CHAPTER 20

CHAPTER 20 Statistical Sampling Concepts for Tests of Controls and Tests of Balances LEARNING OBJECTIVES | | | | |
|PART I |Review |Exercises |Cases |
| |Checkpoints|Problems | |
| | | | |
|1. Explain the role of professional |1, 2, 3, 4,|38, 44 |21, 45, 46 |
|judgment in assigning numbers to risk |5, 6, 7, 8 | | |
|of assessing control risk too low, | | | |
|risk of assessing control risk too | | | |
|high, and tolerable deviation rate. | | | |
| | | | |
|2. Use statistical tables or |9, 10, 11, |39 |21, 45, 46 |
|calculations to determine test of |12 | | |
|controls sample sizes. | | | |
| | | | |
|3. Calculate the effect an test of |13 | |45 |
|controls sample sizes of subdividing a| | | |
|population into two relevant | | | |
|populations. | | | |
| | | | |
|4. Use your imagination to overcome |14, 15 |40, 41 | |
|difficult sampling unit selection | | | |
|problems. | | | |
| | | | |
|5. Use evaluation tables or |16, 17 |42 |22, 45 |
|calculations to compute statistical | | | |
|results (CUL, the computed upper | | | |
|limit) for evidence obtained with | | | |
|detail test of controls procedures. | | | |
| | | | |
|6. Use the discovery sampling |18 |43 | |
|evaluation table for assessment of | | | |
|audit evidence. | | | |
| | | | |
|7. Choose a test of controls sample |19, 20 | |21, 46 |
|size from among several equally | | | |
|acceptable alternative. | | | |
| | | | |
|Ashton Behavioral Cases continues | | |36, 37 |
|before problem 20.21 | | | | | | | | |
|PART II |Review |Exercises and|Cases |
| |Checkpoints|Problems | |
| | | | |
|8. Calculate a risk of incorrect |21,22,23,24| |70 |
|acceptance, given judgments about | | | |
|inherent risk, control risk and | | | |
|analytical procedures risk using the | | | |
|audit risk model. | | | |
| | | | |
|9. Explain the considerations |25, 26, 27 | |85 |
|determining a risk of incorrect | | | |
|rejection. | | | |
| | | | |
|10. Explain the characteristics of |28, 29, 29,|DUS: 41 | |
|dollar-unit sampling and its |30, 31 | | |
|relationships to attribute sampling. | | | |
|11. Calculate a dollar-unit sample | | | |
|size for the audit of the details of |32, 33, 34,| |70 84 |
|an account balance. |35 | | |
| | | | |
|12. Describe a method for selecting a |36, 37, 38 |82 |86 |
|dollar-unit sample, define a "logical | | | |
|unit," and explain the stratification | | | |
|effect of dollar-unit selection. | | | |
| | | | |
|13. Calculate an upper error limit for|39, 40, 41,| |70 71 |
|the evaluation of dollar-value |42, 43 | | |
|evidence, and discuss the relative | | | |
|merits of alternatives for determining| | | |
|an amount by which a monetary balance | | | |
|should be adjusted. | | | |
POWERPOINT SLIDES PowerPoint slides are included on the website. Please take special note of: * Risk and Materiality in Sampling
* Illustration of Dollar Unit Sampling as a Hook SOLUTIONS FOR REVIEW CHECKPOINTS 20.1 Use the model AR = IR x CR x DR to solve for different values of
Audit Risk (AR) when internal control risk (CR) is given different
values. In all cases IR = 0.90 and DR = 0.10, therefore, AR = 0.90 x
CR x 0.10 When CR is AR is
0.10 0.009 or .9 percent
0.50 0.045 or 4.5 percent
0.70 0.063 or 6.3 percent
0.90 0.081 or 8.1 percent
1.00 0.090 or 9.0 percent 20.2 Roberts' method in equation form is: ( RIA at assessed RIA at maximum )
Incremental RIA = RACRTL x ( control risk - control risk ) The method produces low RACRTL at the low control risk levels and high
RACRTL at the higher control risk levels. The logic of the method is: "At the lower control risk levels RACRTL
should be small because assessing control risk quite low makes a big
difference in the substantive sample size and hence in the risk of
incorrect acceptance in the substantive balance-audit work, but at the
higher control risk levels the RACRTL can be high because assessing
control risk slightly too low does not affect the substantive sample
size and risk of incorrect acceptance very much." 20.3 Assessing the control risk too low causes auditors to assign less
control risk (CR) in planning procedures than proper evaluation would
cause them to assign. The result could be (1) inadvertently conducting
less audit work than properly necessary and taking more audit risk
(AR) than originally contemplated, perhaps to the unpleasant results
of failing to detect material misstatements (damaging the
effectiveness of the audit) or (2) discovering in the course of
the audit work that control is not as good as first believed, causing
an increase in the audit work, perhaps at a time when doing to is very
costly (damaging the efficiency of the audit). The important considerations when auditing a particular account are
questions related to (1) How sensitive is the final substantive audit
work to assessing control risk too low?, and (2) Is "recovery"--
increasing the substantive audit work at a later date upon discovery
of the decision error--more expensive and time consuming than planning
more work at the outset (i.e., planning to "overaudit")? 20.4 Assessing the Control Risk Too High The important consideration involved in judging an acceptable risk of
assessing the control risk too high is the efficiency of the audit.
Assessing control risk too high causes auditors to think they need to
perform a level of substantive work which is greater than a proper
evaluation of control would suggest. Assessing control risk too high
leads to overauditing. Some auditors may be willing to accept high risks of assessing the
control risk too high because they intend to overaudit anyway, and the
audit budget can support the work. Other auditors want to minimize their work (within acceptable
professional bounds of audit risk) and thus want to minimize the risk
(probability) of overauditing by mistake. Technically, the risk of assessing control risk too high in relation
to an attribute sample is the probability of finding in the sample (n)
one deviation more than the "acceptable number" for the sampling plan.
For example, if the plan called for a sample of 100 units and a
tolerable rate of 3 percent at a .10 risk of assessing control risk
too low, the "acceptable number" is zero deviations. (Appendix 13-B.3
shows CUL = 3 percent when zero deviations are found in a sample of
100 units.) The probability of finding 1 or more deviations when the population
rate is actually 2 percent is: Probabil