statistical sampling for auditors

7/27/2019 Statistical Sampling for Auditors

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APIPA 2009 1

STATISTICAL SAMPLING

FOR AUDITORS

Jeanne H.

Yamamura


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APIPA 2009 2

OBJECTIVES Review of sampling concepts

Types of sampling Attribute sampling

Steps

Nonstatistical attribute sampling

Compliance auditing

Monetary unit sampling Steps

Nonstatistical monetary unit sampling Classical sampling

Ratio estimation

Difference estimation


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APIPA 2009 3

AUDIT SAMPLING Application of an audit procedure to less

than 100% of the items in a population

Account balance Class of transactions

Examination on a test basis

Key: Sample is intended to berepresentative of the population.


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APIPA 2009 4

SAMPLING RISK Possibility that the sample is NOT

representative of the population

As a result, auditor will reach WRONGconclusion

Decision errors

Type I Risk of incorrect rejection Type II Risk of incorrect acceptance


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APIPA 2009 5

TYPE I RISK OFINCORRECT REJECTION

Internal control: Risk that samplesupports conclusion that control is NOT

operating effectively when it really isAKA Risk of underreliance, risk of

assessing control risk too high

Substantive testing: Risk that samplesupports conclusion that balance is NOTproperly stated when it really is


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APIPA 2009 7

WHICH RISK POSES THEGREATER DANGER TO ANAUDITOR?

Risk of incorrect rejection

Efficiency

Risk of incorrect acceptance Effectiveness

Auditor focus on Type II

Also provides coverage for Type I


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APIPA 2009 8

NONSAMPLING RISK Risk of auditor error

Sample wrong population

Fail to detect a misstatement when applying auditprocedure

Misinterpret audit result

Controlled through

Adequate training Proper planning

Effective supervision


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APIPA 2009 9

SAMPLE SIZE FACTORS Desired level of assurance

(confidence level)

Acceptable defect rate (tolerableerror)

Historical defect rate (expectederror)


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APIPA 2009 10

CONFIDENCE LEVEL Complement of sampling risk

5% sampling risk, 95% confidence level

How much reliance will be placed on testresults

The greater the reliance and the more severethe consequences of Type II error, the higherthe confidence level needed

Sample size increases with confidence level(decreases with sampling risk)


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APIPA 2009 11

TOLERABLE ERROR ANDEXPECTED ERROR

Precision the gap between tolerableerror and expected error

AKA Allowance for sampling risk Sample size increases as precision

decreases


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APIPA 2009 12

WHEN DO YOU SAMPLE? Inspection of tangible assets, e.g.,

inventory observation

Inspection of records or documents, e.g.,internal control testing

Reperformance, e.g., internal controltesting

Confirmation, e.g., verification of ARbalances


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APIPA 2009 13

WHEN IS SAMPLINGINAPPROPRIATE?

Selection of all items with a particularcharacteristic, e.g., all disbursements >$100,000

Testing only one or a few items, e.g.,automated IT controls, walk throughs

Analytical procedures

Scanning Inquiry

Observation


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APIPA 2009 14

WALKTHROUGHS Designed to provide evidence regarding the

design and implementation of controls Can provide some assurance of operating

effectiveness BUT Depends on nature of control (automated or

manual) Depends on nature of auditors procedures to test

control (also includes inquiry and observation

combined with strong control environment andadequate monitoring)

Walkthough = sample of 1


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APIPA 2009 15

STATISTICAL VSNONSTATISTICAL SAMPLING

Statistical sampling Statistical computation of sample size

Statistical evaluation of results

Nonstatistical sampling

Sample sizes should be approximately thesame (AU 350.22)

Sample sizes must be sufficient to supportreliance on controls and assertions beingtested


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APIPA 2009 16

WHEN IS SAMPLINGNONSTATISTICAL?

If sample size determined judgmentally

If sample selected haphazardly

If sample results evaluated judgmentally


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APIPA 2009 17

TYPES OF SAMPLING Attribute sampling

Monetary unit sampling

Classical variables sampling


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APIPA 2009 18

ATTRIBUTE SAMPLING Used to estimate proportion of a

population that possesses a specific

characteristic Most commonly used for T of C

Can also be used for dual purpose

testing (T of C and Substantive T of T)


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APIPA 2009 19

MONETARY-UNITSAMPLING

AKA probability proportional to size(PPS) sampling, cumulative monetary

unit sampling Used to estimate dollar amount of

misstatement


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APIPA 2009 20

CLASSICAL VARIABLESSAMPLING

Uses normal distribution theory to identifyamount of misstatement

Useful when large number of differencesexpected Smaller sample size than MUS

Effective for both overstatements andunderstatements

Can easily incorporate zero balances


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APIPA 2009 21

IN-CLASS EXERCISENO. 1


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APIPA 2009 22


Test Involves

Sampling?

Attribute / Variable / MUS / NA

1 Yes Attribute (ST of T)

2 No NA

3 Yes Attribute (T of C)

4 No NA

5 No NA (Could be MUS if largepopulation)

6 No NA


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APIPA 2009 23


Test Involves

Sampling?

Attribute / Variable / MUS / NA

7 Yes Attribute (T of C)

8 Yes MUS

9 No NA

10 Yes Attribute (T of C/ST of T)

11 No NA


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APIPA 2009 24

STEPS IN STATISTICALATTRIBUTE SAMPLINGAPPLICATION

Planning1. Determine the test objectives2. Define the population characteristics

3. Determine the sample size Performance

4. Select sample items5. Perform the auditing procedures

Evaluation6. Calculate the results7. Draw conclusions


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APIPA 2009 25

STEP 1: DETERMINE THETEST OBJECTIVES

Objective for T of C: To determine theoperating effectiveness of the internal

control Support control risk assessment below

maximum

Identify controls to be tested andunderstand why they are to be tested


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APIPA 2009 26

TESTS OF CONTROLS Concerned primarily with

Were the necessary controls performed?

How were they performed? By whom were they performed?

Appropriate when documentary evidence

of performance exists


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APIPA 2009 27

STEP 2: DEFINE THEPOPULATIONCHARACTERISTICS

Define the sampling population

Assertion

Completeness Define the sampling unit

Determined by available records

Define the control deviation conditions


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APIPA 2009 28

STEP 3: DETERMINE THESAMPLE SIZE

Determine factors Desired confidence level (direct)

Tolerable deviation rate (inverse) Expected population deviation rate (direct)

Desired confidence level If planning to rely on controls, would be 90 to

95% Significance of account and importance of

assertion affected by control being tested


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APIPA 2009 29


Tolerable deviation rate

Maximum deviation rate that auditor willing toaccept and still consider control effective Control would be relied upon

Why any errors acceptable? Control deviation = Misstatement

Assessed importance of control Tolerabledeviation rate

Highly important 3-5%

Moderately important 6-10%


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APIPA 2009 30


Expected population deviation rate

Rate expected to exist in population

Based on prior years results or pilot sample If expected population deviation rate >

tolerable rate, DO NOT TEST

SAMPLE SIZE TABLES


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APIPA 2009 31


Testing multiple attributes on the samesample

Select largest sample size and audit all ofthem for all attributes

Result is some overauditing BUT may takeless time than trying to remember whichsample items need to be tested for whichattribute


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APIPA 2009 32

FINITE POPULATIONCORRECTION FACTOR

When population size < 500

Apply finite population correction factor

1-(n/N) Where n = sample size from table and N =

number of units in population


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APIPA 2009 33

STEP 4: SELECT THESAMPLE ITEMS

Sample must be selected to berepresentative of the population

Each item must have an equalopportunity of being selected


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APIPA 2009 34


Random number selection

Unrestricted random sampling without

replacement (once selected cannot beselected again)


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APIPA 2009 35


Random number table

Need to document

Correspondence: relationship betweenpopulation and random number table

Route: selection path, e.g., up or down columns,and right to left (must be consistent)

Starting point: starting row, column, digit

Stopping point: to enable adding more sampleitems if needed


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APIPA 2009 36

RANDOM NUMBER TABLEILLUSTRATION

Select a sample of 4 items from prenumberedcanceled checks numbered from 1 to 500.Start at row 5, column 1, digit starting position1. Select three-digit numbers. Items selected

are: 145 (sample item #1) 516 (discard because checks numbers do not

exceed 500)

032 (sample item #2) 246 (sample item #3) 840 (discard)181 (sample item #4)


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APIPA 2009 37

RANDOM NUMBER TABLEILLUSTRATION

To minimize discards, table numbers > 500 canbe reduced by 500 to produce a sample itemwithin the population boundary of 1 to 500. The

four sample items selected are: 145 (sample item #1)

016 (sample item #2 = 516 500 = 016)

032 (sample item #2)

246 (sample item #3)

340 (sample item #4 = 840 500 = 340)


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APIPA 2009 39

STEP 4: SELECT THESAMPLE ITEMS - EXCEL

Excel

Select Tools

Select Data Analysis Select Sampling


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APIPA 2009 40

STEP 4: SELECT THESAMPLE ITEMS - EXCEL


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APIPA 2009 41


Input Range

Enter the references for the range of data that contains the population ofvalues you want to sample. Microsoft Excel draws samples from the firstcolumn, then the second column, and so on.

Labels

Select if the first row or column of your input range contains labels. Clearif your input range has no labels; Excel generates appropriate data labelsfor the output table.

Sampling Method

Click Periodic orRandom to indicate the sampling interval you want. Period

Enter the periodic interval at which you want sampling to take place. Theperiod-th value in the input range and every period-th value thereafter iscopied to the output column. Sampling stops when the end of the inputrange is reached.


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APIPA 2009 42


Number of Samples

Enter the number of random values you want in theoutput column. Each value is drawn from a randomposition in the input range, and any number can be

selected more than once. Output Range

Enter the reference for the upper-left cell of the outputtable. Data is written in a single column below the cell.If you select Periodic, the number of values in the

output table is equal to the number of values in theinput range, divided by the sampling rate. If you selectRandom, the number of values in the output table isequal to the number of samples.


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APIPA 2009 43


Systematic selection Determine sampling interval = Population / Sample

Size Ensure population is in random order Select random starting number (within first interval)

Better to use multiple random starting points to reduce riskof missing systematic deviations

Select every nth item Continue sample selection until population is

exhausted (Last sample selected + sampling interval) > Last item in

population In other words, dont stop when desired sample size

reached


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APIPA 2009 44

STEP 5: PERFORM THEAUDITING PROCEDURES

Conduct planned audit procedures

What if?

Voided documents - if properly voided, not adeviation; replace with new sample item

Unused or inapplicable documents replacewith new sample item

Inability to examine sample item deviation Stopping test before completion large

number of deviations detected


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APIPA 2009 45


Deviations observed

Investigate nature, cause, and consequence

of every exception Unintentional error? Or fraud?

Monetary misstatement resulted?

Cause misunderstanding of instructions?

Carelessness? Effect on other areas?


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APIPA 2009 46

STEP 6: CALCULATERESULTS

Summarize deviations for each control

Calculate sample deviation rate and

computed upper deviation rate Sample deviation rate + Allowance for

sampling risk = Computed upper deviationrate

Statistical sampling results evaluation tables


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APIPA 2009 47

STEP 7: DRAWCONCLUSIONS

If Computed Upper Deviation Rate >Tolerable Rate, control is ineffective and

cannot be relied upon. If Computed Upper Deviation Rate expected

population deviation rate, control noteffective


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APIPA 2009 70

COMPLIANCE AUDITING Performance of auditing procedures to

determine whether an entity is complying withspecific requirements of laws, regulations, or

agreements

Governmental entities and other recipients ofgovernmental financial assistance

Compliance with laws and regulations thatmaterially affect each major federal assistanceprogram

COMPLIANCE AUDITING OF


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APIPA 2009 71

FEDERAL ASSISTANCEPROGRAMS

Definition of population for testing of aninternal control procedure that applies to

more than one program Define items from each major program as a

separate population, OR

Define all items to which control is applicable

as a single population

Second choice usually more efficient


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APIPA 2009 72

COMPLIANCE AUDITING -EXAMPLE

Federal financial assistance for IslandCity

Three major federal financial assistanceprograms

Four nonmajor programs

Control: Transaction review to ensurethat only legally allowable costs arecharged to each program


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APIPA 2009 73

COMPLIANCE AUDITING -EXAMPLE

More efficient to select one sample frompopulation of all transactions (major andnonmajor programs)

Confidence level = 95%

Tolerable deviation rate = 9%

Expected population deviation rate = 1%

Sample size: 51

1 allowable deviation

SMALL POPULATIONS AND


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APIPA 2009 74

INFREQUENTLY OPERATINGCONTROLS

Small Population Sample Size Table

Control Frequency and

Popu lat ion Size

Samp le Size

Quarterly (4) 2

Monthly (12) 2-4

Semimonthly (24) 3-8Weekly (52) 5-9


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APIPA 2009 75



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APIPA 2009 76


Selected Payroll T of C

1. Examine the time cardfor approval of a

supervisor

Moderately criticalaffects E/O of S& W

2. Account for asequence of payrollchecks in the payroll

journal

Very critical affects E/Oof S&W

3. Recompute hours onthe time card

Moderately criticalaffects V of S&W


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APIPA 2009 77


4. Compare theemployee name in thepayroll journal to

personnel records

Very critical affectsE/O - affects E/O of S&W; also an area subject

to fraud

5. Review OT chargesfor approval of a

supervisor

Moderately criticalaffects E/O and V of

S&W


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APIPA 2009 78


Selected Cash Disbursement T of C

6. Examine voucher for

supporting invoices,receiving reports, etc.

Very critical affects

E/O of purchasetransactions

7. Examine supportingdocuments for evidence

of cancellation (paid)

Moderately criticalaffects validity of

purchase transactionsand relates to doublepayment


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APIPA 2009 79



8. Ascertain whether

cash discounts weretaken

Least critical affects V

of purchasetransactions; amountsusually minor

9. Review voucher for

clerical accuracy

Moderately critical

affects V of purchasetransactions


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APIPA 2009 80



10. Agree purchase

order price to invoice

Moderately critical

affects V of purchasetransactions


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APIPA 2009 81

MONETARY UNITSAMPLING

Uses attribute sampling theory to expressconclusions in dollar amounts

Estimates the percentage of monetary units in a

population that might be misstated Multiples the percentage by an estimate of how

much the dollars are misstated

Developed by auditors

Assumes little or no misstatements

Designed primarily to test for overstatements


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APIPA 2009 82

ADVANTAGES When no misstatements expected,

results in smaller (more efficient) sample

size than classical variables sampling No need to compute/identify standard

deviation

Automatically stratifies sample


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APIPA 2009 83

DISADVANTAGES Zero or negative balances must be tested

separately

Assumes audited amount of sampleitems is not in error by more than 100%

When more than 1 or 2 misstatementsfound, allowance for sampling risk may

be overstatedAuditor more likely to reject balance and

overaudit


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APIPA 2009 84

STEPS IN MONETARY UNITSAMPLING APPLICATION

Planning1. Determine the test objectives2. Define the population characteristics

3. Determine the sample size Performance

4. Select sample items5. Perform the auditing procedures

Evaluation6. Calculate the results7. Draw conclusions


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APIPA 2009 85

STEP 1: DETERMINE THETEST OBJECTIVES

Substantive testing: To test thereasonableness of an amount, i.e., that

an amount is fairly stated To test the assertion that no material

misstatements exist in an accountbalance, class of transactions, ordisclosure component of the financialstatements

STEP 2: DEFINE THE


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APIPA 2009 86

POPULATIONCHARACTERISTICS

Define the sampling population Monetary value of an account balance

Verify completeness of population

Define the sampling unit - Each individualdollar

Define the logical unit - The account ortransaction that contains the sampling units

Define a misstatement The differencebetween the book value and the audited value


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APIPA 2009 87


Determine factors (effect on sample size)

Desired confidence level (direct)

To increase confidence, more work is required!(larger sample size)

Tolerable misstatement (inverse)

Expected misstatement (direct)

Population size (direct)


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APIPA 2009 88


Computing sample sizes using theattribute sampling tables Select desired confidence level

Compute tolerable misstatement aspercentage of book value

Compute expected misstatement as

percentage of book value Look up sample size in attribute sampling

table


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APIPA 2009 90


Conduct planned audit procedures onlogical units

What if? Missing document consider to be a

misstatement


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APIPA 2009 91


Projected misstatement: Projection ofthe errors to the population

Upper limit on misstatement: Adds anallowance for sampling risk to theprojected misstatement


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APIPA 2009 92


Sort misstatements into two groups Group 1: Logical unit equal to or greater

than the sampling interval

Group 2: Logical unit less than the samplinginterval

For Group 2, compute the tainting factor

for each misstatement Tainting factor = Book value Audit value

Book value


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APIPA 2009 93


Place the Group 2 items in rank order bytainting factor (from largest to smallest)

Compute the projected misstatement

Calculate the upper limit increments (using theMonetary Un it Samp ling Conf idenceFacto rs for Sample Evaluat iontable)

Calculate upper misstatement for each Group2 item

Add differences for Group 1 Total = Upper misstatement limit


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APIPA 2009 94

STEP 6: CALCULATERESULTS - EXAMPLE

Book value = $3,100,000

Tolerable misstatement = $150,000

Expected misstatement = $25,000 Desired confidence level = 95%

Tolerable misstatement rate =4.8%,round to 5%

Expected misstatement rate = .8%, roundto 1%


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APIPA 2009 95


Sample size = 93

Sampling interval = $33,333

Expected misstatement = $25,000


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APIPA 2009 96


Item Book Value Audited Value Difference

Item 1 12,000 3,120 8,880

Item 2 35,000 32,000 3,000

Item 3 1,400 0 1,400

Item 4 45,200 41,000 4,200Item 5 740 555 185


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STEP 6: CALCULATE


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APIPA 2009 98

RESULTS - EXAMPLEItem Difference Book Value Tainting Factor

Group 2: BV < SI (33,333)

Item 1 8,880 12,000 .74

Item 3 1,400 1,400 1.0

Item 5 185 740 .25

STEP 6: CALCULATE


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APIPA 2009 99

RESULTS - EXAMPLEItem Tainting Factor Sampling

Interval

Projected

Misstatement

(Tainting

Factor * SI)

Item 3 1.0 33,333 33,333

Item 1 .74 33,333 24,666

Item 5 .25 33,333 8,333

STEP 6: CALCULATE


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APIPA 2009 100

RESULTS - EXAMPLEItem Projected

Misstatement

95% Upper

Limit

Increment

Upper

Misstatement

Item 3 33,333 3.0 99,999

Item 1 24,666 1.7 41,932

Item 5 8,333 1.5 12,500

154,431

STEP 6: CALCULATE


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APIPA 2009 101

RESULTS - EXAMPLEItem Projected

Misstatement

95% Upper

Limit

Increment

Upper

Misstatement

Group 2 154,431

Group 1 7,200

Upper Misstatement Limit 161,631

STEP 7: DRAW


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APIPA 2009 102

CONCLUSIONS If Upper Misstatement Limit > Tolerable

Misstatement, balance is materiallymisstated.

If Upper Misstatement Limit > TolerableMisstatement, balance is not materiallymisstated

IN-CLASS EXERCISES


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APIPA 2009 103

NO. 5 TO NO. 6


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IN-CLASS EXERCISE


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APIPA 2009 105

NO. 52. Sampling items always included:

The loans > the sampling intervalLoan #1 141,100

Loan #26 131,200

IN-CLASS EXERCISE


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APIPA 2009 106

NO. 6Recorded amount of accounts receivable =

$400,000

Tolerable misstatement: $20,000; 20,000 /

400,000 = 5% Risk of incorrect acceptance: 5%

Expected misstatements: 0

Sample size = 59

Sampling interval = 400,000 / 59 = 6,780

IN-CLASS EXERCISE


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APIPA 2009 107

NO. 6Error Recorded

Amount

Audit

Amount

Difference Tainting

%

1 400 320 80 20%

2 500 0 500 100%

3 7,000 6,500 500 NA

IN-CLASS EXERCISE


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APIPA 2009 108

NO. 6Error Tainting % Sampling

Interval

Projected

Misstate-

ment

Upper

Limit

Increment

Upper

Limit

Misstate-

ment

Logical unit BV < Sampling Interval

2 100 6,780 6,780 1.7 11,526

1 20 6,780 1,356 1.5 2,034


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IN-CLASS EXERCISE


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APIPA 2009 110

NO. 6Error Tainting % Sampling

Interval

Projected

Misstate-

ment

Upper

Limit

Increment

Upper

Limit

Misstate-

ment

Logical unit BV < Sampling Interval 13,560Logical unit BV > Sampling Interval 500

Basic Precision 20,340

Upper Misstatement Limit 34,400Conclusion: The account is materially misstated. The upper misstatement

limit of 34,400 exceeds the tolerable misstatement of 20,000.

NONSTATISTICAL SAMPLING


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APIPA 2009 111

BALANCE TESTING Differences in

Identifying individually significant items

Determining sample size Selecting sample items

Calculating sample results

IDENTIFYING INDIVIDUALLY


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APIPA 2009 112

SIGNIFICANT ITEMS Selected due to large size

Tested 100%

Results similar to PPS selection

For example, selecting all items >$100,000

DETERMINING SAMPLE


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APIPA 2009 113

SIZE Sample size =

Sampling Population BV * Assurance

(Tolerable Expected FactorMisstatement)

where Sampling Population BV excludesindividually significant items

DETERMINING SAMPLE


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APIPA 2009 114

SIZEAssessment

of RMM

Desired Level of Confidence Assurance Factors

Maximum Slightly below

maximum

Moderate Low

Maximum

3.0 2.7 2.3 2.0Slightly below

maximum2.7 2.4 2.0 1.6

Moderate 2.3 2.1 1.6 1.2

Low 2.0 1.6 1.2 1.0

DETERMINING SAMPLE


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APIPA 2009 115

SIZE - EXAMPLE Book value = $3,100,000 Individually significant items = $1,500,000 Tolerable misstatement = $150,000

Expected misstatement = $25,000 Desired confidence level = Maximum Risk of MM = Maximum Sample size = 1,600,000 * 3.0

(150,000 25,000)= 38.4, round to 39

SELECTING SAMPLE


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APIPA 2009 116

ITEMS Random selection

Systematic selection

Haphazard selection

CALCULATING SAMPLE


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APIPA 2009 117

RESULTS Sample misstatement MUST be

projected to population

Two acceptable methodsApply sample misstatement ratio to

population (ratio estimation)

Apply average misstatement $ of each item

in sample to all items in population(difference estimation)


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APIPA 2009 118

CLASSICAL SAMPLING Ratio estimation

Difference estimation


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APIPA 2009 120

DIFFERENCE ESTIMATION Sample misstatements = $19,000

# of sample items with misstatements = 5

Average misstatement per sample item =

$3,800 # items in population = 256

Projected misstatement = $3,800 * 256 =$972,800

Compare projected misstatement to tolerablemisstatement

IN-CLASS EXERCISE


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APIPA 2009 121

NO. 7

IN-CLASS EXERCISE


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APIPA 2009 122

NO. 7Nons tat ist ical Samp le Results : Errors in accounts > $10,000 33,000 Errors in accounts < $10,000: Total errors $ 4,350 Sample BV $81,500 Error rate 5.34% Applied to population: 2,760,000 (465,000) 2,295,000 * 5.34% 122,553 Total estimated error 155,553 Tolerable misstatement 81,500 Conclusion: Account materially misstated

IN-CLASS EXERCISE


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APIPA 2009 123

NO. 7 - PPSPPS Sample Results:

Accounts receivable recorded

balance: $2,760,000

Accounts > $10,000 (tested

separately) (465,000)

Accounts receivable population

PPS $2,295,000

Tolerable misstatement $ 81,500

IN-CLASS EXERCISE


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APIPA 2009 124

NO. 7 - PPSSample and sampling interval:

Tolerable rate: 81,500 / 2,295,000 = 3.55%,round to 4%

Expected rate: 0

5% risk of overreliance (since IR and CR areboth high)

Sample size: 74Sampling interval: 2,295,000 / 74 = 31,014

IN-CLASS EXERCISE


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APIPA 2009 125

NO. 7 - PPSRecorded

ValueAudited

ValueDifference Tainting %

Item 12 5,120 4,820 300 5.85

Item 19 485 385 100 20.6Item 33 1,250 250 1,000 80

Item 35 3,975 3,875 100 25.2

Item 51 1,850 1,825 25 1.4

Item 59 4,200 3,780 420 10

Item 74 2,405 0 2,405 100

IN-CLASS EXERCISE


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APIPA 2009 126

NO. 7 - PPS# of Overstatement

Misstatements5% Upper Limit Increment

0 3.00

1 4.75 1.75

2 6.30 1.55

3 7.76 1.46

4

9.16

1.40

5 10.52 1.36

6 11.85 1.33

7 13.15 1.30

IN-CLASS EXERCISE


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APIPA 2009 127

NO. 7 - PPSTainting

%Sampling

IntervalProjected

MisstatementUpper Limit

FactorUpper

Misstatement

Item 74 100 31,014 31,014 1.75 54,275

Item 33 80 31,014 24,811 1.55 38,457

Item 35 25.2 31,014 7,816 1.46 11,411

Item 19 20.6 31,014 6,389 1.40 8,944

Item 59 10 31,014 3,101 1.36 4,218

Item 12 5.85 31,014 1,814 1.33 2,413

Item 51 1.4 31,014 434 1.30 564

120,282

IN-CLASS EXERCISE


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APIPA 2009 128

NO. 7 - PPS Items < Sampling Interval: 120,282

Items > Sampling Interval: None

Basic precision: 3.0 * 31,014 = 93,042

Upper misstatement limit = 213,324

Conclusion: Account is materially misstated.Upper misstatement limit 213,324 > tolerable

misstatement 81,500


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APIPA 2009 129

RESOURCES Audit Sampling: An Introduction, 3rd

Edition, Guy, Carmichael & Whittington

Audit Guide: Audit Sampling, New Edition

as of May 1, 2008, AICPA Auditing & Assurance Services, 6th

Edition, Messier, Glover, & Prawitt

Auditing & Assurance Services, 12thEdition, Arens, Elder & Beasley


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statistical sampling for auditors

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