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ACCT 422 Chapter 11
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Terms in this set (67)
Audit sampling
is the application of an audit procedure to less than 100% of the items in a population for the purpose of drawing an inference about the entire population.
Purpose of audit sampling
to reach a conclusion about an entire population of items
Audit sampling is commonly used in
vouching and tracing to inspect manually prepared documentary audit trail
IT reduced the extent of use of
audit sampling. Internal auditor: to test reliability of the application program instead
Two general types of audit sampling
statistical sampling and non-statistical sampling
statistical sampling
Allow the auditor to quantify, and therefore control, the risk of making an incorrect decision based on sample evidence
More costly
Use sample that represent the
entire population
Audit risk (sampling and nonsampling risk)
The risk of reaching invalid audit conclusions and/or providing faulty advice based on the audit work conducted.
Sample is not representative of the
population
Sampling risks in tests of controls
The risk that the internal auditor's conclusion based on sample testing may be different than the conclusion reached if the audit procedure was applied to all items in the population
Type I Risk/Alpha Risk
The risk of assessing control risk too high
Risk of under-reliance:
assessed control risk based on sample > assessed control risk per 100% population
Wrong conclusion: control is less effective than it is
Type II Risk/Beta Risk
The risk of assessing control risk too low
Risk of over-reliance:
assessed control risk based on sample < assessed control risk per 100% population
Wrong conclusion: control is more effective than it is.
Control Risk
The risk that controls fail to reduce controllable risk to an acceptable level.
What is the relationship between sample size and sample risk?
Inverse relationship
The risk of assessing control risk too low is at
5%
Controllable risk
The portion of inherent risk that management can reduce through day-to-day operation
Residual Risk
The risk remains after controls have been implemented
If residual risk is greater than Management's tolerance then there is
Ineffective control.
Design of control: inadequate
Operation of control: ineffective
Nonsampling risk
Not associated with testing samples.
Nonsampling risk is the risk that occurs when an internal auditor fails to perform his or her work correctly, such as
Performing inappropriate auditing procedures
Misapplying an appropriate procedure (fail to recognize error or deviation)
Misinterpreting sampling results
Nonsampling risk is controlled through
appropriate audit planning,
supervision of individual audit engagements, and
overall application of appropriate quality assurance procedures
Which of the following is an element of sampling risk as opposed to an element of nonsampling risk?
a. Performing an inappropriate audit procedure
b. Failing to detect a control deviation
c. Forgetting to perform a specified audit procedure
d. Determining a sample size that is too small
d. Determining a sample size that is too small
The primary reason for an internal auditor to use statistical sampling rather than nonstatistical sampling is to:
a. Allow the auditor to quantify, and therefore control, the risk of making incorrect decision based on sample evidence
b. Obtain a smaller sample than would be required if nonstatistical sampling were used
c. Reduce the problems associated with the auditor's judgment concerning the competency of the evidence gathered when nonstatistical sampling is used.
d. Obtain a sample more representative of the population than would be obtained if nonstatistical sampling techniques were used.
a. Allow the auditor to quantify, and therefore control, the risk of making incorrect decision based on sample evidence
Attribute Sampling Approaches
A statistical sampling approach enables the user to reach a conclusion about a population in terms of a rate of occurrence. (Based on binomial distribution theory)
Most common use of attribute sampling approach
Auditor tests the rate of deviation from a prescribed control to determine whether the occurrence rate is "acceptable", and, accordingly, whether reliance on that control is appropriate.
Three variations of attribute sampling approach
Stratified attribute sampling, stop-or-go sampling, discovery sampling
Stratified attribute sampling
From a population that can be subdivided. subdivide sample per levels of control
Stop-or-go sampling
Used when very low deviation rates are expected. minimizes the required sample size for a specified level of sampling risk
Discovery Sampling
Designed to be large enough to detect at least one deviation if the rate of deviations in the population is at or above a specified rate (if the sample does not have any error then the actual error rate is below the minimum acceptable rate). enables auditor to test the likelihood of finding at least one deviation. commonly used for test of fraud
For which of the following would an internal auditor most likely use attribute sampling?
a. Determining whether the year-end inventory balance is overstated
b. Selecting fixed asset additions to inspect
c. Choosing inventory items to test count
d. Inspecting employee timecards for proper approval
d. Inspecting employee timecards for proper approval
Designing an Attribute Sampling Plan, Executing the Plan, and Evaluating the Sample Results—9 steps:
1. Control Objective: identify a specific internal control objective and the prescribed control(s) aimed at achieving that objective
2. Control Deviation: define what is meant by a control deviation.
3. Population & Sampling Units: define the population and sampling unit.
4. Values of Parameters: determine the appropriate values of the parameters affecting sample size.
5. Sample size: determine the appropriate sample size.
6. Sample selection: randomly select the sample.
7. Finding Deviation: audit the sample items selected and count the number of deviations from the prescribed control.
8. Upper Deviation limit: determine the achieved upper deviation limit.
9. Evaluate the sample results.
Two fundamental requirements of statistical sampling:
Sample must be selected randomly
Sample results must be evaluated mathematically based on probability theory
3 factors affecting sample size:
The acceptable risk of assessing control risk too low (how confident the auditor wants to be in drawing a correct inference about tested controls)
The tolerable deviation rate (inversely related to sample size)
The expected population deviation rate
Size of population has little effect on attribute sample size unless the population is very small
Population < 200: sample size directly correlates to population size
200< Population <2000: sample size increases
Population > 2500: use table in exhibit 11-1
The acceptable risk of assessing control risk too low
Risk: Control is concluded as more effective than it is (Type II)
Inversely related to sample size: Sample Size increase then Acceptable Risk decrease
The complement of confidence the auditor's desire of the % of drawing correct conclusion : 1-Risk % = desired confidence level
The tolerable deviation rate
The maximum rate of deviations the internal auditor is willing to accept and still conclude that the control is acceptably effective.
Inversely related to sample size: Sample Size increase -> Tolerable Deviation decrease
Decided based on the relative importance of the control being tested:
Control is critical -> Low Tolerable Deviation Rate is set
The expected population deviation rate
The internal auditor's best estimate of the actual deviation rate in the population of items being examined.
Direct effect on sample size:
Sample Size increase then Expected Population Deviation Rate increase
Less than the tolerable deviation rate:
Tolerable Deviation Rate - Expected Population Deviation Rate = Planned allowance for sampling risk (or, planned precision)
Random Sampling
Each item in the defined population has an equal opportunity of being selected. ->to avoid selecting biased sample
Simple random sampling
Use random number table or random number generator program
The easiest approach when sampling pre-numbered documents
Systematic sampling
Randomly identify a starting point (or multiple starting points) then select every Nth item after that.
Use when:
the equal intervals will not systematically bias the sample
Commonly used when individual items of the population are not pre-numbered
Vouch
PO to the corresponding purchase requisition
Each purchase requisition is inspected for evidence of
Approval by an authorized person, and
Item purchased per the PO = item requested per the purchase requisition
Evaluate the sample results
1. Formulating a statistical conclusion
2. Making an audit decision based on the quantitative sample results
3. Considering qualitative aspects of the sample results
Formulating a statistical conclusion
Risk of assessing control risk too low: 10% -> 90% confident
Considering qualitative aspects of the sample results
Qualitative aspects of deviations:
Are the deviations the result of fraud? if so then control is not effective even if the upper deviation limit is lower than tolerable deviation rate.
What impact the discovery of fraud might have on other aspects of the engagement?
If all other factors specified in an attribute sampling plan remain constant, changing the expected population deviation rate from 1% to 2% and changing the tolerable deviation rate from 7% to 6% would cause the required sample size to:
a. Increase
b. Decrease
c. Remain the same
d. Change by 2%
a. Increase
The achieved upper deviation limit is 7% and the risk of assessing control risk too low is 5%. How should the internal auditor interpret this attribute sampling outcome?
a. There is a 7% chance that the deviation rate in the population is less than or equal to 5%
b. There is a 5% chance that the deviation rate in the population is less than 7%
c. There is a 5% chance that the deviation rate in the population exceeds 7%
d. There is a 95% chance that the deviation rate in the population equals 7%
c. There is a 5% chance that the deviation rate in the population exceeds 7%
An internal auditor should consider the qualitative aspects of deviations found in a sample in addition to evaluating the number of deviations. For which of the following situations should the internal auditor be most concerned?
a. There were fewer deviations in the sample than expected
b. The deviations found are similar in nature to those found during the last audit of the area
c. The deviations found appear to have been caused by an employee's misunderstanding of instructions
d. The deviations found may have been caused intentionally
d. The deviations found may have been caused intentionally
Selecting and Evaluating a Nonstatistical Sample
Allows the internal auditor more latitude regarding sample selection and evaluation
Purpose of Selecting and Evaluating a Nonstatistical Sample
to select sufficient appropriate evidence to support valid conclusion. (unchanged from using statistical sampling)
Major difference between nonstatistical and statistical sampling
Inability to quantify sampling risk statistically
Haphazard Sampling
Is a nonrandom selection technique that is used by internal auditors to select a sample that is expected to be representative of the population
Haphazard, in this context, does not mean careless or reckless. It means that the internal auditor selects the sample without deliberately deciding to include or exclude certain items.
Internal auditor must project the sample results to the population-> larger samples to compensate for the less rigorous selection method and the inability to quantitatively control sampling risk
Population: judgmental
Commonly Used Nonstatistical Sampling Approaches:
Select a relatively small sample haphazardly
Presumption: no control deviations in the population
If one or more deviations found then control is NOT acceptably effective
Shortcoming: does not take into consideration two fundamental factors regarding sample size:
Risk of assessing control risk too low
Tolerable deviation rate
Statistical Sampling in Tests of Monetary Values Purpose
to obtain direct evidence about the correctness of monetary values such as a recorded account balance.
Sampling risk of Statistical Sampling in Tests of Monetary Values
The risk of incorrect rejection (type I risk, alpha risk)
a recorded amount is materially misstated when it is not
The risk of incorrect acceptance (type II risk, beta risk)
a recorded value is not materially misstated when it is
Probability-proportional-to-size (PPS) Sampling:
Also called "monetary-unit sampling", or "dollar-unit sampling"
Is a modified form of attribute sampling that is used to reach conclusions regarding monetary amounts rather than rates of occurrence
Primarily purpose: to test for overstatement when expected number of individual overstatements in the population is small
Selecting a sample for Probability-proportional-to-size (PPS) Sampling
Must be random
Population: the population of individual monetary units
Sampling approach: systematic -> to select every nth monetary unit after a random start (selecting even intervals)
Logic units: the individual transaction or account that includes a sampled dollar (the individual monetary unit) -> audit interest->
larger logical units are more apt to be selected for testing than smaller logical units
Four factors affect PPS sample sizes:
Monetary book value of the population.
Risk of incorrect acceptance.
Tolerable misstatement.
Anticipated misstatement.
Classical Variables Sampling
Is a statistical sampling approach based on normal distribution theory that is used to reach conclusions regarding monetary amounts
Selecting the sample for classical variables sampling:
Must be random
Two approaches:
simple random sampling and
systematic sampling with a random start
Five factors affect PPS sample sizes for Classical variables sampling:
Population size
Estimated population standard deviation
Risk of incorrect acceptance
Risk of incorrect rejection
Tolerable misstatement
Key advantages of PPS sampling over classical variables sampling:
Simpler calculations, easier to use.
The sample size calculation does not involve any measure of estimated population variation.
PPS sampling automatically results in a stratified sample because sample items are selected in proportion to their size.
PPS sample selection automatically identifies any individually significant population items, that is, population items exceeding a predetermined cutoff dollar amount.
PPS sampling generally is more efficient (that is, requires a smaller sample size) when the population contains zero or very few misstatements.
Key disadvantages of PPS sampling over classical variables sampling:
Special design considerations are required when understatements or audit values of less than zero are expected.
Identification of understatements in the sample requires special evaluation considerations.
PPS sampling produces overly conservative results when errors are detected. This increases the risk of incorrect rejection.
The appropriate sample size increases quickly as the number of expected misstatements increases. When more than a few misstatements are expected, PPS sampling may be less efficient.
If all other factors specified in a PPS sampling plan remain constant, changing the specified tolerable misstatement from $200k to $100k and changing the specified risk of incorrect acceptance from 10% to 5% would cause the required sample size to:
a. Increase
b. Decrease
c. Remain the same
d. Change by 5%
a. Increase
An internal auditor selects a sample of sales invoices and matches them to shipping documents. This procedure most directly addresses which of the following assertions:
a. All shipments to customers are recorded as receivables
b. All billed sales are for goods shipped to customers
c. All recorded receivables represent goods shipped to customers
d. All shipments to customers are billed
b. All billed sales are for goods shipped to customers
An internal auditor is testing cash disbursement transactions. Internal control policies require every check request to be accompanied by an approved voucher (that is, a package of documents evidencing that a good or service has been received and invoiced by the vendor). The voucher approval is based on a three-way matching of a purchase order, receiving report, and vendor's invoice. To determine whether checks have proper support, the internal auditor should begin her testing procedures by selecting items from the population of:
a. Check copies
b. Purchase orders
c. Receiving reports
d. Approved vouchers
a. Check copies
An internal auditor wants to test customers' accounts receivable balances for overstatement on a sample basis. Which of the following would be the least valid reason for deciding to use PPS sampling rather than classical variables sampling?
a. PPS sampling is generally thought to be easier to use than classical variables sampling
b. The internal auditor expects to find no misstatements and PPS sampling typically requires a smaller sample size than classical variables sampling in this situation
c. PPS sampling automatically stratifies the population
d. Using PPS sampling eliminates the need for professional judgment in determining the appropriate sample size and evaluating the sample results.
d. Using PPS sampling eliminates the need for professional judgment in determining the appropriate sample size and evaluating the sample results.
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