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## Audit Sampling: An Overview and Application to Tests of Controls

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**1. **Chapter 8 Audit Sampling: An Overview and Application to Tests of Controls

**2. **Introduction

**3. **Introduction

**4. **Definitions and Key Concepts

**5. **Audit Sampling

**6. **Audit Sampling Refers to applying audit procedures to less than 100% of a population.
Audit populations – Items in account balance or class of transactions
Auditor should consider costs and benefits of auditing all items vs. a sample of items.
Sample results projected as population characteristics.

**7. **Audit Sampling Sample should be _____________ of the population (i.e., characteristics of the sample should be similar to the population from which it was drawn).
Sampling can be used in:
tests of controls - compliance tests of details of transactions (TOTc),
substantive tests of details of transactions (TOTs),
and tests of details of account balances (TOBs).
Sampling may include ____________ sampling and ________________ sampling.
According to some recent studies, the use of statistical sampling in sampling applications appears to be declining.

**8. **Types of Audit Populations Items in a class of transactions.
Items (i.e., components) in an account balance.

**9. **Definitions and Key Concepts

**10. **Sampling Risk

**11. **Sampling Risk

**12. **Definitions and Key Concepts

**13. **Confidence Level

**14. **Definitions and Key Concepts

**15. **Tolerable and Expected Error

**16. **Audit Evidence – To Sample or Not?

**17. **Types of Audit Procedures/Tests That Do Not Involve Sampling Inquiry and observation.
Scanning.
Analytical procedures other than regression and time series analysis.
Audit populations where 100 percent of the items are tested (e.g., plant, property & equipment transactions in small businesses).

**18. **Audit Evidence – To Sample or Not?

**19. **Audit Evidence – To Sample or Not?

**20. **Testing All Items with a Particular Characteristic

**21. **Testing Only One or a Few Items

**22. **Definitions and Key Concepts

**23. **Types of Audit Sampling

**24. **Statistical Sampling versusNonstatistical Sampling Statistical sampling ? Auditor uses the ________________ to measure sampling risk, level of reliability, and precision
Nonstatistical sampling ? Auditor does not measure sampling risk, level of reliability, or precision.

**25. **Types of Audit Sampling

**26. **Question

**27. **Purposes of Audit Sampling Compliance tests of details of transactions (TOTc)
Substantive tests of details of transactions (TOTs)
Substantive tests of details of account balances (TOBs)

**28. **Use of Sampling for Compliance Tests of Details of Transactions (TOTc) These are tests of controls.
The objective is to determine if the exception/ deviation/noncompliance rate in the population is low enough to justify assessing control risk at less than the maximum in order to reduce substantive tests (i.e., reduce the level of auditing).
Attributes sampling typically used for tests of controls because results are provided in terms of a rate of occurrence (i.e., deviation/exception /noncompliance rate).

**29. **Use of Sampling for Substantive Tests of Details of Transactions (TOTs) Concerned with monetary correctness of transactions recorded in the account.
Projects the dollar amount of misstatement based on sample results.
Results are provided in dollar terms.
Probability-proportionate-to-size (PPS) sampling is typically used. This sampling technique is sometimes referred to as dollar-unit sampling or monetary-unit sampling.

**30. **Use of Sampling for Substantive Tests of Details of Account Balances Determine whether an account balance is materially misstated.
Results provided in dollar terms.
Either probability proportionate to size (PPS) sampling or classical variables sample may be used.
Probability proportionate to size (PPS) projects the dollar amount of misstatement.
Classical variables sampling projects the dollar amount (i.e., audit value) of an account balance, which can then be compared with the book value of the account balance. The difference between the audit value and book value of an account balance represents the projected dollar amount of misstatement.

**31. **Use of Sampling for Substantive Tests of Details of Account Balances Probability proportionate to size (PPS) sampling is typically used. This sampling technique is sometimes referred to as dollar-unit sampling or monetary-unit sampling.
Classical variables sampling is also used, but to a lesser extent.

**32. **Statistical Sampling Techniques

**33. **Attribute Sampling

**34. **Monetary-Unit Sampling

**35. **Classical Variables Sampling

**36. **Attribute Sampling Applied to

**37. **Sampling Involves Planning the sample
Determining sample size
Selecting the sample ? How to select the items?
Performing the tests – Each sample item is either in error or it is not.
Evaluating results, drawing conclusions, and making/revising audit decisions
Documenting the sampling procedure, including results, conclusions, and audit decisions

**38. **Steps in Attribute Sampling Planning
Determine the test objectives
Define the population characteristics
Determine the sample size
Performance
Select the sample items
Perform the auditing procedure
Evaluation
Calculate the sample deviation rate
Draw final conclusions

**39. **Planning

**40. **Question

**41. **Planning

**42. **Planning

**43. **Planning

**44. **Planning

**45. **Planning

**46. **Planning

**47. **Question

**48. **Planning

**49. **Planning

**50. **Population Size

**51. **How to Select the Sample Random selection?
Systematic selection?
Haphazard selection?
Block selection?

**52. **Performance Select the sample items
Random number selection
Systematic selection
Perform the Audit Procedures
Voided documents
Unused or inapplicable documents
Inability to examine a sample item
Stopping the test before completion
Every item in the population has the same probability of being selected as every other sampling unit in the population.

**53. **Performance Select the sample items
Random number selection
Systematic selection
Perform the Audit Procedures
Voided documents
Unused or inapplicable documents
Inability to examine a sample item
Stopping the test before completion
For example, assume each sales invoice is to have a related shipping document. If the shipping document is present, the control is working properly. If the shipping document is not present a control deviation exist.

**54. **Performance Select the sample items
Random number selection
Systematic selection
Perform the Audit Procedures
Voided documents
Unused or inapplicable documents
Inability to examine a sample item
Stopping the test before completion
Unless the auditor finds something unusual about either of these items, they should be replaced with a new sample item.

**55. **Performance Select the sample items
Random number selection
Systematic selection
Perform the Audit Procedures
Voided documents
Unused or inapplicable documents
Inability to examine a sample item
Stopping the test before completion
If the auditor is unable to examine a document or to use an alternative procedure to test the control, the sample item is a deviation for purposes of evaluating the sample results.

**56. **Performance Select the sample items
Random number selection
Systematic selection
Perform the Audit Procedures
Voided documents
Unused or inapplicable documents
Inability to examine a sample item
Stopping the test before completion
If a large number of deviations are detected early in the tests of controls, the auditor should consider stopping the test, as soon as it is clear that the results of the test will not support the planned assessed level of control risk.

**57. **Performing Audit Procedures
Examine documents
Perform other audit procedures

**58. **Evaluation

**59. **Evaluation

**60. **Evaluating Results, Drawing Conclusions,and Making/Revising Audit Decisions Consider implications of sample results on the audit population:
Attribute sampling - Revise preliminary control risk assessments?
PPS or classical variables sampling ? Develop conclusions about whether there are material misstatements in an account balance or a class of transactions.

**61. **Attribute Sampling Example

**62. **Attribute Sampling Example

**63. **Attribute Sampling Example

**64. **Attribute Sampling Example

**65. **Attribute Sampling Example

**66. **Attribute Sampling Example

**67. **Nonstatistical Sampling for Tests of Control

**68. **Nonstatistical Sampling for Tests of Control

**69. **Nonstatistical Sampling for Tests of Control

**70. **Considering the Effect of Population Size

**71. **Population Size & Attribute Sampling Population size is not an important factor in determining sample size.
Population size has little or no effect on the sample size, unless the population is relatively small, say less than 100 items.

**72. **Inverse Relationship between Beta Risk & Sample Size

**73. **Inverse Relationship between Maximum Tolerable Deviation Rate & Sample Size

**74. **Question Which of the following statements is correct concerning statistical sampling in tests of controls?
Deviations from controls at a given rate usually result in misstatements at a higher rate.
As the populations doubles, the sample size should also double.
The qualitative aspects of deviations are not considered by the auditor.
There is an inverse relationship between sample size and the tolerable deviation rate.
None of the above.

**75. **Direct Relationship between Expected Deviation Rate & Sample Size

**76. **Question The next question is based on the following information:
An auditor desired to test credit approval on 10,000 sales invoices processed during the year. The auditor designed a statistical sample that would provide a 1-percent risk of assessing control risk too low for the assertion that not more than 7 percent of the sales invoices lacked approval. The auditor estimated from previous experience that about 2 ½ percent 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 computed upper deviation rate to be 8 percent.

**77. **In the evaluation of this sample, the auditor decided to increase the level of the preliminary assessment of control risk because the
Tolerable deviation rate (7 percent) was less than the computed upper deviation rate (8 percent).
Expected population deviation rate (7 percent) was more than the percentage of errors in the sample.
Computed upper deviation rate (8 percent) was more than the percentage of errors in the sample (3 ½ percent).
Expected population deviation rate (2 ½ percent) was less than the tolerable deviation rate (7 percent).
None of the above.

**78. **Relationship between Sample Size and Sample Size Factors Risk of Incorrect Acceptance(Beta Risk) Inverse
Expected Deviation Rate Direct
Maximum tolerable Deviation Rate Inverse
Population Size Direct (if at all)

**79. **Question Which of the following combinations results in the greatest decrease in sample size in an attribute sample for a test of controls?
Desired Confidence Tolerable Expected Population Level Deviation Rate Deviation Rate .
Decrease Decrease Increase
Increase Increase Decrease
Decrease Increase Decrease
Decrease Increase Increase
None of the above.

**80. **Risks Involved When Sampling
Nonsampling risk
Sampling risk (also referred to as sampling error)

**81. **Nonsampling Risk Occurs when audit tests do not uncover existing exceptions in sample.
Cannot be measured.
Can be controlled through proper planning, supervision, and review.

**82. **Nonsampling Risk Nonsampling error can occur because auditors:
Fail to recognize exceptions.
Perform inappropriate or ineffective procedures.
Fail to adequately interpret test results (draw incorrect conclusion).
Fail to maintain control over audit procedures (allow client to tamper with evidence).
Do not exercise due care in applying procedures.

**83. **Sampling Risk Risk that the audit sample is not representative of the audit population - The risk that conclusions drawn based on sample are different from conclusions that would have been reached if entire population tested.
Sampling risk can be estimated if statistical sampling techniques are used.
Sampling risk can occur any time that auditors examine less than 100% of a population.

**84. **Two Aspects of Sample Risk:Beta Risk and Alpha Risk Beta Risk ? Risk of Incorrect Acceptance:
Assessing control risk too low (overreliance) or incorrectly “accepting” an account balance as free from material misstatement.
Measured as 1 – Level of Reliability (of 1 – Confidence Level)
Inverse relationship between 1) assessing control risk too low (overreliance) or incorrectly accepting account balance; and 2) sample size.
Beta risk is similar to audit risk.
SAS 39 refers to this risk as a Type II error.

**85. **Two Aspects of Sample Risk:Beta Risk and Alpha Risk Alpha Risk ? Risk of Incorrect Rejection:
Assessing control risk too high (underreliance) or incorrectly “rejecting” an account balance because it likely contains material misstatement.
SAS 39 refers to this risk as a Type I error.

**86. **Sampling Risk for Tests of Controls True State of Population
Deviation Rate Deviation Rate
Exceeds Is Less Than
Auditors’ Conclusion Tolerable Rate Tolerable Rate
from the Sample Is:
Deviation Rate
Exceeds
Tolerable Rate
Deviation Rate
Is Less Than
Tolerable Rate

**87. **Question The following table depicts the auditor’s estimated computer upper deviation rate compared with the tolerable deviation rate, and it also depicts the true population deviation rate compared with the tolerable deviation rate.
True State of Population
Deviation Rate is Deviation Rate
Auditor’s Estimate Based Less than Tolerable Exceeds Tolerable
On Sample Results Deviation Rate Deviation Rate
Computed upper deviation rateis less than the Tolerable
Deviation rate 1 3
Computed upper deviation rateexceeds tolerable deviation rate 2 4

**88. **As a result of tests of controls, the auditor assesses control risk higher than necessary and thereby increases substantive testing. This is illustrated by the situation
1
2
3
4
None of the above.

**89. **Auditor’s Evaluation of Sample Results

**90. **Evaluating Sample Results for Control #1 Using ACL 9

**91. **ACL 9’s Evaluation of Sample Results for Control #1

**92. **Control No. 1 – The Auditor’s Decision
Attribute sampling does not support reliance on the control.

**96. **Question As a result of sampling procedures applied as tests of controls, an auditor incorrectly assesses control risk lower than appropriate. The most likely explanation for this situation is that
The deviation rate of both the auditor’s sample and the population exceed the tolerable deviation rate.
The deviation rate of both the auditor’s sample and the population are less than the tolerable deviation rate.
The deviation rate in the auditor’s sample is less than the tolerable deviation rate, but the deviation rate in the population exceeds the tolerable deviation rate.
The deviation rate in the auditor’s ample is less than the tolerable deviation rate, but the deviation rate in the population is less than the tolerable deviation rate.
None of the above.

**97. **Statistical/Probabilistic Sampling Uses laws of probability to develop a sampling plan.
More precise measurement of the sufficiency of audit evidence.
Allows auditor to optimize sample size given acceptable sampling risk.
More precise quantitative evaluation of sample results.
Sampling risk can be measured quantitatively.
Allows the auditor to make statements or generalizations about a population based on laws of statistics.

**98. **Advantages/Disadvantages of Statistical Sampling Advantages of statistical sampling
Design an efficient sample.
Measure the sufficiency of evidence obtained.
Quantify sampling risk.
Disadvantages of statistical sampling
Training auditors in proper use.
Time to design and conduct sampling application.
Lack of consistent application across audit teams.

**99. **Nonstatistical/Nonprobabilistic Sampling Determine sample size, select sample, and evaluate sample results entirely based on subjective criteria, judgment, and experience rather than on probability concepts.
Professional standards allow auditors to use either statistical or nonstatistical sampling.

**100. **End of Chapter 8