each item in the sample is selected on the basis of some judgmental criteria established by the auditor.
• Block sample selection. Several items in the population are selected in sequence.
• Haphazard sample selection. Sample items are selected from the population without regard to their size, source, or other distinguishing characteristics.
90. medium Describe each of the four types of sample selection methods commonly associated with statistical audit sampling.
Answer: Four types of sample selection methods commonly associated with statistical audit sampling are:
• Simple random sample selection. Every possible combination of elements in the population has an equal chance of constituting the sample.
• Systematic sample selection. A probabilistic method of sampling in which the auditor calculates an interval (the population size divided by the number of sample items desired) and selects the items for the sample based on the size of the interval and a randomly selected number between zero and the interval size.
• Probability proportional to size sample selection. The probability of selecting any individual population item is proportional to its recorded amount.
• Stratified sample selection. A probabilistic method of sampling in which the population is divided into subpopulations, and sub-samples are taken from each of the subpopulations.
91. medium Directed sample selection is the selection of each item in the sample based on some judgment criteria established by the auditor. Discuss three commonly used criteria.
Answer: Commonly-used criteria used in directed sample selection are:
• Items most likely to contain misstatements; for example, unusual or complex transactions, overdue receivables.
• Items containing selected population characteristics, such as transactions selected from each month during the year or from each location.
• Large dollar coverage in which the auditor focuses on selecting the relatively large items in the population for testing.
92. medium What types of exceptions are auditors most concerned with when evaluating populations of accounting data?
Answer: There are three types of exceptions that auditors are generally concerned with when evaluating populations of accounting data. They are:
1. Deviations from client’s established controls.
2. Monetary misstatements in populations of transaction data.
3. Monetary misstatements in populations of account balance details.
93. medium Explain the effect on sample size of increasing each of the following: (1) tolerable exception rate, (2) estimated population exception rate, (3) acceptable risk of assessing control risk too low, and (4) population size.
Answer: The tolerable exception rate and acceptable risk of assessing control risk too low are inversely related to sample size; that is, as TER or ARACR increase, sample size will decrease. The estimated population exception rate and the population size are directly related to sample size; that is, as EPER increases, sample size will also increase, and as population size increases, sample size may slightly increase.
94. challenging There are 14 steps to attributes sampling, divided into three sections: plan the sample, select the sample and perform the audit procedures, and evaluate the results. Discuss each of the steps that comprise the “evaluate the results” section.
Answer: The steps that comprise the “evaluate the results” section in attributes sampling are:
1. Generalize from the sample to the population. Tables can be used to determine the upper precision limit (computed upper exception rate) based on the acceptable risk of assessing control risk too low and the sample exception rate.
2. Analyze exceptions. In this step, the auditor should analyze individual exceptions to determine the breakdown in the internal controls that caused them.
3. Decide the acceptability of the population. In the final step, the auditor compares the computed upper exception rate with the tolerable exception rate. If the computed upper exception rate is less than or equal to the tolerable exception rate, then the population is considered acceptable.
95. challenging There are 14 steps to attributes sampling, divided into three sections: plan the sample, select the sample and perform the audit procedures, and evaluate the results. Discuss each of the steps that comprise the “plan the sample” section.
Answer: The steps that comprise the “plan the sample” section in attributes sampling are:
1. State the objectives of the audit test. Typically, in attributes sampling, the overall objective is to test the application of controls and determine whether transactions contain monetary misstatements.
2. Decide if audit sampling applies. Audit procedures involving documentation normally can be performed using sampling, whereas procedures involving observation, inquiry of the client, and analytical procedures are not suited to audit sampling.
3. Define attributes and exception conditions. In this step, the auditor carefully defines the attributes of interest and the conditions that constitute exceptions or errors.
4. Define the population. The population is the body of data about which the auditor wished to generalize, from which the sample must be drawn.
5. Define the sampling unit. In attributes sampling, the sampling unit is normally a document, identified by document numbers, or a transaction recorded in a journal.
6. Specify tolerable exception rate. This is the exception rate that the auditor will permit in the population and still be willing to rely on internal controls.
7. Specify acceptable risk of assessing control risk too low. This is the risk that the auditor is willing to take in accepting a control as effective when the true population exception rate is greater than the tolerable exception rate.
8. Estimate the population exception rate. This is the exception rate the auditor expects to find in the population before testing begins.
9. Determine the initial sample size. The initial sample size is determined from tables, based on values for the tolerable exception rate, acceptable risk of assessing control risk too low, and the estimated exception rate.
Other Objective Answer Format Questions
96. medium Match eight of the terms (a-k) with the definitions provided below (1-8):
a. Haphazard selection b. Attributes sampling c. Block sample selection d. Judgmental sampling e. Non-probabilistic sample selection f. Probabilistic sample selection g. Random sample h. Representative sample i. Statistical sampling j. Systematic sample selection k. Sampling distribution i 1. The use of mathematical measurement techniques to calculate formal statistical results and quantify sampling risk.
c 2. A non-probabilistic method of sample selection in which items are selected in measured sequences.
h 3. A sample whose characteristics are the same as those of the population.
b 4. A statistical, probabilistic method of sample evaluation that results in an estimate of the proportion of items in a population containing a characteristic of interest.
a 5. A non-probabilistic method of sample selection in which items are chosen without regard to their size, source, or other distinguishing characteristics.
f 6. An auditor selects items such that each population item has a known probability of being included in the sample.
k 7. A frequency distribution of the results of all possible samples of a specified size that could be obtained from a population containing some specific parameters.
g 8. A sample in which every possible combination of elements in the population has an equal chance of constituting the sample.
97. easy b Sampling risk results from the auditor’s failure to recognize exceptions in transaction data.
a. True
b. False
98. easy a Even when nonsampling risk is zero, there is always a chance that a sample is not reasonably representative.
a. True
b. False
99. easy b The prior year’s sample exception rate is the auditor’s best estimate of the exception rate in the population for the current year.
a. True
b. False
100. easy a The tolerable exception rate is the rate that the auditor will permit in the population and still be willing to conclude a control is effective.
a. True
b. False
101. medium a When selecting a sample, random numbers may be obtained either with replacement or without replacement. Although both selection methods are theoretically sound, auditors rarely use replacement sampling.
a. True
b. False
102.
medium a If a particular internal control is not followed by the client exactly 6% of the time, and the auditor’s tests of that control find three control violations in a sample of 50, the sample is considered to be representative.
a. True
b. False
103. medium a In practice, auditors do not know whether a sample is representative, even after all testing is complete.
a. True
b. False
104. medium a The only way to know with certainty whether a sample is representative is to subsequently audit the entire population.
a. True
b. False
105. medium a One way to control sampling risk is to increase sample size.
a. True
b. False
106. medium a A sample of all items in a population will have a zero sampling risk.
a. True
b. False
107. medium a It is virtually impossible to reduce sampling risk to zero.
a. True
b. False
108. medium a It is equally acceptable under professional auditing standards for auditors to use either statistical or nonstatistical sampling methods.
a. True
b. False
109. medium b When using nonstatistical sampling, the sample must be a probabilistic one.
a. True
b. False
110.
medium b The use of haphazard sample selection is encouraged under professional auditing standards.
a. True
b. False
111. medium b Although systematic sample selection is easy to use, its primary disadvantage is that it is not a probabilistic sampling method.
a. True
b. False
112. medium b Acceptable risk of assessing control risk too low is the risk that the auditor is willing to take in accepting a control as effective when the true population exception rate is greater than the estimated population exception rate.
a. True
b. False
113. medium b Directed sample selection, block sample selection, and haphazard sample selection are three types of probabilistic sample selection methods.
a. True
b. False
114. (Public) medium a ARACR is normally lower for a public company audit than a private company audit.
a. True
b. False
115. medium b The conjoined sample exception rate is the auditor’s “best estimate” of the actual exception rate in the entire population.
a. True
b. False
116. medium a When the computed upper exception rate is greater than the tolerable exception rate in attributes sampling, one possible appropriate course of action is to increase sample size.
a. True
b. False
117. medium a Tolerable exception rate (TER) is inversely related to sample size.
a. True
b. False
118. medium b The higher the assessed control risk, the lower will be the acceptable risk of assessing control risk too low.
a. True
b. False
119. challenging a The auditor may estimate the “estimated population exception rate” by taking a small preliminary sample from the current year’s data or by using the prior year’s experience with the client.
a. True
b. False
120. challenging b When a small preliminary sample is used to estimate the population exception rate, it (the preliminary sample) cannot be included in the ultimate sample.
a. True
b. False
121. challenging a In nonstatistical sampling, the calculated sampling error is the difference between the tolerable exception rate and the sample exception rate.
a. True
b. False
Multiple-Choice Questions
1. easy A sample in which the characteristics of the sample are the same as those of the population is a(n): b a. variables sample. b. representative sample. c. attributes sample. d. random sample. 2. easy When the auditor decides to select less than 100 percent of the population for testing, the auditor is said to use: a a. audit sampling. b. representative sampling. c. poor judgment. d. none of the above. 3. In practice, auditors _________ know if a sample is truly a representative one. easy a. sometimes d b. often c. routinely d. never 4. To determine if a sample is truly representative, an auditor must: easy a. conduct multiple samples of the same population. c b. never use sampling because of the expense involved. c. audit the entire population. d. perform none of the above. 5. One of the ways to eliminate nonsampling risk is through: easy a. proper supervision and instruction of the client’s employees. b b. proper supervision and instruction of the audit team. c. the use of attributes sampling rather than variables sampling. d. controls which ensure that the sample drawn is random and representative. 6. One cause of nonsampling risk is: easy a. ineffective use of audit procedures. a b. testing less than the entire population. c. use of extensive tests of controls. d. any of the above. 7. An auditor can increase the likelihood that a sample is representative by using care in: easy a. designing the sampling process. d b. designing the sample selection. c. evaluating the sample results. d. performing all of the above.
8. easy When the auditor goes through a population and selects items for the sample without regard to their size, source, or other distinguishing characteristics, it is called: b a. block sample selection. b. haphazard selection. c. stratfieselection. d. statistical selection. 9. When auditors wish to evaluate a sample statistically, the only acceptable selection method is: easy a. probabilistic selection. a b. judgmental selection. c. haphazard selection. d. block sample selection. 10. easy A sample in which every possible combination of items in the population has an equal chance of constituting the sample is a: a a. random sample. b. statistical sample. c. judgment sample. d. representative sample. 11. easy The process which requires the calculation of an interval and then selects the items based on the size of the interval is: c a. statistical sampling. b. random sample selection. c. systematic sample selection. d. computerized sample selection. 12. ________ is the risk that audit tests will not uncover existing exceptions in a sample. easy a. Sampling risk. b b. Nonsampling risk. c. Audit risk. d. Detection risk. 13. easy ________ is the risk that an auditor will reach an incorrect conclusion because a sample is not representative of the population. a a. Sampling risk b. Nonsampling risk c. Audit risk d. Detection risk 14. easy In systematic sample selection, the population size is divided by the number of sample items desired in order to determine the: a a. sampling interval. b. tolerable exception rate. c. computed upper exceptions rate. d. mean. 15. Sampling risk may be controlled by: easy a. adjusting the sample size. d b. always using random sampling . c. using whatever sample selection technique is appropriate for the population. d. both a and c.
16. Which of the following occurrences would be least likely to attract the auditor’s attention? easy a. Deviations from client’s established control procedures. b b. Deviations from client’s budgeted values. c. Monetary errors in populations of transaction data. d. Monetary errors in populations of account balance details. 17. Which of the following statements is correct? easy d a. A sample of all items of a population will eliminate sampling risk, but increase nonsampling risk. b. The use of an appropriate sample selection technique ensures a representative sample. c. The auditor’s failure to recognize an exception is a significant cause of sampling risk. d. The use of inappropriate audit procedures is a significant cause of nonsampling risk. 18. easy The risk which the auditor is willing to take in accepting a control as being effective when the true population exception rate is greater than a tolerable rate is the: c a. finite correction factor. b. tolerable exception rate. c. acceptable risk of assessing control risk too low. d. estimated population exception rate. 19. easy The exception rate the auditor will permit in the population and still be willing to reduce the assessed level of control risk is called the: a a. tolerable exception rate. b. estimated population exception rate. c. acceptable risk of overreliance. d. sample exception rate. 20. easy If the auditor decides to assess control risk at the maximum level in a private company audit, tests of controls are: c a. increased in number. b. reduced in number. c. not performed. d. unchanged from prior planned settings. 21. Which of the following is not one of the basic phases in audit sampling? easy a. Planning the sample d b. Evaluating the results of the sample c. Selecting the sample and performing the tests d. Each of the above is a phase in audit sampling. 22. easy Attributes sampling would be an appropriate method to use on which one of the following procedures in an audit program? c a. Review sales transactions for large and unreasonable amounts. b. Observe whether the duties of the accounts receivable clerk are separate from handling cash. c. Examine a sample of duplicate sales invoices for credit approval by the credit manager. d. Review the aged schedule of accounts receivable to determine if receivables from officers are included.
23. easy a When the computed upper exception rate is greater than the tolerable exception rate, it is necessary for the auditor to take specific action. Which of the following courses of action would be most difficult to defend if the auditor is ever subject to review by a court? a. Reduce the tolerable exception rate so as to accept the sample results. b. Expand the sample size and perform more tests. c. Revise the assessed control risk. d. Write a letter to management which outlines the control deficiencies. 24. easy Which of the following is not generally considered in determining sample size for tests of controls? d a. Expected population exception rate. b. Risk of assessing control risk too low. c. Tolerable exception rate. d. Population size. 25. Which of the following statement is correct with respect to the quantification of sampling risk? easy a. Sampling risk cannot be quantified. c b. Sampling risk can be quantified only when non-probabilistic selection techniques are used to select the sample. c. Sampling risk can be quantified only when probabilistic selection techniques are used to select the sample. d. None of the above. 26. easy The auditor may use which of the following criteria when using the directed sample selection technique? d a. Items most likely to contain misstatements. b. Items containing selected population characteristics. c. Large dollar coverage. d. Any of the above. 27. Non-sampling errors occur when audit tests do not uncover existing exceptions in the: medium a. population. b b. sample. c. planning stage. d. financial statements. 28. Which of the following statements is correct with respect to the evaluation of sample results? medium c a. It is acceptable to make non-probabilistic evaluations only when probabilistic sample selection is used. b. It is acceptable to make non-probabilistic evaluations only if the auditor cannot quantify sampling risk. c. It is never acceptable to evaluate a non-probabilistic sample as if it were a statistical one. d. All of the above are correct. 29. Which of the following statements is a valid criticism of non-statistical sampling? medium d a. Many audit tests, such as footing of journals, must be performed outside a statistical sampling context. b. The cost of performing random selection or testing often exceeds the benefits. c. Non-statistical sampling does not differ substantially from statistical sampling methods. d. Conclusions may be drawn in more precise ways when using statistical sampling methods.
30. medium Which of the following methods of sample selection is appropriately used when selecting a random sample? d a. Use of random number tables. b. Use of computer generated random numbers. c. Auditor’s random selection of items. d. Both a and b, but not c. 31. Correspondence is established between the random number table and the population by: medium a. identifying each item in the population with a unique number. b b. deciding the number of digits to use in the random number table and their association with the population numbering system. c. defining which digits the auditor uses in a column and the method of reading the table. d. selecting a random starting point on the table. 32. (Public) medium The acceptable risk of assessing control risk to low will normally be assessed at a ____ level when auditing a public company. c a. higher b. compensating c. lower d. nominal 33. Which of the following statements is not correct? medium b a. It is acceptable to pick a starting point on a random number table by using a “blind stab” method. b. It is impossible to draw a six-digit random number from a table that is separated into columns of five digits. c. The only reason for selecting a random starting point on a random number table is to eliminate the predictability of the sample. d. When selecting a three-digit number from a table that is separated into columns of five digits, it is permissible to use the first three digits, the middle three digits, or the last three digits. 34. medium Which of the following is not one of the types of computer tools used to generate random samples? d a. Electronic spreadsheet programs. b. Random number generators. c. Generalized audit software. d. Random application search software. 35. Auditors are concerned with which type of exceptions? medium a. Deviations from a client’s established internal control processes. d b. Monetary misstatements in transaction data. c. Monetary misstatements in account balance details. d. Auditors are concerned with all of these exceptions. 36. medium In using audit sampling for exception rates, the auditor is primarily interested in determining the _____ the exception rate might be. b a. lowest b. most c. average range in which d. none of the above
37. medium The highest estimated exception rate in the population at a particular acceptable risk of assessing control risk too low is: c a. the upper exception rate. b. estimated population exception rate. c. the computed upper exception rate. d. the tolerable exception rate. 38. The advantage of systematic sample selection is that: medium a. it is easy to use. a b. there is limited possibility of it being biased. c. it is unnecessary to determine if the population is arranged randomly. d. all three of the above. 39. medium A statistical method used to estimate the proportion of items in a population containing an attribute of interest is: a a. attributes sampling. b. variables sampling. c. estimation sampling. d. population-proportional-to-size sampling. 40. medium The exception rate that the auditor will permit in the population and still be willing to use the preliminary control risk assessment is called the: d a. acceptable exception rate. b. estimated population exception rate. c. sample exception rate. d. tolerable exception rate. 41. The auditor’s best estimate of the population exception rate is the: medium a. current year’s sample exception rate. a b. tolerable exception rate. c. prior year’s sample exception rate. d. computed upper exception rate. 42. medium c Place the following steps in their proper order:
1. Analyze exceptions
2. Select the sample
3. Define attributes and exception conditions
4. State the objectives of the audit test
5. Specify the tolerable exception rate a. 1,3,2,4,5. b. 4,3,1,2,5. c. 4,3,5,2,1. d. 1,2,3,4,5. 43. medium If an auditor judgmentally selects a sample of one hundred items from a population and finds two exceptions, the auditor: a a. can conclude that the sample exception rate is 2%. b. can conclude that the population exception rate is 2%. c. can calculate the highest exception rate expected in the population. d. cannot make any conclusions about either the sample or the population.
44. _________ represents the auditor’s measure of sampling risk. medium a. TER b b. ARACR c. SER d. EPER 45. For which of the following audit procedures is audit sampling not appropriate? medium a. Review sales transactions for large and unusual amounts. a b. Examine a sample of duplicate sales invoices for credit approval. c. Compare the quantity on duplicate sales invoices with the quantity on related shipping documents. d. Audit sampling is appropriate for each of the above procedures. 46. Which of the following statements about the process of defining the population is not correct? medium a. The auditor can define the population to include the desired data. d b. The auditor may generalize only about that population that has been sampled. c. The population represents the body of data about which the auditor wishes to generalize. d. The auditor can randomly sample from any part of the population that she chooses. 47. Which of the following is the exception rate that the auditor expects to find before testing? medium a. Sample exception rate. b b. Estimated population exception rate. c. Computed exception rate. d. Tolerable exception rate. 48. Which of the following is not determined until after a sample is tested and evaluated? medium a. Sample exception rate. c b. Estimated population exception rate. c. Computed exception rate. d. Tolerable exception rate. 49. The relationship of tolerable exception rate (TER) to sample size is: medium a. direct (larger TER = larger sample). b b. inverse (larger TER = smaller sample). c. variable (sometimes larger, sometimes smaller). d. not determinable. 50. Which of the following must be set prior to testing a sample? medium a. Sample exception rate. d b. Achieved upper precision limit. c. Computed exception rate. d. Tolerable exception rate. 51. The relationship of acceptable risk of accessing control risk too low (ARACR) to sample size is: medium a. variable (sometimes larger, sometimes smaller). c b. direct (larger ARACR = larger sample). c. inverse (larger ARACR = smaller sample). d. nonexistent.
52. medium In attributes sampling, an estimate of the expected population exception rate is necessary to plan the sample size. The relationship of expected population exception rate (EPER) to sample size is: a a. direct (small EPER = small sample). b. inverse (small EPER = large sample). c. a variable (sometimes small, sometimes large) dependent on other factors present. d. indeterminate. 53. The initial sample size is so called because: medium a. there is always another sample to be done. d b. an auditor must take several samples to ensure randomness. c. an auditor must take several samples to ensure that the final sample is representative. d. exceptions must be evaluated before deciding whether the sample is sufficiently large to achieve the objectives. 54. The sample exception rate equals: medium a. the number of exceptions in the population divided by the sample size. c b. the number of items in the population multiplied by the number of exceptions in the sample. c. the number of exceptions in the sample divided by the sample size. d. the number of exceptions in the population divided by the population size. 55. medium Before the population can be considered acceptable based on the acceptable risk of assessing control risk too low, the computed upper exception rate must be: c a. greater than or equal to the tolerable exception rate. b. greater than the tolerable exception rate. c. less than or equal to the tolerable exception rate. d. less than the tolerable exception rate. 56. Which of the following combinations of attributes and exception conditions is not appropriate? medium d a. Existence of sales invoice number in the sales journal – No record of sales invoice number in the sales journal. b. Credit is approved – Lack of initials indicating credit approval. c. Quantity on customer order agrees with duplicate sales invoice – Quantity on customer order does not agree with quantity on duplicate sales invoice. d. Evidence that pricing is checked – Lack of initials on duplicate sales invoice indicating that extensions were checked. 57. Which of the following statements is not true? medium a. Random selection is statistical measurement. a b. It is acceptable to use random selection procedures without drawing statistical conclusions. c. It would be inappropriate to draw a statistical conclusion unless the sample were randomly selected. d. Random selection is a part of statistical sampling. 58. medium An auditor selects a sample from the file of shipping documents to determine whether invoices were prepared. This test is performed to satisfy the audit objective of: d a. accuracy. b. existence. c. control. d. completeness.
59. The acceptable risk of assessing control risk too low is: medium d a. the risk that the auditor is willing to take of accepting a control as ineffective when it is effective. b. the risk that the auditor is willing to take of accepting a control as effective when it is ineffective. c. the auditor’s measure of sampling risk. d. both b and c, but not a. 60. When using statistical sampling, the auditor would probably require a smaller sample if the: medium a. population increases. b b. desired reliability decreases. c. desired precision interval narrows. d. expected exception rate increases. 61. medium A principal advantage of statistical methods of attributes sampling over nonstatistical methods is that they provide a scientific basis for establishing the: d a. risk of assessing control risk too low. b. tolerable exception rate. c. expected population exception rate. d. sample size. 62. medium In performing a review of a client’s cash disbursements, an auditor uses systematic sample selection with a random start. The primary disadvantage of this technique is population items: c a. may occur twice in the sample. b. must be reordered in a systematic pattern before the sample can be drawn. c. may occur in a systematic pattern, thus negating the randomness of the sample. d. must be replaced in the population after sampling to permit valid statistical inference. 63. medium In estimation sampling for attributes, which one of the following must be known to evaluate the sample results? d a. Estimated dollar value of the population. b. Standard exception of the values in the population. c. Actual exception rate of the attribute in the population. d. Sample size. 64. challenging Which of the following statements is not correct regarding probabilistic and non-probabilistic sample selection? b a. In probabilistic selection, every population item has a known chance of being selected. b. It is not acceptable to make non-probabilistic evaluations using probabilistic selection. c. Probabilistic selection is required for all statistical sampling methods. d. Both methods are acceptable and commonly used. 65. Non-probabilistic selection methods are not based on mathematical probabilities; therefore: challenging a. the extent to which a sample is representative may be difficult to determine. a b. they are discouraged by the AICPA. c. they are forbidden by the Statements on Auditing Standards. d. they are not as good as statistical sampling.
66. Which of the following statements regarding block sampling is not true? challenging a. Block sampling is the selection of several items in sequence. c b. It is acceptable to use block sampling for tests of transactions only if a reasonable number of blocks is used. c. A “reasonable number” for most situations is probably at least six blocks from six different periods, locations, divisions, and so forth. d. Once the first item in the block is selected, the remainder of the block is chosen automatically. 67. A means of reducing the potential bias in systematic sample selection is to: challenging a. use multiple starts. a b. use a random number table. c. include a large block of the population. d. include only the high-dollar-value items. 68. When deciding on the acceptable risk of assessing control risk too low, the auditor should: challenging a. rely on his/her professional judgment. a b. err on the side of being conservative. c. consult the professional standards. d. do any of the above. 69. Which of the following statements is true? challenging d a. The audit procedures will vary as a result of using either statistical or nonstatistical sampling. b. The audit procedures will be the same for either statistical or nonstatistical sampling but they must be performed differently for each. c. Statistical sampling requires quantitative audit procedures whereas nonstatistical sampling requires judgmental audit procedures. d. The same audit procedures are performed in the same manner for either statistical or nonstatistical sampling. 70. challenging b When audit procedures have been completed for an attributes sampling application, the auditor must generalize from the sample to the population. Which of the following statements would be incorrect regarding this process? a. The auditor would use an attributes sampling table to determine the computed upper exception rate. b. The computed upper exception rate is the highest exception rate in the population that the auditor is willing to accept. c. It would be wrong for the auditor to conclude that the population exception rate is exactly the same as the sample exception rate. d. In selecting the table corresponding to the risk of overreliance, it should be the same as the ARACR used for determining the initial sample size. 71. challenging When performing tests of controls and tests of transactions for sales, the auditor generally defines the population as: b a. all accounts receivable transactions for the year. b. all sales invoices for the year. c. all cash receipts transactions for the year. d. all of the above.
72. challenging The difference between the tolerable exception rate and the estimated population exception rate is called: c a. accuracy of the initial sample estimate. b. inflation factor of the initial sample estimate. c. precision of the initial sample estimate. d. none of the above. 73. challenging 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: b a. random sampling with replacement. b. sampling for attributes. c. sampling for variables. d. stratified random sampling. 74. challenging If the result obtained from a particular sample is critical to the formation of an audit opinion, which of the following is the most important to the auditor? a a. Acceptable risk of assessing control risk too low. b. Estimated population exception rate. c. Tolerable exception rate. d. Size of the population. 75. The tolerable rate of exceptions for tests of controls is generally: challenging a. lower than the expected rate of errors in the related accounting records. b b. higher than the expected rate of errors in the related accounting records. c. identical to the expected rate of errors in the related accounting records. d. unrelated to the expected rate of errors in the related accounting records. 76. An advantage of using statistical sampling techniques is that such techniques: challenging a. mathematically measure risk. a b. eliminate the need for judgmental decisions. c. define the values of precision and reliability required to provide audit satisfaction. d. have been established in the courts to be superior to judgmental sampling. 77. challenging Auditors who prefer statistical to nonstatistical sampling believe that the principal advantage of statistical sampling flows from its unique ability to: a a. provide a mathematical measurement of uncertainty. b. promote a more legally defensible procedural approach. c. define the precision required to provide audit satisfaction. d. establish conclusive audit evidence with decreased audit effort. 78. challenging Which of the following is an advantage of systematic sample selection over random number sampling? d a. It provides a stronger basis for statistical conclusions. b. It enables the auditor to use the more efficient “sampling with replacement” tables. c. There may be correlation between the location of items in the population, the feature of sampling interest, and the sampling interval. d. It does not require establishment of correspondence between random numbers and items in the population.
79. challenging b What is an auditor’s evaluation of a statistical sample for attributes when a test of 100 documents results in four exceptions if the tolerable exception rate is 5%, the expected population exception rate is 3%, and the allowance for sampling risk is 2%? a. Accept the sample results as support for planned reliance on the control because the tolerable rate less the allowance for sampling risk equals the expected population exception rate. b. Modify planned reliance on the control because the sample exception rate plus the allowance for sampling risk exceeds the tolerable rate. c. Modify planned reliance on the control because the tolerable rate plus the allowance for sampling risk exceeds the expected population exception rate. d. Accept the sample results as support for planned reliance on the control because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate. 80. challenging a In the evaluation of the results of an attributes sample, the fact that the exception rate in the sample was 2% rather than the estimated population exception rate of 4% would cause the computed upper exception rate to: a. be less than the tolerable exception rate. b. equal the tolerable exception rate. c. exceed the tolerable exception rate. d. cannot be determined from the information given. 81. challenging If the size of the sample to be used in a test of attributes is not determined by using statistical concepts, but the sample is chosen in accordance with random selection procedures: c a. no inferences can be drawn from the sample. b. the auditor has committed a nonsampling error. c. the auditor may or may not achieve the tolerable exception rate at the acceptable risk of assessing control risk too low. d. the auditor will have to evaluate results using the principles of discovery sampling.
Essay Questions
82. easy Briefly explain why auditors utilize audit sampling.
Answer: Auditors use sampling techniques primarily because it is generally impractical to audit all transactions or balances. Consequently, auditors must design strategies to select items from the population that are likely to be representative of the remaining unaudited population items. In addition, auditors often use sampling techniques because of economic realities. That is, clients generally do not want to incur the substantial fees associated with auditing every transaction or balance.
83. easy Discuss what is meant by “sampling risk.”
Answer: Sampling risk occurs when the sample is not representative of the population; that is, the characteristics of interest in the sample are not the same as those in the population.
84. easy Discuss what is meant by “nonsampling risk.”
Answer: Nonsampling risk occurs when audit tests do not uncover existing exceptions in the sample.
85. easy Explain the difference between sampling with replacement and without replacement. Which method is more common in audit practice?
Answer: In replacement sampling, an element in the population can be included in the sample more than once, whereas in nonreplacement sampling, an element can be included only once. Nonreplacement sampling is more common in audit practice.
86. medium Discuss two causes of nonsampling risk. Also discuss ways the auditor can control nonsampling risk.
Answer: The two causes of nonsampling risk are (1) the auditor’s failure to recognize exceptions and (2) inappropriate or ineffective audit procedures. The auditor can control nonsampling risk through careful design of audit procedures and through proper instruction, supervision, and review.
87. medium What is the key advantage and disadvantage associated with systematic sample selection? How must auditors address this disadvantage?
Answer: The key advantage is its ease of use. Generally, systematic samples are easily drawn from the population and supporting documentation is easily developed. The key disadvantage is the potential for bias. Once the first item in the sample is selected, all other items are chosen automatically. Auditors should be careful to consider any potential pattern in the data prior to selecting their sample to ensure that their selection considers the possible bias.
88. medium Describe the differences between statistical and nonstatistical sampling in terms of (1) the sample selection methods used, and (2) quantification of sampling risk.
Answer: Nonstatistical sampling differs from statistical sampling in that non-probabilistic sampling can be used for the former but not the latter. In addition, sampling risk can be quantified when using statistical sampling but not when using nonstatistical sampling.
89. medium Describe each of the three types of sample selection methods commonly associated with nonstatistical audit sampling.
Answer: Three types of sample selection methods commonly associated with nonstatistical audit sampling are:
• Directed sample selection. Each item in the sample is selected on the basis of some judgmental criteria established by the auditor.
• Block sample selection. Several items in the population are selected in sequence.
• Haphazard sample selection. Sample items are selected from the population without regard to their size, source, or other distinguishing characteristics.
90. medium Describe each of the four types of sample selection methods commonly associated with statistical audit sampling.
Answer: Four types of sample selection methods commonly associated with statistical audit sampling are:
• Simple random sample selection. Every possible combination of elements in the population has an equal chance of constituting the sample.
• Systematic sample selection. A probabilistic method of sampling in which the auditor calculates an interval (the population size divided by the number of sample items desired) and selects the items for the sample based on the size of the interval and a randomly selected number between zero and the interval size.
• Probability proportional to size sample selection. The probability of selecting any individual population item is proportional to its recorded amount.
• Stratified sample selection. A probabilistic method of sampling in which the population is divided into subpopulations, and sub-samples are taken from each of the subpopulations.
91. medium Directed sample selection is the selection of each item in the sample based on some judgment criteria established by the auditor. Discuss three commonly used criteria.
Answer: Commonly-used criteria used in directed sample selection are:
• Items most likely to contain misstatements; for example, unusual or complex transactions, overdue receivables.
• Items containing selected population characteristics, such as transactions selected from each month during the year or from each location.
• Large dollar coverage in which the auditor focuses on selecting the relatively large items in the population for testing.
92. medium What types of exceptions are auditors most concerned with when evaluating populations of accounting data?
Answer: There are three types of exceptions that auditors are generally concerned with when evaluating populations of accounting data. They are:
1. Deviations from client’s established controls.
2. Monetary misstatements in populations of transaction data.
3. Monetary misstatements in populations of account balance details.
93. medium Explain the effect on sample size of increasing each of the following: (1) tolerable exception rate, (2) estimated population exception rate, (3) acceptable risk of assessing control risk too low, and (4) population size.
Answer: The tolerable exception rate and acceptable risk of assessing control risk too low are inversely related to sample size; that is, as TER or ARACR increase, sample size will decrease. The estimated population exception rate and the population size are directly related to sample size; that is, as EPER increases, sample size will also increase, and as population size increases, sample size may slightly increase.
94. challenging There are 14 steps to attributes sampling, divided into three sections: plan the sample, select the sample and perform the audit procedures, and evaluate the results. Discuss each of the steps that comprise the “evaluate the results” section.
Answer: The steps that comprise the “evaluate the results” section in attributes sampling are:
1. Generalize from the sample to the population. Tables can be used to determine the upper precision limit (computed upper exception rate) based on the acceptable risk of assessing control risk too low and the sample exception rate.
2. Analyze exceptions. In this step, the auditor should analyze individual exceptions to determine the breakdown in the internal controls that caused them.
3. Decide the acceptability of the population. In the final step, the auditor compares the computed upper exception rate with the tolerable exception rate. If the computed upper exception rate is less than or equal to the tolerable exception rate, then the population is considered acceptable.
95. challenging There are 14 steps to attributes sampling, divided into three sections: plan the sample, select the sample and perform the audit procedures, and evaluate the results. Discuss each of the steps that comprise the “plan the sample” section.
Answer: The steps that comprise the “plan the sample” section in attributes sampling are:
1. State the objectives of the audit test. Typically, in attributes sampling, the overall objective is to test the application of controls and determine whether transactions contain monetary misstatements.
2. Decide if audit sampling applies. Audit procedures involving documentation normally can be performed using sampling, whereas procedures involving observation, inquiry of the client, and analytical procedures are not suited to audit sampling.
3. Define attributes and exception conditions. In this step, the auditor carefully defines the attributes of interest and the conditions that constitute exceptions or errors.
4. Define the population. The population is the body of data about which the auditor wished to generalize, from which the sample must be drawn.
5. Define the sampling unit. In attributes sampling, the sampling unit is normally a document, identified by document numbers, or a transaction recorded in a journal.
6. Specify tolerable exception rate. This is the exception rate that the auditor will permit in the population and still be willing to rely on internal controls.
7. Specify acceptable risk of assessing control risk too low. This is the risk that the auditor is willing to take in accepting a control as effective when the true population exception rate is greater than the tolerable exception rate.
8. Estimate the population exception rate. This is the exception rate the auditor expects to find in the population before testing begins.
9. Determine the initial sample size. The initial sample size is determined from tables, based on values for the tolerable exception rate, acceptable risk of assessing control risk too low, and the estimated exception rate.
Other Objective Answer Format Questions
96. medium Match eight of the terms (a-k) with the definitions provided below (1-8):
a. Haphazard selection b. Attributes sampling c. Block sample selection d. Judgmental sampling e. Non-probabilistic sample selection f. Probabilistic sample selection g. Random sample h. Representative sample i. Statistical sampling j. Systematic sample selection k. Sampling distribution i 1. The use of mathematical measurement techniques to calculate formal statistical results and quantify sampling risk.
c 2. A non-probabilistic method of sample selection in which items are selected in measured sequences.
h 3. A sample whose characteristics are the same as those of the population.
b 4. A statistical, probabilistic method of sample evaluation that results in an estimate of the proportion of items in a population containing a characteristic of interest.
a 5. A non-probabilistic method of sample selection in which items are chosen without regard to their size, source, or other distinguishing characteristics.
f 6. An auditor selects items such that each population item has a known probability of being included in the sample.
k 7. A frequency distribution of the results of all possible samples of a specified size that could be obtained from a population containing some specific parameters.
g 8. A sample in which every possible combination of elements in the population has an equal chance of constituting the sample.
97. easy b Sampling risk results from the auditor’s failure to recognize exceptions in transaction data.
a. True
b. False
98. easy a Even when nonsampling risk is zero, there is always a chance that a sample is not reasonably representative.
a. True
b. False
99. easy b The prior year’s sample exception rate is the auditor’s best estimate of the exception rate in the population for the current year.
a. True
b. False
100. easy a The tolerable exception rate is the rate that the auditor will permit in the population and still be willing to conclude a control is effective.
a. True
b. False
101. medium a When selecting a sample, random numbers may be obtained either with replacement or without replacement. Although both selection methods are theoretically sound, auditors rarely use replacement sampling.
a. True
b. False
102.
medium a If a particular internal control is not followed by the client exactly 6% of the time, and the auditor’s tests of that control find three control violations in a sample of 50, the sample is considered to be representative.
a. True
b. False
103. medium a In practice, auditors do not know whether a sample is representative, even after all testing is complete.
a. True
b. False
104. medium a The only way to know with certainty whether a sample is representative is to subsequently audit the entire population.
a. True
b. False
105. medium a One way to control sampling risk is to increase sample size.
a. True
b. False
106. medium a A sample of all items in a population will have a zero sampling risk.
a. True
b. False
107. medium a It is virtually impossible to reduce sampling risk to zero.
a. True
b. False
108. medium a It is equally acceptable under professional auditing standards for auditors to use either statistical or nonstatistical sampling methods.
a. True
b. False
109. medium b When using nonstatistical sampling, the sample must be a probabilistic one.
a. True
b. False
110.
medium b The use of haphazard sample selection is encouraged under professional auditing standards.
a. True
b. False
111. medium b Although systematic sample selection is easy to use, its primary disadvantage is that it is not a probabilistic sampling method.
a. True
b. False
112. medium b Acceptable risk of assessing control risk too low is the risk that the auditor is willing to take in accepting a control as effective when the true population exception rate is greater than the estimated population exception rate.
a. True
b. False
113. medium b Directed sample selection, block sample selection, and haphazard sample selection are three types of probabilistic sample selection methods.
a. True
b. False
114. (Public) medium a ARACR is normally lower for a public company audit than a private company audit.
a. True
b. False
115. medium b The conjoined sample exception rate is the auditor’s “best estimate” of the actual exception rate in the entire population.
a. True
b. False
116. medium a When the computed upper exception rate is greater than the tolerable exception rate in attributes sampling, one possible appropriate course of action is to increase sample size.
a. True
b. False
117. medium a Tolerable exception rate (TER) is inversely related to sample size.
a. True
b. False
118. medium b The higher the assessed control risk, the lower will be the acceptable risk of assessing control risk too low.
a. True
b. False
119. challenging a The auditor may estimate the “estimated population exception rate” by taking a small preliminary sample from the current year’s data or by using the prior year’s experience with the client.
a. True
b. False
120. challenging b When a small preliminary sample is used to estimate the population exception rate, it (the preliminary sample) cannot be included in the ultimate sample.
a. True
b. False
121. challenging a In nonstatistical sampling, the calculated sampling error is the difference between the tolerable exception rate and the sample exception rate.
a. True
b. False
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