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## Sampling for Tests of Transactions

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Sampling for Tests of Transactions

- Objective of Tests
- TOC - Determine if control is effective
- STOT- Determine existence of monetary errors in transactions

Objective of TOC and STOT

- Both are tests of transactions
- Evaluated yes / no
- control is / is noteffective
- transaction is / is notcorrectly recorded
- Auditor should consider qualitative aspectsof deviations

Evaluation of Results

- TOC- assessment of control risk
- affects PDR and evidence (STOT and TODB)
- STOT - are transactions correctly recorded
- affects extend to TODB
- also has implications for control risk

Risk Model

- TOC CR
- Lower CR PDR
- Evidence
- (less STOT & TODB for related objective)

Risk Model

- STOT
- CR PDR
- STOT affect CR assessment.
- Good results also lowers TODB
- (STOT and TODB both part of PDR)

Relationship between selection and evaluation

- Statistical Sampling must be
- evaluation random(probabilistic)
- Nonstatistical Judgmental selection
- evaluation allowed, but random
- selection is still preferable
- Point: Random selection is always desirable

Selection Methods

- Random - Each item has equal chance of selection (TOT)
- Probabilistic - each item has a know probability of selection (TODB)

Sampling Risk

- Sampling Risk- Risk the sample is not representative; inherent with sampling. Reduce by:
- Using appropriate sampling
- Increasing sample size
- Is a random sample representative?

Nonsampling Risk

- Nonsampling error- is the risk the auditor fails to uncover existing errors in the sample. Reduce by:
- Carefully defining and performing the test(text example of incorrectly selecting an existence sample from shipping documents)
- Control over sample

15-27 (a) - Test with attributes sampling?

- Review CR journal for unusual transactions.
- Trace prelisting amts. to CR journal
- Compare info on prelisting with CR journal
- Examine remittance advices to see if discounts approved
- Trace entries from prelist to deposit

15-27 (a) - Test with attributes sampling?

- Review CR journal for unusual transactions.
- Trace prelisting amts. to CR journal
- Compare info on prelisting with CR journal
- Examine remittance advices to see if discounts approved
- Trace entries from prelist to deposit

Sample Selection

- 2. Trace prelisting amts. to CR journal (completeness)
- 3. Compare info on prelisting with CR journal (accuracy)
- 4. Examine remittance advices to see if discounts approved (accuracy)
- 5. Trace entries from prelist to deposit (completeness)
- Draw sample from prelist (source for directional completeness tests)

Sampling for Exception Rates

- Objective- Estimate maximum error rate in population based on sample
- determine if control can be relied on or results for STOT acceptable

Maximum Error Rate (CUER)

- Sample exception rate (SER) is best estimator of population exception rate
- Maximum rate is the computed upper exception rate (CUER) and includes allowance for sampling risk (ASR)
- CUER = SER + ASR

Larger n

- sample exception rateCUER
- (SER)

Variable Description Definition

- EPER Expected Last year’s results
- population or auditor exception rate expectations
- TER Tolerable Maximum rate
- (precision) exception that auditor will rate allow. Lower for imp. objectives
- ARACR Acceptable Risk of relying
- (confidence risk of on control/STOT level) assessing CR when it is too low ineffective

Changes in variables on sample size

- Planning relation:
- TER = EPER + ASR (allowance for sample risk)
- Increases in sample size lower sampling risk

Effect on Changes in Variables on

- Sample Size
- Change in Effect
- Factor on n Reason
- EPER increase Increase Less allowance for
- sampling risk for given TER
- TERincrease Decrease More allowance for sampling risk for given EPER
- ARACR Decrease Less reliance on increase controls; less evidence needed

The biggest effect on sample size is TER - EPER

- Bigger differences provides larger allowance for sampling risk

15-22(a)

- If all other factors remain constant, changing ARACR from 10% to 5% would cause sample size to:
- 1. Increase
- 2. Remain the same
- 3. Decrease
- 4. Become indeterminate

Problem 15-28 Part c: (increase in ARACR)

- 12 34
- ARACR 10 5 5 5
- TER 6 6 5 6
- EPER 2 2 2 2
- Population
- size 1,000 100,000 6,000 1,000
- Sample
- Size 88 127 181 127

Problem 15-28 Part c: (increase in TER)

- 1 2 34
- ARACR 10 5 5 5
- TER 6 6 5 6
- EPER 2 2 2 2
- Population
- size 1,000 100,000 6,000 1,000
- Sample
- Size 88 127 181127

Problem 15-28 Part c: (increase in EPER)

- 5 67
- ARACR 10 10 5
- TER 20 20 2
- EPER 8 2 0
- Population
- size 500 500 1,000,000
- Sample
- Size 25 18149

Problem 15-28 Part c: (increase in POP)

- 1 2 3 4
- ARACR 10 5 5 5
- TER 6 6 5 6
- EPER 2 2 2 2
- Population
- size 1,000 100,000 6,000 1,000
- Sample
- Size 88 127181127

Evaluating the Sample

- TER, ARACR, and n as before
- SER = Sample exception rate
- (# of exceptions/n)
- CUER = maximum error rate
- = SER + ASR

Evaluation Decision - Nonstatistical sampling

- Approach 1:
- Accept if CUER < TER
- Approach 2:
- ASR = TER - SER
- Accept if ASR large enough (SER sufficiently less than TER)

Options when CUER exceeds TER

- 1. Increase sample size - lowers ASR and CUER
- (may also reduce SER if initial sample not representative)
- 2. Don’t rely upon control/STOT
- CR and substantive tests

Options when CUER > TER

- TOC fails -can increase STOT or TODB. Usually increase STOT
- STOT fails- Increase TODB
- 3. Revise TER or ARACR -
- usually not recommended

Change in variables on CUER

- Evaluation relation:
- CUER = SER + ASR
- Remember: increase in sample size lowers sampling risk
- Increase in n may also lower SER if initial sample not representative

Effect of Changes in Variables on CUER

- Change in Effect on
- Factor CUER Reason
- SER Increase Increase CUER = SER+ASR
- n increase Decrease Lower sampling risk
- ARACR Decrease Less reliance on
- increase controls; threshold for accepting a control is lower

15-23 (a)

- An auditor estimates with 10% ARACR (90% confidence) that CUER is between 4% and 6%. The auditor’s major concern is that there is one chance in 20 that the true exception rate is:
- 1. More than 6%
- 2. Less than 6%
- 3. More than 4%
- 4. Less than 4%

Problem 15-29 Part c: (decrease ARACR)

- 1 23 4
- ARACR 10 5 5 5
- Population Size 5,000 5,000 5,000 50,000
- Sample size 200 200 50 200
- Number of
- exceptions 4 4 1 4
- CUER 4.0 4.59.1 4.5

Problem 15-29 Part c:(decrease n)

- 1 2 3 4
- ARACR 10 5 5 5
- Population Size 5,000 5,000 5,000 50,000
- Sample size 200 200 50 200
- Number of
- exceptions 4 4 1 4
- CUER 4.0 4.5 9.1 4.5

Problem 15-29 Part c:(decrease exceptions)

- 5 6 7 8
- ARACR 5 5 5 5
- Population Size 500 900 5,000 500
- Sample size 100 100 100 25
- Number of
- exceptions 2 10 0 0
- CUER 6.2 16.4 3.0 11.3

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