Sampling Techniques Flashcards
A principal advantage of statistical methods of attribute sampling over nonstatistical methods is that they provide a scientific basis for planning the
A. Risk of assessing control risk too low
B. Expected population deviation rate
C. Tolerable rate
D. Sample size
D.
The principal advantage of statistical over nonstatistical sampling methods is that statistical methods provide a model for determining sample size while explicitly recognizing relevant factors (e.g. risk of assessing control risk too low, tolerable rate, and expected deviation rate). In nonstatistical sampling, the auditor implicitly recognizes the relevant factors while determining the sample size based on his or her own judgment and experience.
An advantage of statistical sampling over nonstatistical sampling is that statistical sampling helps an auditor to
A. Eliminate the risk of nonsampling errors
B. Reduce the level of audit risk and materiality to a relatively low amount
C. Measure the sufficiency of the audit evidence obtained
D. Minimize the failure to detect errors and fraud
C.
Both statistical and nonstatistical sampling plans can provide sufficient audit evidence if properly applied. The distinguishing feature of statistical sampling methods as opposed to nonstatistical methods is that the user is able to provide a mathematical measurement of the degree of uncertainty that results from examining only part of a population. Statistical sampling, as well as nonstatistical sampling, is subject to nonsampling errors (procedural mistakes or human error). Both methods of sampling may be used to reduce audit risk, but neither would affect the level of materiality. Both can be used to reduce the risk of failing to detect errors and fraud, which is the risk of incorrect acceptance.
An auditor desired to test credit approval on 10,000 sales invoices processed during the year. The auditor designed a statistical sample that would provide 1% risk of assessing control risk too low (99% confidence) that not more than 7% of the sales invoices lacked approval. The auditor estimated from previous experience that about 2.5% of the sales invoices lacked approval. A sample of 200 invoices was examined and 7 of them were lacking approval. The auditor then determined the achieved upper precision limit to be 8%. The allowance for sampling risk was:
A. 5.5%
B. 4.5%
C. 3.5%
D. 1.0%
B.
The allowance for sampling risk is the difference between the observed sample rate and the achieved upper precision limit. The observed sample rate was 7/200 = 3.5%. Therefore, the allowance for sampling risk is 4.5% ( 8% - 3.5%).
An auditor established a $60,000 tolerable misstatement for an asset with an account balance of $1,000,000. The auditor selected a sample of every twentieth item from the population that represented the asset account balance and discovered overstatements of $3,700 and understatements of $200. Under these circumstances, the auditor most likely would conclude that
A. There is an unacceptably high risk that the actual misstatements in the population exceed the tolerable misstatement because the total projected misstatement is more than the tolerable misstatement.
B. There is an unacceptably high risk that the tolerable misstatement exceeds the sum of actual overstatements and understatements.
C. The asset account is fairly stated because the total projected misstatement is less than the tolerable misstatement.
D. The asset account is fairly stated because the tolerable misstatement exceeds the net of projected actual overstatements and understatements.
A.
The net of projected actual misstatements [($3,700 - $200) x 20 =] is $70,000, which is larger than the tolerable misstatement of $60,000. If the tolerable misstatement exceeds the sum of actual overstatements and understatements, the auditor may consider the account fairly stated.
An auditor examining inventory most likely would use variables sampling rather than attributes sampling to
A. Identify whether inventory items are properly priced
B. Estimate whether the dollar amount of inventory is reasonable
C. Discover whether misstatements exist in inventory records
D. Determine whether discounts for inventory are properly recorded
B.
Generally, variables sampling involves the determining of proper dollar value of the sampled items and makes inferences about the fairness of the amounts reported in the financial statements. Variables sampling typically involves deciding whether the dollar value of an account is reasonable. Generally, attributes sampling involves the determination of the rate of occurrence of some characteristic in a population. Proper prices, the number of misstatements, or proper recording are attributes. The other answer choices seem to test whether an outcome of a section of inventory is correct or not.
An auditor is determining the sample size for an inventory observation using mean-per-unit estimation, which is a variables sampling plan. To calculate the required sample size, the auditor usually determines the
Variability in the dollar amounts of inventory items
Risk of incorrect acceptance
A. Yes Yes
B. Yes No
C. No Yes
D. No No
A.
With the mean-per-unit method, stratification of a highly variable population into segments allows an auditor to use a smaller sample size. Thus, variability in the dollar amounts of inventory items is considered. The risk of incorrect assessment has an inverse relationship with sample size.
An auditor is planning a test of control and expects numerous errors in the application of the control. Which approach is most appropriate?
A. Discovery Sampling
B. Sequential Sampling
C. Dual-Purpose Sampling
D. Variables Sampling
B.
If an auditor is planning a test of control and expects numerous errors in the application of the control then the sample size will need to be expanded through sequential, stop or go sampling–each step is conditional on the results of the previous steps. Discovery sampling is used when the auditor expects an extremely low error rate. Dual purpose sampling is used to test attributes and variable simulataneously; usually when a low error rate is expected for the application of the control. Variables sampling is concerned with the details of transactions and account balances (substantive tests) rather than a test of controls.
An auditor is selecting vouchers for testing an entity’s internal control activities related to the proper approval of vouchers before checks are prepared. The auditor is matching random numbers with voucher numbers to determine which vouchers to inspect. If a random number matches a voided voucher, that voucher ordinarily would be replaced by another voucher in the random sample if the voided voucher
A. Cannot be located in the voucher file
B. Represents a dollar amount that is material
C. Indicates a deviation from the prescribed activity
D. Has been properly voided
D.
In an auditor’s test of transactions, if a random number matches the number of a voided voucher, that voucher ordinarily should be replaced by another voucher in the random sample if the voucher has been properly voided. The voucher would be counted as an error and would not be replaced if it could not be located or constituted a deviation. The materiality of the dollar amount is irrelevant because the focus in a test of controls is whether or not procedures are properly performed, not the dollar value of the transaction being tested.
An auditor may decide to increase the risk of incorrect rejection when
A. Increased reliability from the sample is desired.
B. Many differences (audit value minus recorded value) are expected.
C. Initial sample results do not support the planned level of control risk.
D. The cost and effort of selecting additional sample items is low.
D.
The risk of incorrect rejection is the risk that the sample supports the conclusion that the recorded account balance is materially misstated when, in fact, it is not materially misstated. Thus, the risk of incorrect rejection relates to the efficiency of the audit. If the auditor’s evaluation of the audit sample leads him to the initial erroneous conclusion that a balance is materially misstated when it is not, the application of additional audit procedures and consideration of other audit evidence would ordinarily lead the auditor to the correct conclusion. The cost of this mistake is the cost of the additional procedures necessary to discover that the original conclusion was erroneous. If however, the cost and effort of those additional procedures is low, the auditor may well decide to use a high risk of incorrect rejection because doing so will reduce original sample size. If the desired results are achieved with the original small sample, overall audit cost will be lowered. If an incorrect rejection occurs, however, the incremental cost incurred would not be excessive. An increase in the desired reliability would likely result in a decrease (not increase) in the risk of incorrect rejection. The number of differences expected should have no bearing on the risk of incorrect rejection specified. The ‘risk of incorrect rejection’ is not a concept associated with test of controls. ‘Risk of underreliance’ would be the corresponding risk that is associated with control testing.
An auditor may use a systematic sampling technique with a start at any randomly selected item when performing a test of controls with respect to control over cash receipts. The biggest disadvantage of this type of sampling is that the items in the population
A. Must be systematically replaced in the population after sampling
B. May occur in a systematic pattern, thus destroying the sample randomness
C. Must be recorded in a systematic pattern before the sample can be drawn
D. May systematically occur more than once in the sample
B.
When using the systematic sampling technique, the auditor determines a uniform interval by dividing the number of physical units in the population by the sample size. A random number is selected as a starting point for the first interval, and one item is selected throughout the population at each of the uniform intervals from the starting point. The randomness of the sample can be destroyed if the items in the population occur in a systematic pattern. For example, a population of employees on a payroll for a construction company might be organized by teams; each team consists of a crew leader and nine other workers. A selection of every tenth employee will either list every crew leader or no crew leaders, depending on the random start. No combination would include both crew leaders and other employees.
An auditor randomly samples 50 out of 1,000 items and discovers an overstatement of $3,000. What is the projected misstatement for the entire population?
A. $150,000
B. $120,000
C. $60,000
D. $48,000
The correct answer is (C).
Actual misstatement in a sample = $3,000.
Projected Misstatement = Actual Misstatement * Population Size / Sample Size = 3,000 * 1000 / 50 = $60,000. For the account to be misstated, the projected misstatement should be more than the tolerable misstatement.
So if the tolerable misstatement is below $60,000, the account is misstated.
An auditor should consider the tolerable rate of deviation when determining the number of check requests to select for a test to obtain assurance that all check requests have been properly authorized. The auditor should also consider
The average dollar value of the check requests
The allowable risk of assessing control risk too low
A. Yes Yes
B. Yes No
C. No Yes
D. No No
C
Check authorization is an internal control. In tests of internal controls, the auditor is determining the rate of occurrence of a deviation from the control procedure, not testing the dollar amounts reported in the financial statements. The allowable risk of assessing control risk too low affects the degree of assurance desired by the auditor. If a high degree of assurance is sought, sampling risk must be low. Sample size and risk are inversely related.
An auditor who uses statistical sampling for attributes in testing internal controls should reduce the planned reliance on a prescribed control when the
A. Sample rate of deviation plus the allowance for sampling risk equals the tolerable rate.
B. Sample rate of deviation is less than the expected rate of deviation used in planning the sample.
C. Tolerable rate less the allowance for sampling risk exceeds the sample rate of deviation.
D. Sample rate of deviation plus the allowance for sampling risk exceeds the tolerable rate.
D.
When the sample rate of deviation plus the allowance for sampling risk, which is the upper deviation limit, exceeds the tolerable rate, the sample results do not support the assessed level of control risk, and the auditor should reduce the planned reliance on a prescribed control. Answers (a), (b), and (c) represent results that support planned reliance.
As a result of tests of controls, an auditor assessed control risk too low and decreased substantive testing. This assessment occurred because the true deviation rate in the population was
A. Less than the risk of assessing control risk too low, based on the auditor’s sample
B. Less than the deviation rate in the auditor’s sample
C. More than the risk of assessing control risk too low, based on the auditor’s sample
D. More than the deviation rate in the auditor’s sample
D.
If the sample deviation rate is lower than the true deviation rate in the population, the auditor mistakenly assesses control risk too low. The result is that detection risk is allowed to rise too high and substantive testing is decreased.
As a result of tests of controls, an auditor assesses control risk too high. This incorrect assessment most likely occurred because
A. Control risk based on the auditor’s sample is less than the true operating effectiveness of the client’s control activity.
B. The auditor believes that the control activity relates to the client’s assertions when, in fact, it does not.
C. The auditor believes that the control activity will reduce the extent of substantive testing when, in fact, it will not.
D. Control risk based on the auditor’s sample is greater than the true operating effectiveness of the client’s control activity.
D.
The risk of assessing control risk too high is the risk that the assessed level of control risk based on the sample is greater than the true operating effectiveness of the control. If a control activity is unrelated to the client’s assertions, the assessment could have been either too low or too high. The auditor’s decisions reduce the extent of substantive testing, not the control activity itself.
As a result of sampling procedures applied as tests of controls, an auditor incorrectly assesses control risk higher than appropriate. The most likely explanation for this situation is that
A. The deviation rate in the auditor’s sample is less than the tolerable rate, but the deviation rate in the population exceeds the tolerable rate.
B. The deviation rate in the auditor’s sample exceeds the tolerable rate, but the deviation rate in the population is less than the tolerable rate.
C. The deviation rates of both the auditor’s sample and the population exceed the tolerable rate.
D. The deviation rates of both the auditor’s sample and the population are less than the tolerable rate.
B.
The tolerable rate is the maximum rate of deviation from the prescribed internal control policies and procedures that would support the auditor’s assessed level of control risk. In this case, the auditor has assessed control risk too high. The risk of assessing control risk too high is the risk that the assessed level of control risk based on the sample is greater (the deviation rate in the auditor’s sample exceeds the tolerable rate,…) than the true operating effectiveness of the control (…but the deviation rate in the population is less than the tolerable rate). The situation described in answer “a” would result in assessing control risk too low. Answers “c” and “d” would support the auditor’s assessment of control risk.
For which of the following audit tests would a CPA most likely use attribute sampling?
A. Identifying entries posted to incorrect accounts
B. Estimating the amount in an expense account
C. Evaluating the reasonableness of depreciation expense
D. Selecting receivables for confirmation of account balances
A.
Attributes sampling involves the determination of the rate of occurrence of some characteristic (attribute) in a population. In an audit, the attribute of interest is frequently a deviation from a particular control procedure. Identifying entries posted to incorrect accounts is an example of testing compliance with the use of correct accounts (because it’s a yes/no scenario; were the entries posted to the correct accounts or not?). In estimating the amount in an expense account, evaluating the reasonableness of depreciation expense, and selecting receivables for confirmation of balances, a CPA is testing for dollar amounts which would involve variables sampling.
For which of the following audit tests would an auditor most likely use attribute sampling?
A. Selecting accounts receivable for confirmation of account balances
B. Inspecting employee time cards for proper approval by supervisors
C. Making an independent estimate of the amount of a LIFO inventory
D. Examining invoices in support of the valuation of fixed asset additions
B.
In performing tests of controls, the auditor is frequently interested in determining the rate of deviation from prescribed internal control policies and procedures. The sampling generally used in this situation is attribute sampling.
For which of the following audit tests would an auditor most likely use attribute sampling?
A. Inspecting purchase orders for proper approval by supervisors
B. Making an independent estimate of recorded payroll expense
C. Determining that all payables are recorded at year end
D. Selecting accounts receivable for confirmation of account balances
A.
Attribute sampling is used to test the effectiveness of internal control procedures. For example, the auditor may be concerned with estimating the percentage of purchase orders that do not have proper authorization. Variable sampling is utilized when testing details of transactions and account balances.
Given random selection, the same sample size, and the same precision requirement for the testing of two unequal populations, the risk of assessing control risk too low on the smaller population is
A. Higher than assessing control risk too low for the larger population
B. Indeterminate relative to assessing control risk too low for the larger population
C. Lower than assessing control risk too low for the larger population
D. The same as assessing control risk too low for the larger population
C.
The risk of assessing control risk too low is the risk that the assessed level of control risk based on the sample is less than the true operating effectiveness of the control. All things being equal, a sample taken from a smaller population will be more representative of the population than a sample of the same size taken from a larger population. Thus, the risk that the sample taken from the smaller population will yield a result different from the result obtained had the entire population been examined, is lower than such a risk inherent in sampling from a larger population.
How would increases in tolerable misstatement and the assessed level of control risk affect the sample size in a substantive test of details?
Increase in tolerable misstatement
Increase in assessed level of control risk
A. Increase sample size Increase sample size
B. Increase sample size Decrease sample size
C. Decrease sample size Increase sample size
D. Decrease sample size Decrease sample size
C.
Increasing the tolerable misstatement would lead to a decrease in the sample size. Increasing the assessed level of control risk would lead to an increase in the sample size.
In a probability-proportional-to-size sample with a sampling interval of $5,000, an auditor discovered that a selected account receivable with a recorded amount of $10,000 had an audited amount of $6,000. If this were the only misstatement discovered by the auditor, the projected misstatement of this sample would be:
A. $1,000
B. $3,000
C. $4,000
D. $5,000
C.
The interval is $5,000. The observed error is $10,000 – $6,000 = $4,000. Tainting is not required in this instance since the book value of the account is $10,000 and that’s above the interval. So in this case the projected misstatement is equal to the observed error of $4,000.
In a probability-proportional-to-size sample with a sampling interval of $10,000, an auditor discovered that a selected account receivable with a recorded amount of $5,000 had an audited amount of $4,000. If this were the only misstatement discovered by the auditor, the projected misstatement of this sample would be
A. $ 1,000
B. $ 2,000
C. $ 5,000
D. $10,000
B.
Book value less audit value divided by book value is the tainting percentage. [($5,000 - $4,000) / $5,000 = 0.2] The tainting percentage times the sampling interval is the projected error [0.2 x $10,000 = $2,000]. The sum of all the projected errors is the projected misstatement; there was only one error in this sample.
In a test of purchase orders, the auditor selected a random sample of 60 items out of a population of 1,200 purchase orders. The auditor discovered $4,000 in overstatements in the sample. The company’s materiality threshold is $65,000. The tolerable misstatement for purchases is $50,000. Which option best describes what the auditor should do next?
A. Pass on the exceptions.
B. Propose an adjustment to purchases.
C. Consider expanding the size of the sample.
D. Project the detected error to the entire population.
The correct answer is (D).
After identification of misstatements in the sample, the next step is to project the detected error to the entire population. The 60 samples in a test of purchase orders for 1,200 samples resulted in an overstatement of $4,000. In this case, the calculations would be as follows: Expected misstatements in the population:
(Misstatements in the population x Total number of items in the population) / Sample size. = ($4,000 x 1,200) / 60 = $80,000.
(A) is incorrect because the auditor should not pass on the exceptions in the misstatements. These misstatements are relevant and could be material.
(B) is incorrect because the auditor may eventually propose an adjustment to management. However, this is not the next step in the process.
(C) is incorrect because the auditor considers expanding the sample size based on factors other than the actual misstatement in the sample. At this point, the misstatement has been discovered, and the best course of action is to project the detected error to the entire population, not just a larger sample size.
In attribute sampling, a 25% change in which of the following factors will have the smallest effect on the size of the sample?
A. Tolerable rate of deviation
B. Number of items in the population
C. Degree of assurance desired
D. Planned assessed level of control risk
B.
The number of items in the population has virtually no effect on the sample size unless the population is very small.
In confirming a client’s accounts receivable in prior years, an auditor discovered many differences between recorded account balances and confirmation replies. These differences were resolved and were not misstatements. In defining the sampling unit for the current year’s audit, the auditor most likely would choose
A. Customers with credit balances
B. Small account balances
C. Individual overdue balances
D. Individual invoices
The correct answer is (D).
When the auditor discovered differences between recorded account balances and confirmation replies and if these differences were resolved and were not misstatements, an auditor would choose individual invoices as a sample in the current year.
A sampling of individual invoices would make it easier for customers to reply accurately.
Think about it this way: if based on the prior year’s audits you noted that the confirmation replies consistently did not match recorded balances (but AR was still not materially misstated), then in the current year, you would want to try a more efficient approach (i.e. an alternative procedure) and select individual invoices.
You would have assessed RMM low in this area based on no material misstatements in the past and as such perform more efficient procedures in this area.
In determining the number of documents to select for a test to obtain assurance that all sales returns have been properly authorized, an auditor should consider the tolerable rate of deviation from the control activity. The auditor should also consider
I.The likely rate of deviations
II.The allowable risk of assessing control risk too high
A. I only
B. II only
C. Both I and II
D. Neither I nor II
The correct answer is (A).
In determining the sample size to test authorization of sales returns, the auditor should consider
Tolerable rate of deviations
Estimated deviation rate
Allowable risk of assessing control risk too low
In the given options only the expected deviation rate will be considered. The allowable risk of assessing control risk too high will not be considered.
