Chapter 09 Audit Sampling - CPA Diary



Chapter 09

Audit Sampling

 

True / False Questions

 

1. Stratification of the population generally results in a more efficient sampling plan. 

True    False

 

2. Discovery sampling is equivalent to an attributes sampling plan with a specified expected deviation rate of 0 percent. 

True    False

 

3. Increases in the number of deviations in an attributes sample results in an increase in the achieved upper deviation rate of the attributes sample. 

True    False

 

4. The definition of a "deviation" for a test of a control should include only those deviations that result in misstatements in the financial statements. 

True    False

 

5. Statistical sampling cannot be used to test all control activities. 

True    False

 

6. Using ratio and difference estimation for a sample is an example of a dual purpose test. 

True    False

 

7. Increases in the tolerable misstatement result in a decreased sample size when using mean-per-unit estimation. 

True    False

 

8. The mean book value of the items included in a mean-per-unit sample is not directly used in the evaluation of sample results. 

True    False

 

9. When evaluating the results of a variables sampling plan, the projected misstatement is calculated and compared to the tolerable misstatement. 

True    False

 

10. Auditors project the misstatements found in the sample to the population when using statistical sampling, but not when using nonstatistical sampling. 

True    False

 

 

Multiple Choice Questions

 

 The 10,000 accounts receivable of DEF Company have a total book value of $120,000. A CPA has selected and audited a sample of 100 accounts with a total book value of $1,000 and an audited value of $1,200.

 

11. Using the difference estimation technique, estimated total audited value of the population is: 

A. $100,000.

B. $120,000.

C. $140,000.

D. $144,000

 

12. Using the ratio estimation technique, the estimated total audited value of the population is: 

A. $100,000.

B. $120,000.

C. $140,000.

D. $144,000

 

13. Using the mean-per-unit estimation technique, the estimated total audited value of the population is: 

A. $100,000.

B. $120,000.

C. $140,000.

D. $144,000.

 

14. Using the mean-per-unit estimation method an auditor has properly calculated the estimated total audited value of a population as $200,000. Her sample included 200 of the population's 40,000 items. She found that, in her sample the average audited value was $1 less than the average book value. What was the average audited value in the sample? 

A. $4.

B. $5.

C. $6.

D. $10.

 

15. Using difference estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? 

A. $160,000.

B. $161,538.

C. $168,000.

D. $200,000.

 

16. Using ratio estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? 

A. $160,000.

B. $161,538.

C. $168,000.

D. $200,000.

 

17. Using mean-per-unit estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? 

A. $160,000.

B. $161,538.

C. $168,000.

D. $200,000.

 

18. If the projected misstatement in a nonstatistical sampling is $8,000, while the tolerable misstatement is $9,000, what would an auditor likely conclude? 

A. Since the projected misstatement is less than the tolerable misstatement, the account is not misstated.

B. Since the projected misstatement is less than the tolerable misstatement, the account is misstated.

C. The risk is high that the account is materially misstated.

D. The analysis has been improperly performed since the projected misstatement is unequal to the tolerable misstatement.

 

19. A dual purpose test simultaneously. 

A. Addresses two different accounts.

B. Functions as a substantive test and as a test of controls.

C. Functions as an analytical procedure and a substantive test.

D. Substantiates an ending balance and the transactions making up the balance.

 

 The 1000 accounts receivable of Winco Company have a total book value of $20,000 (Average book value = $20). Bob Duffo, CPA, has selected and audited a sample of 50 accounts with the following mean values:

1. Book value of $19.

2. Audited value of $19.60.

 

20. What is the estimated total audited value using mean per unit sampling? 

A. $19,000.

B. $19,600.

C. $20,000.

D. $20,632.

 

21. What is the estimated total audited value using difference estimation sampling? 

A. $19,387.

B. $19,400.

C. $19,600.

D. $20,600.

 

22. If all other factors specified in an attributes sampling plan remain constant, decreasing the tolerable rate and decreasing the risk of assessing control risk too low would have what effect on sample size? 

A. Increase.

B. Remain the same.

C. Decrease.

D. Indeterminate, depends upon exact change being made.

 

23. If all other factors specified in an attributes sampling plan remain constant, decreasing the tolerable rate and increasing the estimated population deviation rate would have what effect on sample size? 

A. Increase.

B. Remain the same.

C. Decrease.

D. Indeterminate, depends upon exact change being made.

 

24. An increase in the tolerable misstatement has what effect on the planned allowance for sampling risk? 

A. Increases.

B. Decreases.

C. No effect.

D. Indeterminate.

 

25. Which of the following is not generally used for selecting samples? 

A. Random number tables.

B. Random number generators.

C. Physical representation numbers.

D. Systematic selection.

 

26. In performing a test of a control last year the auditors specified a tolerable deviation rate of X percent. This year the auditors have specified a tolerable rate of less than X percent. Assuming that all other factors remain the same, which of the following is true regarding the relationship between this year's sample size compared to last year's sample size? 

A. This year's sample is larger than last year's sample.

B. This year's sample is smaller than last year's sample.

C. This year's sample is equal to last year's sample.

D. This year's sample is indeterminate in relation to last year's sample.

 

27. The auditor using nonstatistical attributes sampling, but who nevertheless has chosen the sample in conformity with random selection procedures: 

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 techniques to evaluate the results.

D. Should compare the deviation rate of the sample to the tolerable rate.

 

28. When performing tests of controls over authorization of cash receipts, which of the following sampling methods would be most appropriate? 

A. Attributes.

B. Ratio.

C. Stratified.

D. Variables.

 

29. Which of the following statistical sampling techniques involves taking samples in a series of stages? 

A. Systematic sampling.

B. Sequential sampling.

C. Continuous sampling.

D. Multiple location sampling.

 

30. Which of the following is generally not true about statistical sampling as compared to nonstatistical sampling? 

A. Statistical samples are more representative of the population.

B. Statistical sample plans involve additional costs of evaluation.

C. Statistical sampling allows a more objective evaluation of sample results.

D. Statistical sampling may assist the auditors in designing more efficient samples.

 

31. When using statistical sampling, which of the following need not be known to evaluate the results of an attributes sample? 

A. Sample size.

B. Risk of assessing control risk too low.

C. Number of deviations in the population.

D. Number of deviations found in the sample.

 

32. When the auditors have decided to use statistical rather than nonstatistical sampling, a disadvantage is that: 

A. Designing efficient samples is more difficult.

B. The costs of training staff may be higher.

C. Sampling without replacement must be used.

D. Objectively evaluating results is impossible.

 

33. Changing from a sampling plan using random selection with replacement to random selection without replacement has what effect on the required sample size? 

A. Increases.

B. Decreases

C. No effect.

D. An indeterminate effect.

 

34. When the auditors have chosen to test a control, what relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample? 

A. Exceed.

B. Equal.

C. Be less than.

D. Indefinite.

 

35. Increases in the planned allowance for sampling risk have what effect on required sample size? 

A. Increases.

B. Decreases.

C. No effect.

D. Indeterminate.

 

36. When using sampling for tests of controls, which of the following audit consequences may follow? 

A. If sample results indicate that the control is operating effectively, but in fact it is not, control risk will be assessed too low.

B. If sample results indicate that the control is operating effectively, but in fact it is not, control risk will be assessed too high.

C. If sample results indicate that the control is not operating effectively, but in fact it is operating effectively, the audit is likely to be faulty because of reduced substantive tests.

D. If sample results indicate that the control is not operating effectively, but in fact it is operating effectively, control risk will be assessed too low.

 

37. The auditors expect a population deviation rate of billing errors of two percent, and have established a tolerable rate of five percent. The sampling approach most likely to be used is: 

A. Attributes sampling.

B. Stratified sequential sampling.

C. Discovery sampling.

D. None, as sampling does not seem appropriate in this situation.

 

38. The auditors expect a population deviation rate of billing errors of eight percent, and have established a tolerable rate of five percent. The sampling approach most likely to be used is: 

A. Attributes sampling.

B. Stratified random sampling.

C. Variables sampling.

D. None, as sampling does not seem appropriate in this situation.

 

39. Which of the following may be used to reduce the risk of nonsampling errors? 

A. Increasing the size of audit samples.

B. Stratifying audit samples.

C. Adequately planning audit samples.

D. Using statistical sampling techniques.

 

40. Which of the following types of risk is of critical importance to auditors in performing tests of controls? 

A. The risk of assessing control risk too low.

B. The risk of assessing control risk too high.

C. The risk of incorrect acceptance.

D. The risk of incorrect rejection.

 

41. The auditors' failure to recognize a misstatement in an amount or a deviation in an internal control data processing procedure is described as a: 

A. Statistical error.

B. Sampling misstatement.

C. Standard error of the mean.

D. Nonsampling error.

 

42. What effect does obtaining a sample with a standard deviation larger than that estimated during planning have on the adjusted allowance for sampling risk? 

A. Increases.

B. Decreases.

C. No effect.

D. Indeterminate.

 

 The 2000 accounts receivable of ABC Company have a total book value of $40,000. Bob Rotter, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,950. The audited value of the 100 accounts in the sample is $1,875.

 

43. Using the mean-per-unit estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: 

A. $37,500

B. $38,462

C. $38,500

D. $41,600

 

44. Using the ratio estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: 

A. $37,500

B. $38,462

C. $38,500

D. $41,600

 

45. Using the difference estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: 

A. $37,500

B. $38,462

C. $38,500

D. $41,600

 

46. The 3000 accounts receivable of DEF Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $2,100. Using the difference estimation technique, Smith has properly estimated a projected misstatement of an overstatement of $6,000 for the entire population. The audited value of Smith's sample is: 

A. $1,700

B. $1,800

C. $1,900

D. $2,300

 

47. The 3000 accounts receivable of DEF Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $2,100. Using the difference estimation technique, Smith has properly estimated a projected misstatement of a $9,000 overstatement for the entire population. The estimated total audited value of the population is: 

A. $51,000

B. $58,000

C. $60,000

D. $69,000

 

48. The 4000 accounts receivable of GHI Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,600. Using the mean-per-unit estimation technique, Smith has properly estimated a projected misstatement of a $8,000 overstatement for the entire population. The audited value of Smith's sample is: 

A. $1,300

B. $1,400

C. $1,600

D. $1,800

 

49. Which of the following is a correct statement with respect to evaluating results when using nonstatistical sampling for substantive tests? 

A. When the projected misstatement exceeds the tolerable misstatement, the auditor should conclude that the population is not misstated.

B. The closer the projected misstatement is to the tolerable misstatement, the higher the risk of material misstatement.

C. When the projected misstatement is equal to zero, the auditors may conclude with certainty that no misstatements exist in the account.

D. When the projected misstatement percentage exceeds the risk of incorrect acceptance the auditors will generally conclude that the population is materially misstated.

 

50. Assume a mean-per-unit estimation variables sampling application with a tolerable misstatement of $70,000 and a book value of $700,000. After performing the sampling plan, the auditors calculated an adjusted allowance for sampling risk of $45,000 and a point estimate of the population's total audited value to be $650,000. Based on these results, the auditor would: 

A. Because the tolerable misstatement exceeds the adjusted allowance for sampling risk, conclude that the population does not contain a material misstatement.

B. Because the total audited value ( tolerable misstatement includes the book value, conclude that the population does not contain a material misstatement.

C. Because the tolerable misstatement exceeds the adjusted allowance for sampling risk, conclude that there is too great a risk that the account balance is materially misstated.

D. Because the total audited value ( adjusted allowance for sampling risk does not include the book value, conclude that there is too great a risk that the account balance is materially misstated.

 

51. Assume a mean-per-unit estimation variables sampling application with a tolerable misstatement of $70,000 and a book value of $700,000. After performing the sampling plan, the auditors calculated an adjusted allowance for sampling risk of $45,000 and a point estimate of the population's total audited value to be $640,000. The projected misstatement based on this sample is: 

A. $ 5,000

B. $45,000

C. $60,000

D. $70,000

 

52. The auditors have audited a sample with a standard deviation of audited values larger than they had originally estimated. In this situation, to maintain the risk of incorrect acceptance at its predetermined level without increasing the size of the sample, which of the following statements is correct? 

A. The adjusted allowance for sampling risk will be smaller than had been planned.

B. The adjusted allowance for sampling risk will be larger than had been planned.

C. The risk of incorrect rejection will necessarily decrease.

D. The size of the population must be decreased.

 

53. In the past, the auditors have found that the book value of a receivable account has been related to the amount the account is misstated (i.e., large accounts have large misstatements and small accounts have small misstatements). Which of the following techniques is most likely to be efficient? 

A. Mean-per-unit estimation.

B. Ratio estimation.

C. Difference estimation.

D. Sequential sampling estimation.

 

54. Which of the following statements is correct concerning the use of nonstatistical sampling for substantive tests? 

A. Its use is generally acceptable only for populations with an immaterial book value.

B. It requires the use of structured sample size selection techniques to be acceptable.

C. It may be especially useful in circumstances in which the combination of inherent and control risk is at the maximum level.

D. Results will be projected to the population.

 

55. Which of the following situations will result in the auditors concluding that the risk of material misstatement is too high when using nonstatistical sampling for substantive tests? 

A. The projected misstatement exceeds the tolerable misstatement.

B. The allowance for sampling risk exceeds the projected misstatement.

C. The risk of incorrect acceptance exceeds the risk of incorrect rejection.

D. The tolerable misstatement exceeds the sample net misstatement.

 

56. During the final planning of the accounts receivable program a CPA specified a tolerable misstatement of $30,000, instead of the $20,000 contained in the preliminary audit program. What would be the impact of this change? 

A. A decrease in population standard deviation.

B. An increase in sample standard deviation.

C. An increase in required sample size.

D. A decrease in the required sample size.

 

57. Which of the following is an advantage of systematic selection over random number selection? 

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.

 

58. Statistical sampling generally may be applied to test internal control when the client's internal control procedures: 

A. Depend primarily on appropriate segregation of duties.

B. Are carefully reduced to writing and are included in client accounting manuals.

C. Leave an audit trail in the form of evidence of compliance.

D. Enable the detection of material fraud in the accounting records.

 

59. Which of the following statements is correct about the sample size in statistical sampling when testing internal controls? 

A. The auditor should consider the tolerable rate of deviation from the controls being tested in determining sample size.

B. As the likely rate of deviation decreases, the auditor should increase the planned sample size.

C. The allowable risk of assessing control risk too low has no effect on the planned sample size.

D. Of all the factors to be considered, the population size has the greatest effect on the sample size.

 

60. To determine sample size in an attribute sampling application, what must be specified? 

A. Population mean, expected error rate, allowance for sampling risk.

B. Allowance for sampling risk, risk of assessing control risk too low, standard deviation.

C. Allowance for sampling risk, risk of assessing control risk too low, expected deviation rate.

D. Population mean, standard deviation, allowance for sampling risk.

 

61. The tolerable deviation rate in sampling for tests of controls is: 

A. Used to determine the probability of the auditor's conclusion based upon reliance factors.

B. The probability that the financial statements are not materially in error.

C. A measure of the reliability of substantive tests.

D. The rate the auditor will tolerate without modifying the planned assessment of control risk.

 

62. In testing accounts receivable, an auditor sends out positive confirmation requests to 100 randomly selected customers. A customer returns the confirmation indicating that the balance is correct when, in fact, the balance is overstated. This is an example of: 

A. Projected misstatement.

B. Sampling error.

C. Standard error.

D. Nonsampling error.

 

63. An auditor wishes to estimate inventory shrinkage by weighing a sample of inventory items. From experience, the auditor knows that a few specific items are subject to unusually large amounts of shrinkage. In using statistical sampling, the auditor's best course of action is to: 

A. Eliminate any of the items known to be subject to unusually large amounts of shrinkage.

B. Increase the sample size to lessen the effect of the items subject to unusually large amounts of shrinkage.

C. Stratify the inventory population so that items subject to unusually large amounts of shrinkage are reviewed separately.

D. Continue to draw new samples until a sample is drawn which includes none of the items known to be subject to large amounts of shrinkage.

 

64. If all other factors specified in an attributes sampling plan remain constant, changing the specified tolerable rate from 6% to 10%, and changing the specified risk of assessing control risk too low from 3% to 7% would cause the required sample size to: 

A. Increase.

B. Remain the same.

C. Decrease.

D. Change by 4%.

 

65. Which of the following factors does an auditor need to consider in planning a particular audit sample for a test of control? 

A. Number of items in the population.

B. Total dollar amount of the items to be sampled.

C. Acceptable level of risk of assessing control risk too low.

D. Tolerable misstatement.

 

66. When using a statistical sampling plan, the auditors would probably require a smaller sample if the: 

A. Population increases.

B. Desired allowance for sampling risk decreases.

C. Desired risk of incorrect acceptance increases.

D. Expected deviation rate increases.

 

67. Which of the following statements is correct concerning statistical sampling in tests of controls? 

A. The population size has little 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.

 

68. An advantage of using statistical sampling techniques is that such techniques: 

A. Mathematically measure risk.

B. Eliminate the need for judgmental decisions.

C. Define the values of allowance for sampling risk and tolerable misstatement required to provide audit satisfaction.

D. Have been established in the courts to be superior to judgmental sampling.

 

69. 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.

 

70. When performing a test of a control over cash disbursements, a CPA 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 recorded in a systematic pattern before the sample can be drawn.

B. May occur in a systematic pattern and destroy the sample randomness.

C. May systematically occur more than once in the sample.

D. Must be systematically replaced in the population after sampling.

 

71. While performing a substantive test of details during an audit, the 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. Incorrect acceptance.

B. Incorrect rejection.

C. Assessing control risk too high.

D. Assessing control risk too low.

 

72. An auditor plans to examine a sample of 20 checks for counter signatures as prescribed by the client's control procedures. One of the checks in the chosen sample of 20 cannot be found. The auditor should consider the reasons for this limitation and: 

A. Evaluate the results as if the sample size had been 19.

B. Treat the missing check as a deviation for the purpose of evaluating the sample.

C. Treat the missing check in the same manner as the majority of the other 19 checks, i.e., countersigned or not.

D. Choose another check to replace the missing check in the sample.

 

73. There are many kinds of statistical estimates that an auditor may find useful, but basically every statistical estimate in auditing is of either a quantity or of an error rate. The statistical terms that roughly correspond to "quantities" and "occurrence rate", respectively, are: 

A. Attributes and variable.

B. Variables and attributes.

C. Constants and attributes.

D. Constants and variables.

 

74. 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 deviations in the documents examined for the chosen sample.

D. The documents related to the chosen sample may not be available for inspection.

 

75. 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.

 

76. Various factors influence 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. Lower assessment of control risk.

B. Greater reliance on analytical procedures.

C. Smaller expected frequency of misstatements.

D. Smaller measure of tolerable misstatement.

 

77. An important statistic to consider when using a statistical sampling audit plan is the population variability. The population variability is measured by the: 

A. Sample mean.

B. Standard deviation.

C. Standard error of the sample mean.

D. Estimated population total minus the actual population total.

 

78. In variables estimation sampling, the sample standard deviation is used to calculate the 

A. Point estimate of central tendency.

B. Tainting of the sample interval.

C. Risk of incorrect acceptance.

D. Adjusted allowance for sampling risk.

 

79. Use of the ratio estimation sampling technique to estimate 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 value.

 

 

Essay Questions

 

80. Audit sampling is used in conjunction with many audit tests, and may be performed on a statistical or nonstatistical basis.

a. Define the term audit sampling.

b. List and explain two advantages of the use of statistical sampling as compared to nonstatistical sampling. 

 

 

 

 

81. Teal Corporation has 2,000 accounts receivable, with a total book value of $200,000. Ricardo Ramaro, CPA, has selected and audited a sample of 100 of the accounts with a combined book value of $10,100; the total of their audited values was $11,000. Using the mean-per-unit method, calculate the:

a. Accounts receivable estimated audited value.

b. Projected misstatement. 

 

 

 

 

82. The auditors are using mean-per-unit sampling to evaluate the reasonableness of the book value of the accounts receivable of Smith, Inc. Smith has 10,000 receivable accounts with a total book value of $800,000. The auditors estimate the population's standard deviation as being equal to $25. After examining the overall audit plan, the auditors believe that the account's tolerable misstatement is $40,000, and that a risk of incorrect rejection of .10 (risk coefficient = 1.64) and a risk of incorrect acceptance of .15 (risk coefficient = 1.04) should be used.

Required:

a. Calculate the required sample size.

Now ignore your sample size calculation in part "a," and assume that your answer was a sample size of 289 (the square root of 289 is 17) and that you obtained the following results:

Average audited value of items in sample: $76

Average book value of items in sample: $78

Standard Deviation in the sample (audited values): $24

Standard Deviation in the sample (book values): $26

b. Using mean-per-unit sampling, calculate the projected misstatement for the population.

c. Using mean-per-unit sampling, calculate the adjusted allowance for sampling risk and use it to form a statistical conclusion concerning the book value of the population ($800,000). That is, calculate an interval and either "accept" or "reject" the client's book value. 

 

 

 

 

Chapter 09 Audit Sampling Answer Key

 

 

True / False Questions

 

1. Stratification of the population generally results in a more efficient sampling plan. 

TRUE

 

Difficulty: Medium

 

2. Discovery sampling is equivalent to an attributes sampling plan with a specified expected deviation rate of 0 percent. 

TRUE

 

Difficulty: Medium

 

3. Increases in the number of deviations in an attributes sample results in an increase in the achieved upper deviation rate of the attributes sample. 

TRUE

 

Difficulty: Medium

 

4. The definition of a "deviation" for a test of a control should include only those deviations that result in misstatements in the financial statements. 

FALSE

 

Difficulty: Hard

 

5. Statistical sampling cannot be used to test all control activities. 

TRUE

 

Difficulty: Medium

 

6. Using ratio and difference estimation for a sample is an example of a dual purpose test. 

FALSE

 

Difficulty: Medium

 

7. Increases in the tolerable misstatement result in a decreased sample size when using mean-per-unit estimation. 

TRUE

 

Difficulty: Medium

 

8. The mean book value of the items included in a mean-per-unit sample is not directly used in the evaluation of sample results. 

TRUE

 

Difficulty: Hard

 

9. When evaluating the results of a variables sampling plan, the projected misstatement is calculated and compared to the tolerable misstatement. 

TRUE

 

Difficulty: Easy

 

10. Auditors project the misstatements found in the sample to the population when using statistical sampling, but not when using nonstatistical sampling. 

FALSE

 

Difficulty: Medium

 

 

Multiple Choice Questions

 

 The 10,000 accounts receivable of DEF Company have a total book value of $120,000. A CPA has selected and audited a sample of 100 accounts with a total book value of $1,000 and an audited value of $1,200.

 

11. Using the difference estimation technique, estimated total audited value of the population is: 

A. $100,000.

B. $120,000.

C. $140,000.

D. $144,000

 

Difficulty: Medium

 

12. Using the ratio estimation technique, the estimated total audited value of the population is: 

A. $100,000.

B. $120,000.

C. $140,000.

D. $144,000

 

Difficulty: Medium

 

13. Using the mean-per-unit estimation technique, the estimated total audited value of the population is: 

A. $100,000.

B. $120,000.

C. $140,000.

D. $144,000.

 

Difficulty: Medium

 

14. Using the mean-per-unit estimation method an auditor has properly calculated the estimated total audited value of a population as $200,000. Her sample included 200 of the population's 40,000 items. She found that, in her sample the average audited value was $1 less than the average book value. What was the average audited value in the sample? 

A. $4.

B. $5.

C. $6.

D. $10.

 

Difficulty: Hard

 

15. Using difference estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? 

A. $160,000.

B. $161,538.

C. $168,000.

D. $200,000.

 

Difficulty: Medium

 

16. Using ratio estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? 

A. $160,000.

B. $161,538.

C. $168,000.

D. $200,000.

 

Difficulty: Medium

 

17. Using mean-per-unit estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? 

A. $160,000.

B. $161,538.

C. $168,000.

D. $200,000.

 

Difficulty: Medium

 

18. If the projected misstatement in a nonstatistical sampling is $8,000, while the tolerable misstatement is $9,000, what would an auditor likely conclude? 

A. Since the projected misstatement is less than the tolerable misstatement, the account is not misstated.

B. Since the projected misstatement is less than the tolerable misstatement, the account is misstated.

C. The risk is high that the account is materially misstated.

D. The analysis has been improperly performed since the projected misstatement is unequal to the tolerable misstatement.

 

Difficulty: Hard

 

19. A dual purpose test simultaneously. 

A. Addresses two different accounts.

B. Functions as a substantive test and as a test of controls.

C. Functions as an analytical procedure and a substantive test.

D. Substantiates an ending balance and the transactions making up the balance.

 

Difficulty: Medium

 

 The 1000 accounts receivable of Winco Company have a total book value of $20,000 (Average book value = $20). Bob Duffo, CPA, has selected and audited a sample of 50 accounts with the following mean values:

1. Book value of $19.

2. Audited value of $19.60.

 

20. What is the estimated total audited value using mean per unit sampling? 

A. $19,000.

B. $19,600.

C. $20,000.

D. $20,632.

 

Difficulty: Medium

 

21. What is the estimated total audited value using difference estimation sampling? 

A. $19,387.

B. $19,400.

C. $19,600.

D. $20,600.

 

Difficulty: Hard

 

22. If all other factors specified in an attributes sampling plan remain constant, decreasing the tolerable rate and decreasing the risk of assessing control risk too low would have what effect on sample size? 

A. Increase.

B. Remain the same.

C. Decrease.

D. Indeterminate, depends upon exact change being made.

 

Difficulty: Hard

 

23. If all other factors specified in an attributes sampling plan remain constant, decreasing the tolerable rate and increasing the estimated population deviation rate would have what effect on sample size? 

A. Increase.

B. Remain the same.

C. Decrease.

D. Indeterminate, depends upon exact change being made.

 

Difficulty: Hard

 

24. An increase in the tolerable misstatement has what effect on the planned allowance for sampling risk? 

A. Increases.

B. Decreases.

C. No effect.

D. Indeterminate.

 

Difficulty: Medium

 

25. Which of the following is not generally used for selecting samples? 

A. Random number tables.

B. Random number generators.

C. Physical representation numbers.

D. Systematic selection.

 

Difficulty: Easy

 

26. In performing a test of a control last year the auditors specified a tolerable deviation rate of X percent. This year the auditors have specified a tolerable rate of less than X percent. Assuming that all other factors remain the same, which of the following is true regarding the relationship between this year's sample size compared to last year's sample size? 

A. This year's sample is larger than last year's sample.

B. This year's sample is smaller than last year's sample.

C. This year's sample is equal to last year's sample.

D. This year's sample is indeterminate in relation to last year's sample.

 

Difficulty: Medium

 

27. The auditor using nonstatistical attributes sampling, but who nevertheless has chosen the sample in conformity with random selection procedures: 

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 techniques to evaluate the results.

D. Should compare the deviation rate of the sample to the tolerable rate.

 

Difficulty: Medium

 

28. When performing tests of controls over authorization of cash receipts, which of the following sampling methods would be most appropriate? 

A. Attributes.

B. Ratio.

C. Stratified.

D. Variables.

 

Difficulty: Easy

 

29. Which of the following statistical sampling techniques involves taking samples in a series of stages? 

A. Systematic sampling.

B. Sequential sampling.

C. Continuous sampling.

D. Multiple location sampling.

 

Difficulty: Easy

 

30. Which of the following is generally not true about statistical sampling as compared to nonstatistical sampling? 

A. Statistical samples are more representative of the population.

B. Statistical sample plans involve additional costs of evaluation.

C. Statistical sampling allows a more objective evaluation of sample results.

D. Statistical sampling may assist the auditors in designing more efficient samples.

 

Difficulty: Medium

 

31. When using statistical sampling, which of the following need not be known to evaluate the results of an attributes sample? 

A. Sample size.

B. Risk of assessing control risk too low.

C. Number of deviations in the population.

D. Number of deviations found in the sample.

 

Difficulty: Easy

 

32. When the auditors have decided to use statistical rather than nonstatistical sampling, a disadvantage is that: 

A. Designing efficient samples is more difficult.

B. The costs of training staff may be higher.

C. Sampling without replacement must be used.

D. Objectively evaluating results is impossible.

 

Difficulty: Easy

 

33. Changing from a sampling plan using random selection with replacement to random selection without replacement has what effect on the required sample size? 

A. Increases.

B. Decreases

C. No effect.

D. An indeterminate effect.

 

Difficulty: Medium

 

34. When the auditors have chosen to test a control, what relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample? 

A. Exceed.

B. Equal.

C. Be less than.

D. Indefinite.

 

Difficulty: Hard

 

35. Increases in the planned allowance for sampling risk have what effect on required sample size? 

A. Increases.

B. Decreases.

C. No effect.

D. Indeterminate.

 

Difficulty: Medium

 

36. When using sampling for tests of controls, which of the following audit consequences may follow? 

A. If sample results indicate that the control is operating effectively, but in fact it is not, control risk will be assessed too low.

B. If sample results indicate that the control is operating effectively, but in fact it is not, control risk will be assessed too high.

C. If sample results indicate that the control is not operating effectively, but in fact it is operating effectively, the audit is likely to be faulty because of reduced substantive tests.

D. If sample results indicate that the control is not operating effectively, but in fact it is operating effectively, control risk will be assessed too low.

 

Difficulty: Hard

 

37. The auditors expect a population deviation rate of billing errors of two percent, and have established a tolerable rate of five percent. The sampling approach most likely to be used is: 

A. Attributes sampling.

B. Stratified sequential sampling.

C. Discovery sampling.

D. None, as sampling does not seem appropriate in this situation.

 

Difficulty: Easy

 

38. The auditors expect a population deviation rate of billing errors of eight percent, and have established a tolerable rate of five percent. The sampling approach most likely to be used is: 

A. Attributes sampling.

B. Stratified random sampling.

C. Variables sampling.

D. None, as sampling does not seem appropriate in this situation.

 

Difficulty: Medium

 

39. Which of the following may be used to reduce the risk of nonsampling errors? 

A. Increasing the size of audit samples.

B. Stratifying audit samples.

C. Adequately planning audit samples.

D. Using statistical sampling techniques.

 

Difficulty: Medium

 

40. Which of the following types of risk is of critical importance to auditors in performing tests of controls? 

A. The risk of assessing control risk too low.

B. The risk of assessing control risk too high.

C. The risk of incorrect acceptance.

D. The risk of incorrect rejection.

 

Difficulty: Medium

 

41. The auditors' failure to recognize a misstatement in an amount or a deviation in an internal control data processing procedure is described as a: 

A. Statistical error.

B. Sampling misstatement.

C. Standard error of the mean.

D. Nonsampling error.

 

Difficulty: Easy

 

42. What effect does obtaining a sample with a standard deviation larger than that estimated during planning have on the adjusted allowance for sampling risk? 

A. Increases.

B. Decreases.

C. No effect.

D. Indeterminate.

 

Difficulty: Hard

 

 The 2000 accounts receivable of ABC Company have a total book value of $40,000. Bob Rotter, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,950. The audited value of the 100 accounts in the sample is $1,875.

 

43. Using the mean-per-unit estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: 

A. $37,500

B. $38,462

C. $38,500

D. $41,600

 

Difficulty: Medium

 

44. Using the ratio estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: 

A. $37,500

B. $38,462

C. $38,500

D. $41,600

 

Difficulty: Hard

 

45. Using the difference estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: 

A. $37,500

B. $38,462

C. $38,500

D. $41,600

 

Difficulty: Hard

 

46. The 3000 accounts receivable of DEF Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $2,100. Using the difference estimation technique, Smith has properly estimated a projected misstatement of an overstatement of $6,000 for the entire population. The audited value of Smith's sample is: 

A. $1,700

B. $1,800

C. $1,900

D. $2,300

 

Difficulty: Hard

 

47. The 3000 accounts receivable of DEF Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $2,100. Using the difference estimation technique, Smith has properly estimated a projected misstatement of a $9,000 overstatement for the entire population. The estimated total audited value of the population is: 

A. $51,000

B. $58,000

C. $60,000

D. $69,000

 

Difficulty: Medium

 

48. The 4000 accounts receivable of GHI Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,600. Using the mean-per-unit estimation technique, Smith has properly estimated a projected misstatement of a $8,000 overstatement for the entire population. The audited value of Smith's sample is: 

A. $1,300

B. $1,400

C. $1,600

D. $1,800

 

Difficulty: Hard

 

49. Which of the following is a correct statement with respect to evaluating results when using nonstatistical sampling for substantive tests? 

A. When the projected misstatement exceeds the tolerable misstatement, the auditor should conclude that the population is not misstated.

B. The closer the projected misstatement is to the tolerable misstatement, the higher the risk of material misstatement.

C. When the projected misstatement is equal to zero, the auditors may conclude with certainty that no misstatements exist in the account.

D. When the projected misstatement percentage exceeds the risk of incorrect acceptance the auditors will generally conclude that the population is materially misstated.

 

Difficulty: Medium

 

50. Assume a mean-per-unit estimation variables sampling application with a tolerable misstatement of $70,000 and a book value of $700,000. After performing the sampling plan, the auditors calculated an adjusted allowance for sampling risk of $45,000 and a point estimate of the population's total audited value to be $650,000. Based on these results, the auditor would: 

A. Because the tolerable misstatement exceeds the adjusted allowance for sampling risk, conclude that the population does not contain a material misstatement.

B. Because the total audited value ( tolerable misstatement includes the book value, conclude that the population does not contain a material misstatement.

C. Because the tolerable misstatement exceeds the adjusted allowance for sampling risk, conclude that there is too great a risk that the account balance is materially misstated.

D. Because the total audited value ( adjusted allowance for sampling risk does not include the book value, conclude that there is too great a risk that the account balance is materially misstated.

 

Difficulty: Hard

 

51. Assume a mean-per-unit estimation variables sampling application with a tolerable misstatement of $70,000 and a book value of $700,000. After performing the sampling plan, the auditors calculated an adjusted allowance for sampling risk of $45,000 and a point estimate of the population's total audited value to be $640,000. The projected misstatement based on this sample is: 

A. $ 5,000

B. $45,000

C. $60,000

D. $70,000

 

Difficulty: Medium

 

52. The auditors have audited a sample with a standard deviation of audited values larger than they had originally estimated. In this situation, to maintain the risk of incorrect acceptance at its predetermined level without increasing the size of the sample, which of the following statements is correct? 

A. The adjusted allowance for sampling risk will be smaller than had been planned.

B. The adjusted allowance for sampling risk will be larger than had been planned.

C. The risk of incorrect rejection will necessarily decrease.

D. The size of the population must be decreased.

 

Difficulty: Hard

 

53. In the past, the auditors have found that the book value of a receivable account has been related to the amount the account is misstated (i.e., large accounts have large misstatements and small accounts have small misstatements). Which of the following techniques is most likely to be efficient? 

A. Mean-per-unit estimation.

B. Ratio estimation.

C. Difference estimation.

D. Sequential sampling estimation.

 

Difficulty: Medium

 

54. Which of the following statements is correct concerning the use of nonstatistical sampling for substantive tests? 

A. Its use is generally acceptable only for populations with an immaterial book value.

B. It requires the use of structured sample size selection techniques to be acceptable.

C. It may be especially useful in circumstances in which the combination of inherent and control risk is at the maximum level.

D. Results will be projected to the population.

 

Difficulty: Medium

 

55. Which of the following situations will result in the auditors concluding that the risk of material misstatement is too high when using nonstatistical sampling for substantive tests? 

A. The projected misstatement exceeds the tolerable misstatement.

B. The allowance for sampling risk exceeds the projected misstatement.

C. The risk of incorrect acceptance exceeds the risk of incorrect rejection.

D. The tolerable misstatement exceeds the sample net misstatement.

 

Difficulty: Hard

 

56. During the final planning of the accounts receivable program a CPA specified a tolerable misstatement of $30,000, instead of the $20,000 contained in the preliminary audit program. What would be the impact of this change? 

A. A decrease in population standard deviation.

B. An increase in sample standard deviation.

C. An increase in required sample size.

D. A decrease in the required sample size.

 

Difficulty: Medium

 

57. Which of the following is an advantage of systematic selection over random number selection? 

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.

 

Difficulty: Medium

Source: AICPA

 

58. Statistical sampling generally may be applied to test internal control when the client's internal control procedures: 

A. Depend primarily on appropriate segregation of duties.

B. Are carefully reduced to writing and are included in client accounting manuals.

C. Leave an audit trail in the form of evidence of compliance.

D. Enable the detection of material fraud in the accounting records.

 

Difficulty: Medium

Source: AICPA

 

59. Which of the following statements is correct about the sample size in statistical sampling when testing internal controls? 

A. The auditor should consider the tolerable rate of deviation from the controls being tested in determining sample size.

B. As the likely rate of deviation decreases, the auditor should increase the planned sample size.

C. The allowable risk of assessing control risk too low has no effect on the planned sample size.

D. Of all the factors to be considered, the population size has the greatest effect on the sample size.

 

Difficulty: Medium

Source: AICPA

 

60. To determine sample size in an attribute sampling application, what must be specified? 

A. Population mean, expected error rate, allowance for sampling risk.

B. Allowance for sampling risk, risk of assessing control risk too low, standard deviation.

C. Allowance for sampling risk, risk of assessing control risk too low, expected deviation rate.

D. Population mean, standard deviation, allowance for sampling risk.

 

Difficulty: Hard

Source: IIA

 

61. The tolerable deviation rate in sampling for tests of controls is: 

A. Used to determine the probability of the auditor's conclusion based upon reliance factors.

B. The probability that the financial statements are not materially in error.

C. A measure of the reliability of substantive tests.

D. The rate the auditor will tolerate without modifying the planned assessment of control risk.

 

Difficulty: Easy

 

62. In testing accounts receivable, an auditor sends out positive confirmation requests to 100 randomly selected customers. A customer returns the confirmation indicating that the balance is correct when, in fact, the balance is overstated. This is an example of: 

A. Projected misstatement.

B. Sampling error.

C. Standard error.

D. Nonsampling error.

 

Difficulty: Medium

Source: IIA

 

63. An auditor wishes to estimate inventory shrinkage by weighing a sample of inventory items. From experience, the auditor knows that a few specific items are subject to unusually large amounts of shrinkage. In using statistical sampling, the auditor's best course of action is to: 

A. Eliminate any of the items known to be subject to unusually large amounts of shrinkage.

B. Increase the sample size to lessen the effect of the items subject to unusually large amounts of shrinkage.

C. Stratify the inventory population so that items subject to unusually large amounts of shrinkage are reviewed separately.

D. Continue to draw new samples until a sample is drawn which includes none of the items known to be subject to large amounts of shrinkage.

 

Difficulty: Hard

Source: IIA

 

64. If all other factors specified in an attributes sampling plan remain constant, changing the specified tolerable rate from 6% to 10%, and changing the specified risk of assessing control risk too low from 3% to 7% would cause the required sample size to: 

A. Increase.

B. Remain the same.

C. Decrease.

D. Change by 4%.

 

Difficulty: Hard

Source: AICPA

 

65. Which of the following factors does an auditor need to consider in planning a particular audit sample for a test of control? 

A. Number of items in the population.

B. Total dollar amount of the items to be sampled.

C. Acceptable level of risk of assessing control risk too low.

D. Tolerable misstatement.

 

Difficulty: Medium

Source: AICPA

 

66. When using a statistical sampling plan, the auditors would probably require a smaller sample if the: 

A. Population increases.

B. Desired allowance for sampling risk decreases.

C. Desired risk of incorrect acceptance increases.

D. Expected deviation rate increases.

 

Difficulty: Medium

Source: AICPA

 

67. Which of the following statements is correct concerning statistical sampling in tests of controls? 

A. The population size has little 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.

 

Difficulty: Medium

Source: AICPA

 

68. An advantage of using statistical sampling techniques is that such techniques: 

A. Mathematically measure risk.

B. Eliminate the need for judgmental decisions.

C. Define the values of allowance for sampling risk and tolerable misstatement required to provide audit satisfaction.

D. Have been established in the courts to be superior to judgmental sampling.

 

Difficulty: Medium

Source: AICPA

 

69. 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.

 

Difficulty: Medium

Source: AICPA

 

70. When performing a test of a control over cash disbursements, a CPA 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 recorded in a systematic pattern before the sample can be drawn.

B. May occur in a systematic pattern and destroy the sample randomness.

C. May systematically occur more than once in the sample.

D. Must be systematically replaced in the population after sampling.

 

Difficulty: Easy

Source: AICPA

 

71. While performing a substantive test of details during an audit, the 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. Incorrect acceptance.

B. Incorrect rejection.

C. Assessing control risk too high.

D. Assessing control risk too low.

 

Difficulty: Medium

Source: AICPA

 

72. An auditor plans to examine a sample of 20 checks for counter signatures as prescribed by the client's control procedures. One of the checks in the chosen sample of 20 cannot be found. The auditor should consider the reasons for this limitation and: 

A. Evaluate the results as if the sample size had been 19.

B. Treat the missing check as a deviation for the purpose of evaluating the sample.

C. Treat the missing check in the same manner as the majority of the other 19 checks, i.e., countersigned or not.

D. Choose another check to replace the missing check in the sample.

 

Difficulty: Medium

Source: AICPA

 

73. There are many kinds of statistical estimates that an auditor may find useful, but basically every statistical estimate in auditing is of either a quantity or of an error rate. The statistical terms that roughly correspond to "quantities" and "occurrence rate", respectively, are: 

A. Attributes and variable.

B. Variables and attributes.

C. Constants and attributes.

D. Constants and variables.

 

Difficulty: Easy

Source: AICPA

 

74. 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 deviations in the documents examined for the chosen sample.

D. The documents related to the chosen sample may not be available for inspection.

 

Difficulty: Easy

Source: AICPA

 

75. 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.

 

Difficulty: Medium

Source: AICPA

 

76. Various factors influence 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. Lower assessment of control risk.

B. Greater reliance on analytical procedures.

C. Smaller expected frequency of misstatements.

D. Smaller measure of tolerable misstatement.

 

Difficulty: Hard

Source: AICPA

 

77. An important statistic to consider when using a statistical sampling audit plan is the population variability. The population variability is measured by the: 

A. Sample mean.

B. Standard deviation.

C. Standard error of the sample mean.

D. Estimated population total minus the actual population total.

 

Difficulty: Easy

Source: AICPA

 

78. In variables estimation sampling, the sample standard deviation is used to calculate the 

A. Point estimate of central tendency.

B. Tainting of the sample interval.

C. Risk of incorrect acceptance.

D. Adjusted allowance for sampling risk.

 

Difficulty: Easy

Source: AICPA

 

79. Use of the ratio estimation sampling technique to estimate 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 value.

 

Difficulty: Medium

Source: AICPA

 

 

Essay Questions

 

80. Audit sampling is used in conjunction with many audit tests, and may be performed on a statistical or nonstatistical basis.

a. Define the term audit sampling.

b. List and explain two advantages of the use of statistical sampling as compared to nonstatistical sampling. 

a. Audit sampling is performing a test on less than 100 percent of an audit population to make a conclusion about a characteristic of the population.

b. Statistical sampling may assist the auditors in (only two required):

( Designing efficient samples.

( Measuring the sufficiency of the evidence obtained.

( Objectively evaluating sample results (measuring sampling risk).

 

Difficulty: Medium

 

81. Teal Corporation has 2,000 accounts receivable, with a total book value of $200,000. Ricardo Ramaro, CPA, has selected and audited a sample of 100 of the accounts with a combined book value of $10,100; the total of their audited values was $11,000. Using the mean-per-unit method, calculate the:

a. Accounts receivable estimated audited value.

b. Projected misstatement. 

a. The accounts receivable estimated audited value is calculated as:

 [pic] 

b. The projected misstatement is calculated as the difference between the estimated total audited value and the book value, calculated as follows:

 [pic] 

 

Difficulty: Medium

 

82. The auditors are using mean-per-unit sampling to evaluate the reasonableness of the book value of the accounts receivable of Smith, Inc. Smith has 10,000 receivable accounts with a total book value of $800,000. The auditors estimate the population's standard deviation as being equal to $25. After examining the overall audit plan, the auditors believe that the account's tolerable misstatement is $40,000, and that a risk of incorrect rejection of .10 (risk coefficient = 1.64) and a risk of incorrect acceptance of .15 (risk coefficient = 1.04) should be used.

Required:

a. Calculate the required sample size.

Now ignore your sample size calculation in part "a," and assume that your answer was a sample size of 289 (the square root of 289 is 17) and that you obtained the following results:

Average audited value of items in sample: $76

Average book value of items in sample: $78

Standard Deviation in the sample (audited values): $24

Standard Deviation in the sample (book values): $26

b. Using mean-per-unit sampling, calculate the projected misstatement for the population.

c. Using mean-per-unit sampling, calculate the adjusted allowance for sampling risk and use it to form a statistical conclusion concerning the book value of the population ($800,000). That is, calculate an interval and either "accept" or "reject" the client's book value. 

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Difficulty: Hard

 

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