Substantive Tests of Details of Account Balances

Chapter 9 Chapter 9 Audit Sampling: An Application to Substantive Tests of McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Account Balances LO# 1 Substantive Tests of Details of Account Balances The statistical concepts we discussed in the last The statistical concepts we discussed in the last

  chapter apply to this chapter as well. Three important chapter apply to this chapter as well. Three important determinants of sample size are determinants of sample size are

  1. Desired confidence level.

  1. Desired confidence level.

  2 T l Tolerable misstatement. T l bl bl i i t t t t t t 3.

  2

  2.

  2. Tolerable misstatement.

  3. Estimated misstatement. Estimated misstatement.

  Population plays a bigger role in some of the sampling Population plays a bigger role in some of the sampling techniques used for substantive testing. techniques used for substantive testing. Misstatements discovered in the audit sample must be Misstatements discovered in the audit sample must be projected to the population, and there must be an projected to the population, and there must be an allowance for sampling risk. allowance for sampling risk. _9-2

  LO# 1 Substantive Tests of Details of Account Balances

  Consider the following information about the inventory account balance of an audit client:

  Book value of inventory account balance $ 3,000,000 Book value of items sampled $ 100,000 Audited value of items sampled A dit d l f it l d 98,000 98 000 Total amount of overstatement observed in audit sample $ 2,000

The ratio of misstatement in the sample is 2% The ratio of misstatement in the sample is 2% ($2,000 ÷ ($2,000 ÷ $100,000) $100,000)

  Applying the ratio to the entire population produces a best estimate of misstatement of inventory of $60,000.

  ($3,000,000 × 2%) Substantive Tests of Details of Account Balances The results of our audit test depend upon The results of our audit test depend upon the tolerable misstatement associated the tolerable misstatement associated with the inventory account. If the tolerable with the inventory account. If the tolerable misstatement is $50 000 we cannot misstatement is $50 000 we cannot

  9-4 misstatement is $50,000, we cannot misstatement is $50,000, we cannot conclude that the account is fairly stated conclude that the account is fairly stated because our best estimate of the because our best estimate of the projected misstatement is greater than projected misstatement is greater than the tolerable misstatement. the tolerable misstatement.

  Monetary-Unit Sampling (MUS) MUS uses attribute MUS uses attribute--sampling theory to sampling theory to express a conclusion in dollar amounts rather express a conclusion in dollar amounts rather than as a rate of occurrence. It is commonly than as a rate of occurrence. It is commonly used by auditors to test accounts such as used by auditors to test accounts such as ^{LO# 2}

  9-5 accounts receivable accounts receivable , , loans receivable loans receivable , , investment securities investment securities , and , and inventory inventory . .

Monetary-Unit Sampling (MUS)

  MUS uses attribute MUS uses attribute--sampling theory (used sampling theory (used primarily to test controls) to estimate the primarily to test controls) to estimate the percentage of monetary units in a population percentage of monetary units in a population that might be misstated and then multiplies that might be misstated and then multiplies ^{LO# 2} g p g p this percentage by an estimate of how much this percentage by an estimate of how much the dollars are misstated. the dollars are misstated. Monetary-Unit Sampling (MUS)

Advantages of MUS Advantages of MUS

  1. When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical usually results in a smaller sample size than classical variables sampling. variables sampling.

  1. When the auditor expects no misstatement, MUS

  2 Th Th The calculation of the sample size and evaluation of l l l i l i f h f h l l i i d d l l i i f f the sample results are not based on the variation the sample results are not based on the variation between items in the population. between items in the population.

  2. The calculation of the sample size and evaluation of

  2

  2.

  3. When applied using the probability procedure, MUS automatically results in a stratified procedure, MUS automatically results in a stratified sample. sample. _9-7

  3. When applied using the probability--proportional proportional--to to--size size

  LO# 2 Monetary-Unit Sampling (MUS)

Disadvantages of MUS Disadvantages of MUS

  1. The selection of zero or negative balances generally

  1. The selection of zero or negative balances generally requires special design consideration. requires special design consideration.

  2 2.

  2. The general approach to MUS assumes that the The general approach to MUS assumes that the The general approach to MUS assumes that the audited amount of the sample item is not in error by audited amount of the sample item is not in error by more than 100%. more than 100%.

  2 The general approach to MUS assumes that the

  3. When more than one or two misstatements are detected, the sample results calculations may detected, the sample results calculations may overstate the allowance for sampling risk. overstate the allowance for sampling risk. _9-8

  3. When more than one or two misstatements are

  LO# 2 Steps in MUS Sampling

  Steps in MUS Sampling Application Planning 1. Determine the test objectives.

  2. Define the population characteristics. • Define the population. • Define the sample unit. • Define a misstatement.

  3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable misstatement. • The expected population misstatement. • Population size. Performance 4. Select sample items.

  5. Perform the auditing procedures. • Understand an alayzye any missstatements observed. Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement.

  7. Draw final conclusions.

  Steps in MUS Sampling Steps in MUS Sampling Application Planning 1. Determine the test objectives.

  2. Define the population characteristics. • Define the population. • Define the sample unit. • Define a misstatement.

  Sampling may be used for substantive testing to:

  1. Test the reasonableness of assertions about a financial statement amount (i.e., is the amount fairly stated). This is the most common use of sampling for substantive testing.

  2. Develop an estimate of some amount. _9-10

  LO# 2 Steps in MUS Sampling

  Steps in MUS Sampling Application Planning 1. Determine the test objectives.

  2. Define the population characteristics. • Define the population. • Define the sample unit. • Define a misstatement.

  For MUS the population is defined as the monetary value of an account balance, such as accounts receivable, investment securities, or inventory. _9-11

  LO# 2 Steps in MUS Sampling

  Steps in MUS Sampling Application Planning 1. Determine the test objectives.

  2. Define the population characteristics. • Define the population. • Define the sample unit. • Define a misstatement.

  An individual dollar represents the sampling unit.

  Steps in MUS Sampling Steps in MUS Sampling Application Planning 1. Determine the test objectives.

  2. Define the population characteristics. • Define the population. • Define the sample unit. • Define a misstatement. • Define a misstatement

  A misstatement is defined as the difference between monetary amounts in the client’s records and amounts supported by audit evidence. _9-13

  LO# 2 Steps in MUS Sampling

  Steps in MUS Sampling Application

  3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. • The tolerable misstatement. • The expected population misstatement. • Population size. Relationship Change Effect on Factor to Sample Size in Factor Sample Lower Decrease Desired confidence level Direct Higher Increase Lower Increase Tolerable mistatement Inverse Higher Decrease Lower Decrease Expected mistatement Direct Higher Increase Lower Decrease Population size Direct Higher Increase _9-14 LO# 2

  Steps in MUS Sampling Steps in MUS Sampling Application Performance 4. Select sample items.

  5. Perform the auditing procedures. Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement.

  7 Draw final conclusions

  7. Draw final conclusions.

  The auditor selects a sample for MUS by using a systematic selection approach called probability- proportional-to-size selection. The sampling interval can be determined by dividing the book value of the population by the sample size. Each individual dollar in the population has an equal chance of being selected and items or “logical units” greater than the interval will

  Steps in MUS Sampling Assume a client’s book value of accounts receivable is $2,500,000, and the auditor determined a sample size of 93. The sampling interval will be

  $26,882 ($2,500,000 ÷ 93). The random number selected is $3,977 the _{1005 Jen Mara Corp. 3,968 44,641 Account Balance Dollars Item 1002 Admington Hospital 15,495 17,845 $ 3,977 (1) 1006 Zippy Corp. 32,549 77,190 57,741 (3) 1004 Good Hospital Corp. 21,893 40,673 30,859 (2) 1003 Jess Base, Inc. 945 18,780 1001 Ace Emergency Center 1001 Ace Emergency Center $ $ 2,350 2,350 $ $ 2,350 2,350} auditor would select the following items for testing: _{Cumulatvie Sample $ 30,859 $ 3,977 26,882 1008 Bead Hospital Centers 11,860 91,306 84,623 (4)} 1007 Green River Mfg. 2,246 79,436 _{Total Accounts Receivable $ 2,500,000 1215 Janyne Ann Corp. 1,023 $ 2,500,000 1214 Lilly Heather, Inc. 26,945 2,498,977 2,477,121 (93) • • • • • • • • - 1213 Andrew Call Medical 2,472,032 9-16} LO# 3

  Steps in MUS Sampling Steps in MUS Sampling Application Performance 4. Select sample items.

  5. Perform the auditing procedures. Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement.

  7 D fi l l i

  7. Draw final conclusions.

  After the sample items have been selected, the auditor conducts the planned audit procedures on the logical units containing the selected dollar sampling units. _9-17

  LO# 3 Steps in MUS Sampling

  Steps in MUS Sampling Application Evaluation 6. Calculate the projected misstatement and the upper limit on misstatement.

  7. Draw final conclusions.

  The misstatements detected in the sample must be projected to the population. t b j t d t th l ti

  Example Information Book value $ 2,500,000 Tolerable misstatement $ 125,000 Sample size Steps in MUS Sampling Basic Precision using the Tables Basic Precision using the Tables

  If no misstatements are found in the sample, the best estimate of the population misstatement would be zero dollars .

  7.6 125

  9.5

  90

  3.3

  5.2

  6.9

  8.4 100

  3.0

  4.7

  6.2

  2.4

  5.8

  3.8

  5.0

  6.1 $26,882 $26,882 × × 3.0 = 3.0 = $80,646 $80,646 upper misstatement limit upper misstatement limit

  Steps in MUS Sampling Misstatements Detected Misstatements Detected

  In the sample of 93 items, the following misstatements were found: _{Customer Book Value Audit Value Difference Tainting Factory Good Hospital 21,893 $ 18,609 $ 3,284 $ 15% M M di l S l 6 705 4 023 2 682 40%} ^{LO# 3}

  9-20 ^{Marva Medical Supply 6,705 4,023 2,682 40% Axa Corp. 32,549 30,049 2,500 NA Learn Heart Centers 15,000 - 15,000 100%} $3,284 $3,284 ÷ ÷ $21,893 = 15% $21,893 = 15%

  Because the Axa balance of $32,549 is greater than the interval of $26,882 , no sampling risk is added. Since all the dollars in the large accounts are audited, there is no sampling risk associated with large accounts.

  Steps in MUS Sampling Computed Upper Misstatement Limit using Tables Computed Upper Misstatement Limit using Tables

  We compute the upper misstatement limit by calculating basic precision and ranking the detected misstatements based on the size of the tainting factor from the largest to the smallest.

  Tainting Sample Projected 95% Upper Upper ^{LO# 3} Customer Tainting Factor Sample Interval Projected Misstatement 95% Upper Limit Upper Misstatement Basic Precision 1.00 26,882 $ NA 3.0 80,646 $ Learn Heart Centers 1.00 26,882 (26,882) 1.7 (4.7 - 3.0) 45,700 Marva Medical 0.40 26,882 (10,753) 1.5 (6.2 - 4.7) 16,130 Good Hospital 0.15 26,882 (4,032) 1.4 (7.6 - 6.2) 5,645 Add misstatments greater that the sampling interval: Axa Corp. NA 26,882 NA 2,500 Upper Misstatement Limit 150,621 $

  7.7

  3.7

  Sample Size

  9.4

  1

  2

  Size 3 Actual Number of Deviations Found 9-19

  1

  2

  3

  65

  4.6

  7.1

  11.5

  80

  70

  4.2

  6.6

  8.8

  10.8

  85

  4.0

  6.2

  8.2

  10.1

  (0.15 (0.15 × × $26,882 $26,882 × × 1.4 = $5,645) 1.4 = $5,645) Steps in MUS Sampling Steps in MUS Sampling Application Evaluation

  In our example, the final decision is whether the accounts receivable balance whether the accounts receivable balance is materially misstated or not.

  We compare the tolerable misstatement to the upper We compare the tolerable misstatement to the upper misstatement limit. If the upper misstatement limit is misstatement limit. If the upper misstatement limit is less less than or equal to than or equal to the tolerable misstatement, we conclude the tolerable misstatement, we conclude that the balance is that the balance is not materially misstated not materially misstated . . _9-22

  LO# 3

Steps in MUS Sampling

  In our example, the upper misstatement limit of $150,621 is greater than the tolerable misstatement of $125,000 , so the auditor concludes that the accounts receivable balance is materially misstated.

  When faced with this situation, the auditor may: When faced with this situation, the auditor may: , , y y 1. Increase the sample size.

  1. Increase the sample size.

  2. Perform other substantive procedures.

  2. Perform other substantive procedures.

  3. Request the client adjust the accounts receivable balance.

  3. Request the client adjust the accounts receivable balance.

  4. If the client refuses to adjust the account balance, the auditor would consider issuing a qualified or adverse auditor would consider issuing a qualified or adverse opinion. opinion. _9-23

  4. If the client refuses to adjust the account balance, the

  LO# 3 Risk When Evaluating Account Balances

  True State of Financial Statement Account Auditor's Decision Based on Sample Evidence Not Materially Misstated Materially Misstated Supports the fairness of Risk of incorrect Correct decision the account balance acceptance (Type II) Does not support the D t t th fairness of the account Risk of incorrect Correct Decision balance rejection (Type I) Why is the Sampling Interval Rather than the Sample Size Used in Evaluating MUS Results?

  Due to simplifying assumptions about accounting populations, the misstatement factors used in most MUS evaluation approaches are nearly identical to the misstatement factors associated with a sample size of 100, regardless of the actual l i d b th dit Al th f t

  3

  The sampling unit for nonstatistical sampling is normally a customer account, an individual transaction, or a line item on a transactions. When using nonstatistical sampling, the following items must be considered: ^{LO# 4} o o Identifying individually significant items. Identifying individually significant items.

  The most likely error will be reduced by The most likely error will be reduced by $2,688 $2,688 ((– – 0.10 0.10 × × $26,882) $26,882) Nonstatistical Sampling for Tests of Account Balances

  C t Book V l Audit V l Diff Tainting F t ^{LO# 3} 9-26 Customer Value Value Difference Factor Wayne County Medical 2,000 $ 2,200 $ (200) $ -10%

  MUS is not particularly effective at detecting understatements. An understated account is less likely to be selected than an overstated account.

  1.3 95% Confidence Level 90% Confidence Level Effect of Understatement Misstatements

  7.9

  1.4

  9.0

  4

  1.3

  6.6

  1.4

  7.6

  1.4

  9-25

  5.3

  1.5

  6.2

  2

  1.6

  3.9

  1.7

  4.7

  1

  2.3

  3.0

  Number of Misstatement Incremental Misstatement Incremental Errors Factor Increase Factor Increase

  sample size used by the auditor. Always use these factors:

  o o Determining the sample size. Determining the sample size. o o Selecting sample items. Selecting sample items. o o Calculating the sample results. Calculating the sample results. Identifying Individually Significant Items The items to be tested individually are items that may contain potential misstatements that individually exceed the tolerable misstatement. These items are tested 100% because the auditor is not willing to accept any li i k

  9-28 sampling risk.

  2.0

  Auditing standards require that the sample items be selected in such a way that the sample can be expected to represent the population. ^{LO# 4}

  1.0 Desired Level of Confidence

  1.2

  1.6

  2.0

  1.2 Low

  1.6

  2.1

  2.3

  1.6 Moderate

  2.4

  Determining the Sample Size

  2.7

  2.0 Slightly below maximum

  2.3

  2.7

  3.0

  9-29 Assessment of Risk of Slightly Below Material Misstatement Maximum Maximum Moderate Low Maximum

  × Assurance factor ^{LO# 4}

  Sampling Population book value Tolerable – Expected misstatement

  =

  Sample Size

Selecting Sample Items

  Calculating the Sample Results

  One way of projecting the sampling results to the population is to apply the misstatement ratio in the sample to the population.

  Assume the auditor Assume the auditor Assume the auditor Assume the auditor If the population If the population If the population If the population finds $1,500 in finds $1,500 in total is $200,000, total is $200,000, misstatements in a misstatements in a the projected the projected sample of $15,000. sample of $15,000. misstatement would misstatement would The misstatement The misstatement be $20,000 be $20,000 ratio is 10%. ratio is 10%. ($200,000 ($200,000 × × 10%) 10%) _9-31

  LO# 4 Calculating the Sample Results

  A second method is the difference estimation . This method projects the average misstatement of each item in the sample to all items in the population.

  Assume Assume Assume Assume misstatements in a misstatements in a The projected The projected sample of 100 items sample of 100 items misstatement would be misstatement would be total $300 (for total $300 (for $30,000 ($3 $30,000 ( $3 × × 10,000). 10,000). average average misstatement of $3), misstatement of $3), and the population and the population contains 10,000 contains 10,000 items. items. _9-32

  LO# 4 Nonstatistical Sampling Example

  The auditor’s of Calabro Wireless Service have decided to use nonstatistical sampling to examine the accounts receivable balance. Calabro has a total of

  11,800 (15 + 250 + 11,535) accounts with a

  balance of balance of $3 717 900 $3,717,900 . The auditor s stratify the The auditor’s stratify the accounts as follows:

  Number and Size Book of Accounts Value 15 accounts > $25,000 $ 550,000 250 accounts > $3,000 850,500 11,535 accounts < $3,000 2,317,400 Total $ 3,717,900 Nonstatistical Sampling Example The auditor’s decide . . . The auditor’s decide . . . o o There is a low assessment for inherent and control risk. There is a low assessment for inherent and control risk. o o The tolerable misstatement is $40,000, and the expected The tolerable misstatement is $40,000, and the expected misstatement is $15 000 misstatement is $15 000

  9-34 misstatement is $15,000. misstatement is $15,000. o o There is a moderate risk that other auditing procedures There is a moderate risk that other auditing procedures will fail to detect material misstatements. will fail to detect material misstatements. o o All customer account balances greater than $25,000 are All customer account balances greater than $25,000 are to be audited. to be audited.

  Nonstatistical Sampling Example

  Sample Size

  =

  Sampling population book value Tolerable - Estimated misstatement

  × Assurance factor

  $3,717,900 $3,717,900 – – $550,000 $550,000 ^{LO# 4} 9-35

  Sample Size

  = $3,167,900

  $40,000 × 1.2 =

  _{Combined Assessment of Slightly Below} 95 95 (rounded) _{Inherent and Control Risk Maximum Maximum Moderate Low Maximum 3.0 2.7 2.3 2.0 Slightly below maximum 2.7 2.4 2.0 1.6} Moderate ^{2.3 2.1 1.6 1.2} _{Low 2.0 1.6 1.2 1.0} ^{Risk That Other Substantive Procedures Fail to Detect Material Misstatement} $ , , $ , , $ , $ , $55,000 $55,000 – – $15,000 $15,000

  Nonstatistical Sampling Example

  The auditor sent positive confirmations to each of the 110 (95 + 15) accounts selected. Either the confirmations were returned or alternative procedures were successfully used. Four customers indicated that their accounts were overstated and the auditors determined that the ^{LO# 4}

  Amount of Book Value Audit Value Over- Stratum Book Value of Sample of Sample Statement >$25,000 550,000 $ 550,000 $ 549,500 $ 500 $ >$3,000 850,500 425,000 423,000 2,000 <$3,000 2,317,400 92,000 91,750 250

  misstatements were the result of unintentional error by client personnel. Here are the results of the audit testing:

  Nonstatistical Sampling Example

  As a result of the audit procedures, the following projected misstatement was prepared:

  Amount of Ratio of Misstatement Projected Stratum Misstatement in Stratum Tested Misstatement >$25,000 $ 500 Not Applicable--100% Tested $ 500 >$3,000 2,000 $2,000 ÷ 425,000 × $850,500 4,002 <$3,000 250 $250 ÷ 92,000 × $2,317,400 6,298 Total projected misstatement $ 10,800

  The total projected misstatement of $10,800 is less than The total projected misstatement of $10,800 is less than the expected misstatement of $15,000, so the auditors the expected misstatement of $15,000, so the auditors may conclude that there is an acceptably may conclude that there is an acceptably low risk low risk that that the true misstatement exceeds the tolerable the true misstatement exceeds the tolerable misstatement. misstatement. _9-37

  LO# 4 Why Did Statistical Sampling Fall Out Of Favor?

  1.Firms found that some auditors were over relying on statistical sampling techniques to the exclusion of good judgment. judgment

  2.There appears to be poor linkage between the applied audit setting and traditional statistical sampling applications. _9-38

  LO# 5 Classical Variable Sampling

  Classical variables sampling uses normal distribution theory to evaluate the characteristics of a population based on sample data. Auditors most commonly use classical variables sampling to estimate the size of misstatement. misstatement

  Sampling distributions are formed by plotting the Sampling distributions are formed by plotting the projected misstatements yielded by an infinite projected misstatements yielded by an infinite number of audit samples of the same size taken number of audit samples of the same size taken from the same underlying population. from the same underlying population. Classical Variables Sampling

  A sampling distribution is useful because it allows us to estimate the probability of observing any single

  sample result . _9-40 LO# 5

  Classical Variables Sampling

  In classical variables sampling, the sample mean is the of the population mean.

  best estimate _9-41 LO# 5

  Classical Variables Sampling

Advantages Advantages

  1. When the auditor expects a large number of differences between book and audited values, this differences between book and audited values, this method will result in smaller sample size than method will result in smaller sample size than MUS. MUS.

  1. When the auditor expects a large number of

  2. The techniques are effective for both overstatements and understatements. overstatements and understatements.

  2. The techniques are effective for both

  3. The selection of zero balances generally does not require special sample design considerations. require special sample design considerations.

  3. The selection of zero balances generally does not Classical Variables Sampling

Disadvantages Disadvantages

  1. Does not work well when little or not misstatement is expected in the population. is expected in the population.

  1. Does not work well when little or not misstatement

  2. To determine sample size, the auditor must To determine sample size, the auditor must To determine sample size the auditor must estimate the standard deviation of the audited estimate the standard deviation of the audited value or differences. value or differences.

  2 2.

  2 To determine sample size the auditor must

  3. If few misstatements are detected in the sample data, the true variance tends to be data, the true variance tends to be underestimated, and the resulting projection of the underestimated, and the resulting projection of the misstatements to the population is likely not to be misstatements to the population is likely not to be reliable. reliable. _9-43

  3. If few misstatements are detected in the sample

  LO# 6 Applying Classical Variables Sampling

  Defining the Sampling Unit

  The sampling unit can be a customer account, an individual transaction, or a line item. In auditing accounts receivable, the auditor can auditing accounts receivable, the auditor can define the sampling unit to be a customer’s account balance or an individual sales invoice included in the account balance.

  9-44 LO# 6 Applying Classical Variables Sampling

Determining the Sample Size

  2 Population size (in sampling units) × CC × SD Sample

  = Size Tolerable misstatement – Estimated misstatement

  where

  CC = Confidence coefficient SD = Estimated standard deviation.

  Applying Classical Variables Sampling

  The Confidence Coefficient (CC) is associated with the desired level of confidence. The desired level of confidence is the complement of the risk that the auditor will mistakenly accept a population as fairly stated when the true population misstatement is greater than tolerable misstatement misstatement is greater than tolerable misstatement.

   Desired Level of Confidence CC Value 95.0%

  1.96 90.0%

  1.65 80.0%

  1.28 70.0%

  1.04 _9-46 LO# 6

  Applying Classical Variables Sampling

  The year-end balance for accounts receivable contains 5,500 accounts with a book value of $5,500,000. The tolerable misstatement for accounts receivable is set at $50,000. The expected misstatement has been judged to be $20,000. The desired confidence is 95%. Based on work completed last year, the auditor estimates the standard deviation at $31. th dit ti t th t d d d i ti t $31 Let’s L t’

  calculate sample size .

  = = 125 125 Size

  $50,000 – $20,000 _9-47

  LO# 6 Applying Classical Variables Sampling

Calculating the Sample Results

  The sample selection usually relies on random-selection techniques. Upon completion, 30 of the customer accounts selected contained misstatements that totaled $330 20 contained misstatements that totaled $330.20. Our first calculation is the mean misstatement in an individual account which is calculated as follows:

  Mean Total audit difference misstatement

  = Sample size per sampling item

  $330.20

  $2.65 $2.65 =

  125 Applying Classical Variables Sampling The mean misstatement must be projected to the population

  Projected Population size × Mean misstatement population = p p

  (i (in sampling units) li it )

  per sampling item li it misstatement

  $14,575 $14,575 = 5,500 × $2.65 _9-49 LO# 6

  Applying Classical Variables Sampling The formula for the standard deviation is . . .

  Sample Mean difference Total audit

  × ²

• – Size per sampling item

  SD = differences squared

  Sample size – 1

  2

  = $36,018.32 – (125 × 2.65 )

  = $16.83 $16.83 124 _9-50

  LO# 6 Applying Classical Variables Sampling

  SD Confidence Population

  = × ×

  CC bound size Sample size

  16.83

  $16,228 $16,228

  = 5,500 × 1.96 × 125

  √ Confidence Projected Confidence

  =

  ± interval misstatement bound

  = $14,575 ± = $14,575 ± $16,228 $16,228 Applying Classical Variables Sampling Lower limit

  ($1,653) Projected misstatement

  $14,575 Upper limit

  $30,803 9-52

  If both limits are within the bounds of tolerable misstatement, the evidence supports the conclusion that the account is not materially misstated.

  ($50,000) $50,000 $0

  Tolerable Misstatement

  End of Chapter 9 9-53