7: Audit Sampling

5. Which of the following best illustrates the concept of sampling risk? a. A randomly chosen sample may not be representative of the population as a whole on the characteristic of interest. b. An auditor may select audit procedures that are not appropriate to achieve the specific objective. c. An auditor may fail to recognize errors in the documents examined for the chosen sample. d. The documents related to the chosen sample may not be available for inspection.

Correct Answer: A) A randomly chosen sample may not be representative of the population as a whole on the characteristic of interest. Notes (a) The requirement is to determine which answer represents the concept of sampling risk. Sampling risk arises from the possibility that an auditor's conclusions based upon a sample would differ from the conclusions which would be drawn from examining the entire population (i.e., the risk that the sample examined is not representative of the population). Answers (b), (c), and (d) are all incorrect because they relate to errors which could occur even if 100% of the population were examined, that is, nonsampling risk.

27. When assessing the tolerable rate, the auditor should consider that, while deviations from control procedures increase the risk of material misstatements, such deviations do not necessarily result in errors. This explains why a. A recorded disbursement that does not show evidence of required approval may nevertheless be a transaction that is properly authorized and recorded. b. Deviations would result in errors in the accounting records only if the deviations and the errors occurred on different transactions. c. Deviations from pertinent control procedures at a given rate ordinarily would be expected to result in errors at a higher rate. d. A recorded disbursement that is properly authorized may nevertheless be a transaction that contains a material error.

Correct Answer: A) A recorded disbursement that does not show evidence of required approval may nevertheless be a transaction that is properly authorized and recorded. Notes (a) The requirement is to determine why deviations from control procedures do not necessarily result in errors. Answer (a) is correct because it provides an example of a situation in which a deviation from a control procedure exists (lack of documentation of transaction approval), although the entry was authorized and proper. Thus, such a deviation does not necessarily result in an error in the financial statements. Answer (b) is incorrect because a deviation from control procedure and an error may occur in the same transaction. Answer (c) is incorrect since the fact that all deviations do not lead to errors will result in a lower error rate. Answer (d) is incorrect because while it represents a correct statement, it does not follow from the point of the question which is based on the idea that deviations do not directly result in errors.

57. Which of the following statements is correct concerning the auditor's use of statistical sampling? a. An auditor needs to estimate the dollar amount of the standard deviation of the population to use classical variables sampling. b. An assumption of PPS sampling is that the underlying accounting population is normally distributed. c. A classical variables sample needs to be designed with special considerations to include negative balances in the sample. d. The selection of zero balances usually does not require special sample design considerations when using PPS sampling.

Correct Answer: A) An auditor needs to estimate the dollar amount of the standard deviation of the population to use classical variables sampling. Notes (a) The requirement is to identify the correct statement concerning the auditor's use of statistical sampling. Answer (a) is correct because an estimate of the variation of the population, the standard deviation, is needed to use classical variables sampling (AICPA Audit and Accounting Guide, Audit Sampling). Answer (b) is incorrect because PPS sampling does not make an assumption that the underlying population is normally distributed. Answers (c) and (d) are incorrect because classical variables sample selected accounts and therefore need not include special considerations to those with a negative balance.

49. An auditor is determining the sample size for an inventory observation using mean-per-unit estimation, which is a variables sampling plan. To calculate the required sample size, the auditor usually determines the I. Variability in the dollar amounts of inventory items II. Risk of incorrect acceptance a. Both I and II b. I only c. II only d. Neither I nor II

Correct Answer: A) Both I and II Notes (a) The requirement is to determine whether an auditor uses the variability in dollar values, the risk of incorrect acceptance, or both, in a mean-per-unit estimation variables sampling plan. Answer (a) is correct because both factors are included in a sampling plan. Answers (b), (c), and (d) are all incorrect because they suggest that one or both factors are not considered. See AU-C 530 and the AICPA Audit Sampling Guide for information on sampling.

21. Which of the following factors is (are) considered in determining the sample size for a test of controls? I. Expected deviation rate II. Tolerable deviation rate a. Both I and II b. Neither I nor II c. II only d. I only

Correct Answer: A) Both I and II Notes (a) The requirement is to determine whether the expected deviation rate, the tolerable deviation rate, or both affect the sample size for a test of controls. Answer (a) is correct because attribute sampling formulas and tables used in auditing generally require the auditor to specify an expected deviation rate, a tolerable deviation rate and the risk of assessing control risk too low. See AICPA Audit Sampling Guide and AU-C 530 for more information on audit sampling.

30. If the auditor is concerned that a population may contain exceptions, the determination of a sample size sufficient to include at least one such exception is a characteristic of a. Discovery sampling. b. Variables sampling. c. Random sampling. d. Dollar-unit sampling.

Correct Answer: A) Discovery sampling. Notes (a) The requirement is to determine the type of sampling which is most directly related to finding at least one exception. Discovery sample sizes and related discovery sampling tables are constructed to measure the probability of at least one error occurring in a sample if the error rate in the population exceeds the tolerable rate. Answer (b) is incorrect because variables sampling need not include at least one exception (mean per unit sampling, for example, needs no errors). Answer (c) is incorrect since random sampling only deals with the technique used to select items to be included in the sample. Answer (d) is incorrect because dollar-unit sampling results are not directly related to finding at least one exception.

3. The likelihood of assessing control risk too high is the risk that the sample selected to test controls a. Does not support the auditor's planned assessed level of control risk when the true operating effectiveness of the control structure justifies such an assessment. b. Contains misstatements that could be material to the financial statements when aggregated with misstatements in other account balances or transactions classes. c. Contains proportionately fewer monetary errors or deviations from prescribed controls than exist in the balance or class as a whole. d. Does not support the tolerable error for some or all of management's assertions.

Correct Answer: A) Does not support the auditor's planned assessed level of control risk when the true operating effectiveness of the control structure justifies such an assessment. Notes (a) The requirement is to determine the meaning of the likelihood of assessing control risk too high in a test of controls. Answer (a) is correct because the risk of assessing control risk too high is the risk that the sample does not support the auditor's planned assessed level of control risk when the true operating effectiveness of the control structure justifies such an assessment. Answer (b) is incorrect because the risk of assessing control risk too high relates to the deviation rate from a control procedure in a population, not to monetary misstatements. Answer (c) is incorrect because the risk of assessing control risk too high does not directly relate to monetary misstatements. Answer (d) is incorrect because tolerable error (misstatement) relates to variables sampling applied to substantive testing and not to tests of controls and because the meaning of "support the tolerable error" is uncertain.

6. In assessing sampling risk, the risk of incorrect rejection and the risk of assessing control risk too high relate to the a. Efficiency of the audit. b. Effectiveness of the audit. c. Selection of the sample. d. Audit quality controls.

Correct Answer: A) Efficiency of the audit. Notes (a) The requirement is to determine what is related to the risk of incorrect rejection and the risk of assessing control risk too high. Answer (a) is correct because AU-C 530 states that the risk of incorrect rejection and the risk of assessing control risk too high relate to the efficiency of the audit. These two errors generally result in an auditor performing unnecessary additional procedures. Answer (b) is incorrect because the risk of incorrect acceptance and the risk of assessing control risk too low relate to the effectiveness of an audit. Answer (c) is incorrect because the risks do not relate directly to the actual selection of the sample. Answer (d) is incorrect because the audit quality controls do not directly mention either of these risks.

31. In determining the number of documents to select for a test to obtain assurance that all sales have been properly authorized, an auditor should consider the tolerable rate of deviation from the control activity. The auditor should also consider the I. Likely rate of deviations. II. Allowable risk of assessing control risk too high. a. I only b. II only c. Both I and II d. Either I or II

Correct Answer: A) I only Notes (a) The requirement is to determine whether an auditor should consider the likely rate of deviation, the allowable risk of assessing control risk too high, or both, when performing a test of a control. Answer (a) is correct because an auditor will consider the likely rate of deviations, but will not ordinarily consider the allowable risk of assessing control risk too high when following the approach outlined in the AICPA Audit Sampling Guide.

51. The use of the ratio estimation sampling technique is most effective when a. The calculated audit amounts are approximately proportional to the client's book amounts. b. A relatively small number of differences exist in the population. c. Estimating populations whose records consist of quantities, but not book values. d. Large overstatement differences and large understatement differences exist in the population.

Correct Answer: A) The calculated audit amounts are approximately proportional to the client's book amounts. Notes (a) The requirement is to determine when ratio estimation sampling is most effective. The ratio estimation sampling technique uses the ratio between the audited to book amounts as a measure of standard deviation in its sample size computation. Answer (a) is correct because when audit differences are approximately proportional to account size the standard deviation of the ratio is small and this results in a relatively small required sample size. Answer (b) is incorrect because a relatively large number of differences between book and audited values must exist to calculate a reliable standard deviation under the ratio method. Answer (c) is incorrect because while the ratio estimation sampling technique may be used with quantities, it offers no particular advantage over other methods. Answer (d) is incorrect because the absolute size of differences does not make the ratio estimation method most effective.

10. The size of a sample designed for dual-purpose testing should be a. The larger of the samples that would otherwise have been designed for the two separate purposes. b. The smaller of the samples that would otherwise have been designed for the two separate purposes. c. The combined total of the samples that would otherwise have been designed for the two separate purposes. d. More than the larger of the samples that would otherwise have been designated for the two separate purposes, but less than the combined total of the samples that would otherwise have been designed for the two separate purposes.

Correct Answer: A) The larger of the samples that would otherwise have been designed for the two separate purposes. Notes (a) The requirement is to identify the correct statement with respect to the size of a sample required for dual purpose testing. Answer (a) is correct because the auditor should select the larger of the required sample sizes.

37. Which of the following statements is correct concerning statistical sampling in tests of controls? a. The population size has little or no effect on determining sample size except for very small populations. b. The expected population deviation 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.

Correct Answer: A) The population size has little or no effect on determining sample size except for very small populations. Notes (a) The requirement is to identify the correct statement concerning statistical sampling for tests of controls. Answer (a) is correct because population size has little or no effect on sample size. Answer (b) is incorrect because the population deviation rate has a significant effect on sample size. Answer (c) is incorrect because sample size increases to a much lesser extent than doubling as the population size doubles. Answer (d) is incorrect because for a given tolerable rate, a smaller, and not a larger, sample size should be selected as the expected population deviation rate decreases.

45. An auditor established a $60,000 tolerable misstatement for an asset with an account balance of $1,000,000. The auditor selected a sample of every twentieth item from the population that represented the asset account balance and discovered overstatements of $3,700 and understatements of $200. Under these circumstances, the auditor most likely would conclude that a. There is an unacceptably high risk that the actual misstatements in the population exceed the tolerable misstatement because the total projected misstatement is more than the tolerable misstatement. b. There is an unacceptably high risk that the tolerable misstatement exceeds the sum of actual overstatements and understatements. c. The asset account is fairly stated because the total projected misstatement is less than the tolerable misstatement. d. The asset account is fairly stated because the tolerable misstatement exceeds the net of projected actual overstatements and understatements.

Correct Answer: A) There is an unacceptably high risk that the actual misstatements in the population exceed the tolerable misstatement because the total projected misstatement is more than the tolerable misstatement. Notes (a) The requirement is to identify an auditor's most likely response to a circumstance in which there is a tolerable misstatement of $60,000, and the auditor has discovered misstatement of a net overstatement of $3,500 ($3,700 - $200) when 1/20 of the account has been included in the sample. Because auditors must project the misstatements to the entire population, one would expect a misstatement of approximately $70,000 (20 times the misstatement of $3,500). Since this exceeds the tolerable misstatement, there is little question that the risk of material misstatement is too high and that the misstatement in the population exceeds the tolerable misstatement, therefore answer (a) is correct. Answer (b) is incorrect because it seems that the sum of actual overstatement and understatement is likely to exceed the tolerable misstatement. Also, answer (b) makes little sense since there probably is no such thing as "an unacceptably high risk" that the tolerable misstatement exceeds the sum of actual overstatements and understatements; in such a circumstance the auditor simply accepts the population as being materially correct. Answers (c) and (d) are incorrect because the total projected misstatement must be calculated as indicated above. See AU-C 530 and the Audit Sampling Guide for information on sampling.

23. In determining the sample size for a test of controls, an auditor should consider the likely rate of deviations, the allowable risk of assessing control risk too low, and the a. Tolerable deviation rate. b. Risk of incorrect acceptance. c. Nature and cause of deviations. d. Population size

Correct Answer: A) Tolerable deviation rate. Notes (a) The requirement is to identify the information needed in addition to the likely rate of deviations and the allowable risk of assessing control risk too low to determine the sample size for a test of controls in an attributes sampling plan. Answer (a) is correct because the tolerable deviation rate is also needed. Answer (b) is incorrect because the risk of incorrect acceptance relates to variables sampling applied to substantive testing, not attributes sampling applied to tests of controls. Answer (c) is incorrect because the auditor will examine the nature and cause of deviations after the sample has been selected. Answer (d) is incorrect because auditors often do not consider population size when performing attributes sampling applied to tests of controls.

35. 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 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 achieved upper precision 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 precision limit (8%). b. Expected deviation rate (7%) was more than the percentage of errors in the sample (3 1/2%). c. Achieved upper precision limit (8%) was more than the percentage of errors in the sample (3 1/2%). d. Expected deviation rate (2 1/2%) was less than the tolerable rate (7%).

Correct Answer: A) Tolerable rate (7%) was less than the achieved upper precision limit (8%). Notes (a) The requirement is to determine the circumstance in which an auditor would decide to increase the level of the preliminary assessment of control risk. Answer (a) is correct because the assessment of control risk will increase when the achieved upper precision limit (here 8%) exceeds the tolerable rate (here 7%). Answer (b) is incorrect because the expected deviation rate was 2 1/2%, not 7%. Also, if the expected deviation rate is higher than the percentage of error in the sample, the preliminary assessment does not need to be increased. Answer (c) is incorrect because the achieved upper precision limit will always exceed the percentage of errors in the sample. Answer (d) is incorrect because, in circumstances in which the auditor decides to sample the population, the expected deviation rate will always be less than the tolerable rate.

52. In the application of statistical techniques to the estimation of dollar amounts, a preliminary sample is usually taken primarily for the purpose of estimating the population a. Variability. b. Mode. c. Range. d. Median.

Correct Answer: A) Variability. Notes (a) The requirement is to determine the purpose of taking a preliminary sample when one uses statistical techniques. It is necessary to obtain an estimate of a population's standard deviation (variability) when calculating the required sample size and when using sampling techniques. Answers (b), (c), and (d) are incorrect because, in most statistical techniques used by auditors, the mode (most frequent balance), the median (middle balance) and the range (difference between the highest and lowest values) are not used.

48. In a probability-proportional-to-size sample with a sampling interval of $5,000, an auditor discovered that a selected account receivable with a recorded amount of $10,000 had an audit amount of $8,000. If this were the only error discovered by the auditor, the projected error of this sample would be a. $1,000 b. $2,000 c. $4,000 d. $5,000

Correct Answer: B) $2,000 Notes (b) The requirement is to determine the projected error (misstatement) of a probability-proportional-to-size (PPS) sample with a sampling interval of $5,000, when an auditor has discovered that an account with a recorded amount of $10,000 had an audit amount of $8,000. Answer (b) is correct since, when an account's recorded amount exceeds the sampling interval, the projected error equals the actual misstatement, here $2,000 ($10,000 - $8,000).

53. Using statistical sampling to assist in verifying the year-end accounts payable balance, an auditor has accumulated the following data: Using the ratio estimation technique, the auditor's estimate of year-end accounts payable balance would be Population: Accounts: 4,100 Book Balance: $5,000,000 Balance determined by the auditor: ? Sample: Accounts: 200 Book Balance: $250,000 Balance determined by the auditor: $300,000 a. $6,150,000 b. $6,000,000 c. $5,125,000 d. $5,050,000

Correct Answer: B) $6,000,000 Notes (b) The requirement is to determine the estimated audited accounts payable balance using the ratio estimation technique. Answer (b) is correct because the ratio estimation technique estimates the audited value by multiplying the audited value/book value of the sample times the population book value. In this case, ($300,000/$250,000) × $5,000,000 = $6,000,000.

36. 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 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 achieved upper precision limit to be 8%. The allowance for sampling risk was a. 5 1/2% b. 4 1/2% c. 3 1/2% d. 1%

Correct Answer: B) 4 1/2% Notes (b) The requirement is to determine the allowance for sampling risk of the presented sample. When considering the allowance for sampling risk, one may consider both the planned allowance for sampling risk or the adjusted allowance based on the sample results. Answer (b) is correct because both the planned and adjusted allowance for sampling risk are 4 1/2% (7% - 2.5% for planning purposes, and 8% - 3.5% [7/200] as adjusted).

54. Use of the ratio estimation sampling technique to estimated dollar amounts is inappropriate when a. The total book value is known and corresponds to the sum of all the individual book values. b. A book value for each sample item is unknown. c. There are some observed differences between audited values and book values. d. The audited values are nearly proportional to the book values.

Correct Answer: B) A book value for each sample item is unknown. Notes (b) The ratio estimation sampling technique is based on comparing the ratio of the book value to the audited value of the sampled items. Answer (b) is correct because this method cannot be used when there is no book value to make the comparison. The circumstances described in answers (a) and (c) are necessary for ratio point and interval estimation. Answer (d) describes the circumstances in which the use of ratio estimation will be efficient in terms of required sample size.

41. Which of the following sample planning factors would influence the sample size for a substantive test of details for a specific account? I. Expected amount of misstatements II. Measure of tolerable misstatement a. Neither I nor II b. Both I and II c. II only d. I only

Correct Answer: B) Both I and II Notes (b) The requirement is to determine whether either or both of the expected amount of misstatement and the measure of tolerable misstatement influence sample size for a substantive test of details. Answer (b) is correct because both the expected amount of misstatement and the tolerable misstatement affect sample size (AICPA Audit Sampling Guide). Increases in the expected amount of misstatements increase sample size, while increases in the tolerable misstatement decrease sample size.

33. Which of the following statements is correct concerning statistical sampling in tests of controls? a. As the population size increases, the sample size should increase proportionately. b. Deviations from specific internal control procedures at a given rate ordinarily result in misstatements at a lower rate. c. There is an inverse relationship between the expected population deviation rate and the sample size. d. In determining tolerable rate, an auditor considers detection risk and the sample size.

Correct Answer: B) Deviations from specific internal control procedures at a given rate ordinarily result in misstatements at a lower rate. Notes (b) The requirement is to identify the correct statement concerning statistical sampling in tests of controls. Answer (b) is correct because while deviations from pertinent control procedures increase the risk of material misstatements, any specific deviation need not necessarily result in a misstatement. For example, a recorded disbursement that does not show evidence of required approval might nevertheless be a transaction that is properly authorized and recorded (AICPA Audit Sampling Guide). Answer (a) is incorrect because increases in population size result in small increases in sample size. Answer (c) is incorrect because a direct relationship, not an inverse relationship, exists between the expected population deviation rate and the sample size—that is, increases in the expected population deviation rate result in an increase in the required sample size. Answer (d) is incorrect because when determining the tolerable rate, the auditor does not yet have the required sample size.

25. An auditor is testing internal control procedures that are evidenced on an entity's vouchers by matching random numbers with voucher numbers. If a random number matches the number of a voided voucher, that voucher ordinarily should be replaced by another voucher in the random sample if the voucher a. Constitutes a deviation. b. Has been properly voided. c. Cannot be located. d. Represents an immaterial dollar amount.

Correct Answer: B) Has been properly voided. Notes (b) The requirement is to identify the correct statement with respect to treatment of a voided voucher that has been selected in a sample. Answer (b) is correct because the AICPA Audit Sampling Guide states that the auditor should obtain reasonable assurance that the voucher has been properly voided, and should then replace it with another voucher. Answer (a) is incorrect because the voided voucher is not normally considered to be a deviation. Answer (c) is incorrect because the auditor must obtain reasonable assurance that the misplaced voucher has been voided. Answer (d) is incorrect because the level of materiality normally does not directly affect the decision.

29. The tolerable rate of deviations for a test of a control is generally a. Lower than the expected rate of errors in the related accounting records. b. Higher than the expected rate of errors in the related accounting records. c. Identical to the expected rate of errors in related accounting records. d. Unrelated to the expected rate of errors in the related accounting records.

Correct Answer: B) Higher than the expected rate of errors in the related accounting records. Notes (b) The requirement is to determine the correct relationship between the tolerable rate of deviations and the expected rate of deviations for a test of a control. The tolerable rate of deviations is the maximum rate of deviations from a prescribed control procedure that an auditor would be willing to accept and, unless the expected error rate is lower, reliance on internal control is not justified. Answer (a) is incorrect because if the tolerable rate of deviations is less than the expected rate, the auditor would not plan to rely on internal control and would therefore omit tests of controls. Answer (c) is incorrect because testing of controls is inappropriate if the expected rate of errors equals the tolerable rate of deviations (mathematically, the precision of zero makes the sample size equal to population size). Answer (d) is incorrect because, as indicated above, to perform tests of controls one must assume that the tolerable rate of deviations is more than the expected error rate.

16. Which of the following statistical sampling plans does not use a fixed sample size for tests of controls? a. Dollar-unit sampling. b. Sequential sampling. c. PPS sampling. d. Variables sampling.

Correct Answer: B) Sequential sampling. Notes (b) The requirement is to identify the type of sampling plan that does not use a fixed sample size for tests of controls. Answer (b) is correct because sequential sampling results in the selection of a sample in several steps, with each step conditional on the result of the previous steps. Therefore, sample size will vary depending upon the number of stages that prove necessary. Answers (a), (c), and (d) are all incorrect because dollar-unit sampling, PPS sampling, and variables sampling all use a fixed sample size.

40. Which of the following courses of action would an auditor most likely follow in planning a sample of cash disbursements if the auditor is aware of several unusually large cash disbursements? a. Set the tolerable rate of deviation at a lower level than originally planned. b. Stratify the cash disbursements population so that the unusually large disbursements are selected. c. Increase the sample size to reduce the effect of the unusually large disbursements. d. Continue to draw new samples until all the unusually large disbursements appear in the sample.

Correct Answer: B) Stratify the cash disbursements population so that the unusually large disbursements are selected. Notes (b) The requirement is to determine the proper course of action when an auditor is planning a sample of cash disbursements and he or she is aware of several unusually large cash disbursements. Given the description of the several disbursements as "unusually large," an auditor will generally test them. Answer (b) is therefore correct because stratifying the population will allow the auditor to ensure inclusion of the disbursements. The sampling procedure (selecting less than all items) will then be applied only to the smaller disbursements. Answer (a) is incorrect because the existence of the large disbursements will have no necessary relationship to the tolerable rate of deviation when attributes sampling is being used. Answer (c) is incorrect because while increasing the sample size might be appropriate in some variables sampling applications (we are not told in this problem whether attributes or variables sampling is being followed), the fact that the disbursements are described as "unusually large" leads one to include them. Answer (d) is incorrect because an auditor will not draw numerous samples to assure inclusion of the large disbursements.

17. 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.

Correct Answer: B) Systematic sampling may be appropriate. Notes (b) The requirement is to identify the correct statement concerning a statistical sampling application where the population consists of forms which are not consecutively numbered. Answer (b) is correct because systematic sampling is a procedure where a random start is obtained and then every nth item is selected. For example, a sample of forty from a population of a thousand would require selecting every 25th item after obtaining a random start between items 1 through 25. Answer (a) is incorrect because selection of a random sample is possible even though the population is not consecutively numbered. Answer (c) is incorrect because there is no special reason for using stratified sampling. Stratified sampling breaks down the population into subpopulations and applies different selection methods to each subpopulation. This selection method is used when the population consists of different types of items (e.g., large balances and small balances). Answer (d) is incorrect because random number tables can be used even though the forms are not consecutively numbered. If random numbers are selected for which there are no forms, they are ignored. This is the same as if there were 86,000 items in a consecutively numbered population and random numbers selected between 86,000 and 99,999 are ignored.

50. In statistical sampling methods used in substantive testing, an auditor most likely would stratify a population into meaningful groups if a. Probability-proportional-to-size (PPS) sampling is used. b. The population has highly variable recorded amounts. c. The auditor's estimated tolerable misstatement is extremely small. d. The standard deviation of recorded amounts is relatively small.

Correct Answer: B) The population has highly variable recorded amounts. Notes (b) The requirement is to identify the circumstance in which an auditor most likely would stratify a population into meaningful groups. Answer (b) is correct because stratified sampling is used to minimize the effect on sample size of variation within the overall population and results in the largest savings for populations with high variability. Answer (a) is incorrect because while PPS sampling may in essence stratify a population, the items selected, other than those larger than the sampling interval, are not in "meaningful groups." Answer (c) is incorrect because the tolerable misstatement in and of itself will not lead to stratification. Answer (d) is incorrect because stratification is used primarily when there is a relatively large standard deviation, not a relatively small standard deviation.

42. When planning a sample for a substantive test of details, an auditor should consider tolerable misstatement for the sample. This consideration should a. Be related to the auditor's business risk. b. Not be adjusted for qualitative factors. c. Be related to preliminary judgments about materiality levels. d. Not be changed during the audit process.

Correct Answer: C) Be related to preliminary judgments about materiality levels. Notes (c) The requirement is to determine the correct statement concerning the auditor's consideration of tolerable misstatement. Answer (c) is correct because the consideration of tolerable misstatement is related to preliminary judgments in a manner such that when the auditor's preliminary judgments about tolerable misstatement levels for accounts or transaction types are combined for the entire audit plan, the preliminary judgments about materiality levels for the financial statements are not exceeded. Answer (a) is incorrect because the auditor's judgment of business risk related to a client is not directly related to tolerable misstatement. Answer (b) is incorrect because tolerable misstatement may be adjusted for qualitative factors. Answer (d) is incorrect because tolerable misstatement may be changed during the audit process, especially as misstatements are identified and the auditor considers the nature of the misstatements.

15. Which of the following statistical selection techniques is least desirable for use by an auditor? a. Systematic selection. b. Stratified selection. c. Block selection. d. Sequential selection.

Correct Answer: C) Block selection. Notes (c) The requirement is to determine the least desirable statistical selection technique. Answer (c), block selection, is correct because, ideally, a sample should be selected from the entire set of data to which the resulting conclusions are to be applied. When block sampling is used, the selection of blocks often precludes items from being so selected. In most cases, systematic [answer (a)], stratified [answer (b)], and sequential [answer (d)] selection techniques all provide a better representation of the entire population than does block selection.

39. How would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details? I. Increase in tolerable misstatement II. Increase in assessed level of control risk a. I. Increase sample size ; II. Increase sample size b. I. Increase sample size ; II. Decrease sample size c. I. Decrease sample size ; II. Increase sample size d. I. Decrease sample size ; II. Decrease sample size

Correct Answer: C) I. Decrease sample size ; II. Increase sample size Notes (c) The requirement is to determine whether either or both of an increase in tolerable misstatement and an increase in the assessed level of control risk increase sample size in a substantive test of details. Answer (c) is correct because while an increase in tolerable misstatement decreases sample size for a substantive test of details, an increase in the assessed level of control risk increases the sample size for a substantive test of details because a lower level of detection risk is required.

24. Which of the following combinations results in a decrease in sample size in a sample for attributes? I. Risk of assessing control risk too low II. Tolerable rate III. Expected population deviation rate a. I. Increase ; II. Decrease ; III. Increase b. I. Decrease ; II. Increase ; III. Decrease c. I. Increase ; II. Increase ; III. Decrease d. I. Increase ; II. Increase ; III. Increase

Correct Answer: C) I. Increase ; II. Increase ; III. Decrease Notes (c) The requirement is to determine when a sample size would be decreased when sampling for attributes. Answer (c) is correct because the sample size will decrease when the risk of assessing control risk too low is increased, the tolerable rate is increased, and the expected population deviation rate is decreased (Audit and Accounting Guide, Audit Sampling). Answers (a), (b), and (d) are all incorrect because they include combinations of changes that would not necessarily decrease sample size.

32. An auditor should consider the tolerable rate of deviation when determining the number of check requests to select for a test to obtain assurance that all check requests have been properly authorized. The auditor should also consider I. The average dollar value of the check requests II. The allowable risk of assessing control risk too low a. Both I and II b. I only c. II only d. Neither I nor II

Correct Answer: C) II only Notes (c) The requirement is to determine whether an auditor would consider the average dollar value of check requests, the allowable risk of assessing control risk too low, or both, when testing whether check requests have been properly authorized. Answer (c) is correct because a test of authorization such as this is an attributes test which requires the auditor to determine an allowable risk of assessing control risk too low, but does not deal directly with dollar values. Answers (a), (b), and (d) are all incorrect because they include incorrect combinations of the replies. See AU-C 530 and the AICPA Audit Sampling Guide for information on sampling.

58. Which of the following most likely would be an advantage in using classical variables sampling rather than probability-proportional-to-size (PPS) sampling? a. An estimate of the standard deviation of the population's recorded amounts is not required. b. The auditor rarely needs the assistance of a computer program to design an efficient sample. c. Inclusion of zero and negative balances generally does not require special design considerations. d. Any amount that is individually significant is automatically identified and selected.

Correct Answer: C) Inclusion of zero and negative balances generally does not require special design considerations. Notes (c) The requirement is to identify an advantage in using classical variables sampling rather than probability-proportional-to-size sampling. Answer (c) is correct because the inclusion of zero and negative balances generally does not require special design considerations when using classical sampling, while it does when using probability-proportional-to-size sampling (AICPA Audit Sampling Guide). Answer (a) is incorrect because classical variables sampling does require an estimate of the standard deviation of the population's recorded amounts. Answer (b) is incorrect because the computational process involved with classical variables sampling may make use of a computer program desirable. Answer (d) is incorrect because probability-proportional-to-size sampling, not classical sampling, automatically stratifies individually significant items.

9. While performing a test of details during an audit, an auditor determined that the sample results supported the conclusion that the recorded account balance was materially misstated. It was, in fact, not materially misstated. This situation illustrates the risk of a. Assessing control risk too high. b. Assessing control risk too low. c. Incorrect rejection. d. Incorrect acceptance.

Correct Answer: C) Incorrect rejection. Notes (c) The requirement is to determine the type of risk demonstrated when an auditor concludes that an account is misstated when in fact it is not. Answer (c) is correct because the risk of incorrect rejection is the risk that the sample supports the conclusion that the recorded account balance is materially misstated when the account is not misstated. Answers (a) and (b) are incorrect because the risk of assessing control risk too high and the risk of assessing control risk too low relate to tests of controls, and not to substantive tests of details. Answer (d) is incorrect because the risk of incorrect acceptance is the risk that the sample support the conclusion that the account is not misstated when in fact it is misstated.

14. An underlying feature of random-based selection of items is that each a. Stratum of the accounting population be given equal representation in the sample. b. Item in the accounting population be randomly ordered. c. Item in the accounting population should have an opportunity to be selected. d. Item must be systematically selected using replacement.

Correct Answer: C) Item in the accounting population should have an opportunity to be selected. Notes (c) The requirement is to determine the correct statement with respect to random sampling. Answer (c) is correct because every item in the accounting population should have an opportunity to be selected. Answer (a) is incorrect because with stratified random sampling, each stratum need not be given equal representation. Answer (b) is incorrect because while sample units should be randomly selected, there is no requirement that the accounting population be randomly ordered. Answer (d) is incorrect because random sampling, by its very nature, is not systematic. Additionally, random sampling may be performed without replacement.

2. An advantage of statistical sampling over nonstatistical sampling is that statistical sampling helps an auditor to a. Eliminate the risk of nonsampling errors. b. Reduce the level of audit risk and materiality to a relatively low amount. c. Measure the sufficiency of the evidential matter obtained. d. Minimize the failure to detect errors and fraud.

Correct Answer: C) Measure the sufficiency of the evidential matter obtained. Notes (c) The requirement is to identify an advantage of statistical sampling over nonstatistical sampling. Answer (c) is correct because statistical sampling helps the auditor to: (1) design an efficient sample, (2) measure the sufficiency of the evidential matter obtained, and (3) evaluate the sample results (AICPA Audit Sampling Guide). Answer (a) is incorrect because the risk of nonsampling errors is not directly affected by whether statistical or nonstatistical sampling is used. Answer (b) is incorrect because either statistical or nonstatistical sampling can be used to reduce the level of audit risk to a low level; the materiality level should not be affected by the type of sampling used. Answer (d) is incorrect because either statistical or nonstatistical sampling may be used to minimize the failure to detect errors and fraud.

44. In estimation sampling for variables, which of the following must be known in order to estimate the appropriate sample size required to meet the auditor's needs in a given situation? a. The qualitative aspects of errors. b. The total dollar amount of the population. c. The acceptable level of risk. d. The estimated rate of misstatements in the population.

Correct Answer: C) The acceptable level of risk. Notes (c) The requirement is to identify the factor which must be known in order to estimate the appropriate sample size when using variables sampling. Answer (c) is correct because the auditor must set an acceptable level of risk for both variables sampling and attribute sampling. Answer (a) is incorrect because while the auditor will consider the qualitative aspects of errors when evaluating the sample, they need not be considered in determining an appropriate sample size. Answer (b) is incorrect because a primary objective of variables sampling is to estimate the audited dollar amount of the population. Also, in some forms of variables sampling, knowledge of book values is not necessary (e.g., mean-perunit). Answer (d) is incorrect because a rate of error in the population relates to attribute sampling.

46. Which of the following statements is correct concerning probability-proportional-to-size (PPS) sampling, also known as dollar unit sampling? a. The sampling distribution should approximate the normal distribution. b. Overstated units have a lower probability of sample selection than units that are understated. c. The auditor controls the risk of incorrect acceptance by specifying that risk level for the sampling plan. d. The sampling interval is calculated by dividing the number of physical units in the population by the sample size.

Correct Answer: C) The auditor controls the risk of incorrect acceptance by specifying that risk level for the sampling plan. Notes (c) The requirement is to identify the correct statement regarding probability-proportional-to-size (PPS) sampling. Answer (c) is correct because when using PPS sampling, the auditor controls the risk of incorrect acceptance by specifying a risk level when planning the sample. Answer (a) is incorrect because PPS sampling does not assume a normal distribution. Answer (b) is incorrect because the book value of the unit determines how probable it is that it will be included in the sample, not whether it is over or understated. Answer (d) is incorrect because the sampling interval is calculated by dividing the book value of the population by the sample size.

19. What is the primary objective of using stratification as a sampling method in auditing? a. To increase the confidence level at which a decision will be reached from the results of the sample selected. b. To determine the occurrence rate for a given characteristic in the population being studied. c. To decrease the effect of variance in the total population. d. To determine the precision range of the sample selected.

Correct Answer: C) To decrease the effect of variance in the total population. Notes (c) Stratified sampling is a technique of breaking the population down into subpopulations and applying different sample selection methods to the subpopulations. Stratified sampling is used to minimize the variance within the overall population [answer (c)]. Recall that as variance increases, so does the required sample size (because of the extreme values). Thus, stratification allows the selection of subpopulations to reduce the effect of dispersion in the population.

26. An auditor plans to examine a sample of twenty purchase orders for proper approvals as prescribed by the client's control procedures. One of the purchase orders in the chosen sample of twenty cannot be found, and the auditor is unable to use alternative procedures to test whether that purchase order was properly approved. The auditor should a. Choose another purchase order to replace the missing purchase order in the sample. b. Consider this test of control invalid and proceed with substantive tests since internal control cannot be relied upon. c. Treat the missing purchase order as a deviation for the purpose of evaluating the sample. d. Select a completely new set of twenty purchase orders.

Correct Answer: C) Treat the missing purchase order as a deviation for the purpose of evaluating the sample. Notes (c) The requirement is to determine the proper method of handling a sample item which cannot be located for evaluation purposes. Answer (c) is correct because an auditor would ordinarily consider the selected item to be a deviation. Answers (a) and (d) are incorrect since a possible cause for the missing purchase order could be a breakdown in one of the controls of the system. Thus, in selecting a new sample item(s) the auditor may be ignoring a portion of the population which is in error and may be artificially skewing the results of the tests performed on the sample. Answer (b) is incorrect because there is no reason to believe that the entire test is invalid and cannot be relied upon.

12. Which of the following sampling methods would be used to estimate a numerical measurement of a population, such as a dollar value? a. Attribute sampling. b. Stop-or-go sampling. c. Variables sampling. d. Random-number sampling.

Correct Answer: C) Variables sampling. Notes (c) The requirement is to identify the sampling method that would be used to estimate a numerical measurement such as a dollar value of a population. Answer (c) is correct because sampling for variables addresses such numerical measurements. Answer (a) is incorrect because attributes sampling deals with deviation rates. Answer (b) is incorrect because stop-or-go sampling (also referred to as sequential sampling) is a form of attributes sampling. Answer (d) is incorrect because random-number sampling is simply a sample selection technique that may be used with either an attributes or a variables form of sampling; accordingly, a numerical measurement such as a dollar value is not necessary for random-number sampling.

11. The expected population deviation 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.

Correct Answer: D) Attribute sampling. Notes (d) The requirement is to identify the type of sampling involved in a review of client invoices in which an expected population deviation rate and an established tolerable rate are provided. Answer (d) is correct because attribute sampling is used to reach a conclusion about a population in terms of a rate of occurrence (Audit Sampling Guide). Answer (a) is incorrect because stratified sampling is generally used to reach a dollar-based conclusion in variables sampling approaches. Answer (b) is incorrect because, as indicated, variables sampling deals with a dollar amount conclusion, not deviation rates. Answer (c) is incorrect because discovery sampling is only used in cases in which the auditor expects deviation rates to be extremely low (approaching zero).

4. The risk of incorrect acceptance and the likelihood of assessing control risk too low relate to the a. Allowable risk of tolerable misstatement. b. Preliminary estimates of materiality levels. c. Efficiency of the audit. d. Effectiveness of the audit.

Correct Answer: D) Effectiveness of the audit. Notes (d) The requirement is to determine the nature of the risk of incorrect acceptance and the risk of assessing control risk too low. Answer (d) is correct because the risk of incorrect acceptance and the risk of assessing control risk too low relate to the effectiveness of an audit in detecting an existing material misstatement or deviation. Answer (a) is incorrect because the term "allowable risk of tolerable misstatement" is not used in the professional standards. Answer (b) is incorrect because preliminary estimates of materiality levels relate most directly to the risk of incorrect acceptance, and only indirectly to the risk of assessing control risk too low. Answer (c) is incorrect because the risk of incorrect rejection and the risk of assessing control risk too high relate to the efficiency of the audit.

28. The objective of the tolerable rate in sampling for tests of controls of internal control is to a. Determine the probability of the auditor's conclusion based upon reliance factors. b. Determine that financial statements taken as a whole are not materially in error. c. Estimate the reliability of substantive tests. d. Estimate the range of procedural deviations in the population.

Correct Answer: D) Estimate the range of procedural deviations in the population. Notes (d) The requirement is to determine the objective of the tolerable rate in sampling. Tolerable rate is calculated to determine the range of procedural deviations in the population. Answer (a) is incorrect because probabilities relate more directly to reliability. Answer (b) is incorrect because errors on financial statements in materiality terms relate to variables sampling. Answer (c) is incorrect because the tolerable rate does not relate directly to substantive tests.

13. For which of the following audit tests would an auditor most likely use attribute sampling? a. Making an independent estimate of the amount of a LIFO inventory. b. Examining invoices in support of the valuation of fixed asset additions. c. Selecting accounts receivable for confirmation of account balances. d. Inspecting employee time cards for proper approval by supervisors.

Correct Answer: D) Inspecting employee time cards for proper approval by supervisors. Notes (d) The requirement is to determine the audit test for which an auditor would most likely use attribute sampling. Answer (d) is correct because attribute sampling is used to reach a conclusion about a population in terms of a rate of occurrence. Here the rate of occurrence will be the rate of (un) approved time cards. Answers (a), (b), and (c) are all incorrect because they all relate more directly to variables sampling which is generally used to reach conclusion about a population in terms of a dollar amount. See the AICPA Audit and Accounting Guide, Audit Sampling, and AU-C 530 for more information on audit sampling.

18. When performing a test of a control with respect to control over cash receipts, an auditor may use a systematic sampling technique with a start at any randomly selected item. The biggest disadvantage of this type of sampling is that the items in the population a. Must be systematically replaced in the population after sampling. b. May systematically occur more than once in the sample. c. Must be recorded in a systematic pattern before the sample can be drawn. d. May occur in a systematic pattern, thus destroying the sample randomness.

Correct Answer: D) May occur in a systematic pattern, thus destroying the sample randomness. Notes (d) Answer (d) is correct because systematic items occurrence in a population may destroy a sample's randomness. Answer (a) is incorrect because items need not be replaced in the population, and therefore is not a disadvantage of systematic sampling. Answer (b) is incorrect because an individual item will not occur more than once in a sample when systematic sampling is being used (because the auditor selects every nth item). Answer (c) is incorrect because systematic sampling refers to the type of sampling selection plan used and not the manner in which items in the population are recorded. Also, as indicated in (d) above, a systematic pattern in the population is a hindrance to systematic sampling.

34. What is an auditor's evaluation of a statistical sample for attributes when a test of fifty documents results in three deviations if tolerable rate is 7%, the expected population deviation rate is 5%, and the allowance for sampling risk is 2%? a. Modify the planned assessed level of control risk because the tolerable rate plus the allowance for sampling risk exceeds the expected population deviation rate. b. Accept the sample results as support for the planned assessed level of control risk because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate. c. Accept the sample results as support for the planned assessed level of control risk because the tolerable rate less the allowance for sampling risk equals the expected population deviation rate. d. Modify the planned assessed level of control risk because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate.

Correct Answer: D) Modify the planned assessed level of control risk because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate. Notes (d) The requirement is to determine the proper evaluation of a statistical sample for attributes when a test of 50 documents results in 3 deviations, given a tolerable rate of 7%, an expected population deviation rate of 5%, and an allowance for sampling risk of 2%. Answer (d) is correct because when the deviation rate plus the allowance for sampling risk exceeds the tolerable rate, the assessed level of control risk may increase. Here the deviation rate of 6% (3 deviations/50 documents) plus the allowance for sampling risk of 2% equals 8% and exceeds the tolerable rate of 7%. Answer (a) is incorrect because the tolerable rate plus the allowance for sampling risk will always exceed the expected population deviation rate when tests of controls are being performed. Answer (b) is incorrect because when the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate the sample results do not support the planned assessed level of control risk. Answer (c) is incorrect because the tolerable rate less the allowance for sampling risk should be compared with the actual deviation rate.

20. As a result of tests of controls, an auditor assessed control risk too low and decreased substantive testing. This assessment occurred because the true deviation rate in the population was a. Less than the risk of assessing control risk too low, based on the auditor's sample. b. Less than the deviation rate in the auditor's sample. c. More than the risk of assessing control risk too low, based on the auditor's sample. d. More than the deviation rate in the auditor's sample.

Correct Answer: D) More than the deviation rate in the auditor's sample. Notes (d) The requirement is to identify the circumstance that would cause an auditor to assess control risk too low and decrease substantive testing inappropriately. Answer (d) is correct because when the true deviation rate in the population exceeds that in the sample, the auditor may assess control risk too low. The AICPA Audit Sampling Guide discusses tests of controls and attributes sampling in its second chapter. Answers (a) and (c) are incorrect because the true deviation rate and the risk of assessing control risk too low do not have such a relationship, either positive or negative. Answer (b) is incorrect because a deviation rate in the population that is less than the deviation rate in the auditor's sample may lead the auditor to assess control risk too high.

1. An advantage of using statistical over nonstatistical sampling methods in tests of controls is that the statistical methods a. Can more easily convert the sample into a dualpurpose test useful for substantive testing. b. Eliminate the need to use judgment in determining appropriate sample sizes. c. Afford greater assurance than a nonstatistical sample of equal size. d. Provide an objective basis for quantitatively evaluating sample risk.

Correct Answer: D) Provide an objective basis for quantitatively evaluating sample risk. Notes (d) The requirement is to identify an advantage of statistical sampling over nonstatistical sampling. Answer (d) is correct because statistical sampling helps the auditor to: (1) design an efficient sample, (2) measures the sufficiency of the evidential matter obtained, and (3) evaluate the sample results (AICPA Audit Sampling Guide). Answer (a) is incorrect because dual-purpose tests, which both test a control and serve as substantive test, may be performed with either a statistical or a nonstatistical sample. Answer (b) is incorrect because both statistical and nonstatistical sampling require the use of judgment, although that judgment is quantified when statistical sampling is used. Answer (c) is incorrect because either statistical or nonstatistical sampling may provide equal assurance to the auditor.

55. An auditor is performing substantive tests of pricing and extensions of perpetual inventory balances consisting of a large number of items. Past experience indicates numerous pricing and extension errors. Which of the following statistical sampling approaches is most appropriate? a. Unstratified mean-per-unit. b. Probability-proportional-to-size. c. Stop or go. d. Ratio estimation.

Correct Answer: D) Ratio estimation. Notes (d) The requirement is to determine the most appropriate sampling approach for substantive tests of pricing and extensions of perpetual inventory balances consisting of a large number of items for which past experience indicates numerous expected pricing and extension errors. Answer (d) is correct because ratio estimation is appropriate when testing a population for which a large number of errors of this nature is expected (Audit and Accounting Guide, Audit Sampling). Answer (a) is incorrect because the unstratified mean-per-unit method will typically provide a larger sample size than the ratio estimation method to achieve the same level of sampling risk. Thus, the ratio estimation method would be more appropriate. Answer (b) is incorrect because probability-proportional-to-size sampling is most efficient for testing populations with relatively low expected error rates. Answer (c) is incorrect because "stop or go" or "sequential" sampling is most frequently used in attribute sampling.

38. When an auditor has chosen a random sample and is using nonstatistical attributes sampling, that auditor a. Need not consider the risk of assessing control risk too low. b. Has committed a nonsampling error. c. Will have to use discovery sampling to evaluate the results. d. Should compare the deviation rate of the sample to the tolerable deviation rate.

Correct Answer: D) Should compare the deviation rate of the sample to the tolerable deviation rate. Notes (d) The requirement is to identify the proper statement concerning a random sample when nonstatistical attributes sampling is being used. Answer (d) is correct because the deviation rate of the sample should be compared to the tolerable deviation rate regardless of whether statistical or nonstatistical sampling is being used. Answer (a) is incorrect because the risk of assessing control risk too low should be considered, although it may be done judgmentally. Answer (b) is incorrect because nonsampling error relates to "human" type errors such as not identifying a deviation, and not specifically to the use of nonstatistical sampling. Answer (c) is incorrect because discovery sampling will not be used to evaluate the results.

43. A number of factors influences the sample size for a substantive test of details of an account balance. All other factors being equal, which of the following would lead to a larger sample size? a. Greater reliance on internal control. b. Greater reliance on analytical procedures. c. Smaller expected frequency of errors. d. Smaller measure of tolerable misstatement.

Correct Answer: D) Smaller measure of tolerable misstatement. Notes (d) The requirement is to determine the factor that would lead to larger sample size in a substantive test of details. Answer (d) is correct because the sample size required to achieve the auditor's objective at a given risk of incorrect acceptance increases as the auditor's assessment of tolerable misstatement for the balance or class decreases. Answer (a) is incorrect because a greater reliance on internal control will lead to a smaller sample size in a substantive test of details. Answer (b) is incorrect because greater reliance upon analytical procedures will result in a need for less reliance on substantive tests of details and therefore will result in a smaller sample. Answer (c) is incorrect because a smaller expected frequency of errors will generally include properly functioning internal control and will therefore result in a smaller sample for substantive tests of details.

22. Which of the following statements is correct concerning statistical sampling in tests of controls? a. Deviations from control procedures at a given rate usually result in misstatements at a higher rate. b. As the population size doubles, the sample size should also double. c. The qualitative aspects of deviations are not considered by the auditor. d. There is an inverse relationship between the sample size and the tolerable rate.

Correct Answer: D) There is an inverse relationship between the sample size and the tolerable rate. Notes (d) The requirement is to identify the correct statement about sampling for attributes. Answer (d) is correct because the sample size increases as the tolerable rate decreases, an inverse relationship. Answer (a) is incorrect because many deviations do not necessarily result in a misstatement. Answer (b) is incorrect because a doubling of the population size will result in less than a doubling of the required sample size. Answer (c) is incorrect because auditors must consider the qualitative aspects of deviations.

56. The major reason that the difference and ratio estimation methods would be expected to produce audit efficiency is that the a. Number of members of the populations of differences or ratios is smaller than the number of members of the population of book values. b. Beta risk may be completely ignored. c. Calculations required in using difference or ratio estimation are less arduous and fewer than those required when using direct estimation. d. Variability of the populations of differences or ratios is less than that of the populations of book values or audited values.

Correct Answer: D) Variability of the populations of differences or ratios is less than that of the populations of book values or audited values. Notes (d) Difference and ratio estimation methods are statistical sampling methods. They measure the difference between audit and book values or the ratio of audit to book values. As these differences should not be great, the population of these differences will have little variance. In statistical sampling, the less variation in a population, the smaller the required sample to provide an estimate of the population. In other words, difference and ratio estimation methods are more efficient because the differences between audit and book values are expected to vary less than the actual items in the population. Answer (a) is incorrect because the number of members in the population for differences or ratio methods would be the same as the number of items in the population for a direct estimation method. In difference sampling, many items would be zero because audit and book are the same, and in ratio sampling, many of the members would be one for the same reason. Answer (b) is incorrect because beta risk can never be ignored, as beta risk is the risk of accepting an incorrect (unacceptable) population. Answer (c) is incorrect because the calculations required in difference and ratio sampling are similar to those used in direct estimation sampling.

True or False: A PPS sample eliminates the need to project results to the overall population.

False

True or False: One does not need a book value for individual items to evaluate a PPS sample.

False

True or False: PPS sampling is "preferred" by the professional standards.

False

True or False: PPS sampling results in a smaller sample size when numerous small misstatements are expected.

False

True or False: If no misstatements are expected, PPS sampling will usually result in a smaller sample size than classical variables sampling methods.

True

True or False: Individually significant items are automatically identified.

True

True or False: PPS sampling results in a stratified sample.

True

True or False: Size of a PPS sample is not based on the estimated variation of audited amounts.

True