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.
In examining cash disbursements, an auditor plans to choose a sample using systematic selection with a random start. The primary advantage of such a systematic selection is that population items: A. Which include errors will not be overlooked B. May occur in a systematic pattern, thus making the sample more representative C. May occur more than once in a sample D. Do not have to be prenumbered in order for the auditor to use the technique
D. The primary advantage of such a systematic selection is that population items do not have to be prenumbered in order for the auditor to use the technique.
In performing tests of controls over authorization of cash disbursements, which of the following statistical sampling methods would be most appropriate? A. Variables B. Stratified C. Ratio D. Attributes
D. When performing tests of controls the auditor is looking for the deviation rate from established control procedures set by the client. For testing the controls, the auditor performs attributes sampling procedures. Answers (a) and (c) represent substantive sampling procedures. Answer (b) describes a selection method that is not relevant to attribute sampling.
In statistical sampling methods used in substantive testing, an auditor most likely would stratify a population into meaningful groups if A. Probability proportional to size (PPS) sampling is used. B. The population has highly variable recorded amounts. C. The auditor's estimated tolerable misstatement is extremely small. D. The standard deviation of recorded amounts is relatively small.
B. Stratified sampling can be particularly useful in reducing the overall sample size on populations that have a wide range of dollar values (or highly variable recorded amounts). The primary objective is to decrease the effect of variance in the total population, thereby reducing sample size. PPS sampling ensures items with large amounts all make it into the sample, but not by stratifying the population. The estimated tolerable misstatement and standard deviation are irrelevant to a decision to stratify.
The degree of audit risk always present in an audit engagement is referred to as a combination of nonsampling and sampling risk. Which of the following is an example of nonsampling risk? A. The auditor selecting inappropriate auditing procedures B. The internal control being more effective than the auditor believes C. The auditor concluding the account balance is not materially misstated, but is, in fact, materially misstated D. The internal control not being as effective as the auditor believes
A. Sampling risk results from the possibility that if a test is restricted to a sample, the conclusions reached may be different than the conclusions that would have resulted if the entire population was examined. Nonsampling risk includes all aspects of audit risk not due to sampling. Examples of nonsampling risks include failure to select appropriate audit procedures for a given objective, and failure to recognize misstatements, thus making a procedure ineffective.
The expected population deviation rate of client billing misstatements is 2%. The auditor has established a tolerable rate of 3%. In the review of client invoices the auditor should use A. Stratified sampling B. Discovery sampling C. Variable sampling D. Attribute sampling
D. Attribute sampling provides evidence of the rate of occurrence of a specified characteristic in a population at auditor-specified levels of precision and reliability. Variable sampling is used by the auditor to estimate the total dollar amount of a population at auditor-specified levels of precision and reliability. Discovery sampling is a form of attribute sampling that is designed to locate at least one exception if the rate of occurrence in the population is at or above a specified rate. This method is used to search for critical occurrences that may indicate the existence of an irregularity, and is appropriate when the expected occurrence rate is quite low (usually near zero) and the auditor wants a sample that will provide a specified chance to observe one occurrence. Stratified sampling should not be used as the population is not divided into groups.
The likelihood of assessing control risk too high is the risk that the sample selected to test controls A. Does not support the auditor's planned assessed level of control risk when the true operating effectiveness of the internal control justifies such an assessment B. Contains misstatements that could be material to the financial statements when aggregated with misstatements in other account balances or transactions classes C. Contains proportionately fewer monetary errors or deviations from prescribed internal control structure policies or procedures than exist in the balance or class as a whole D. Does not support the tolerable error for some or all of management's assertions
A. 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 structure policy or procedure. Answer (B) is incorrect because fewer errors or deviations would be discovered; therefore, the auditor would not identify those misstatements. Answer (C) is incorrect because the true operating effectiveness of internal control would not support such an assessment; the auditor would find fewer errors or deviations. Answer (D) is incorrect because the sample would support the tolerable error for misstatements because the sample would reveal fewer errors or deviations than exist in the balance or class of transactions.
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.
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.
The risk of incorrect acceptance and the likelihood of assessing control risk too low relate to the A. Allowable risk of tolerable misstatement B. Preliminary estimates of materiality levels C. Efficiency of the audit D. Effectiveness of the audit
D. The risk of incorrect acceptance and the risk of assessing control risk too low relate to the effectiveness of an audit in detecting an existing material misstatement. If the auditor incorrectly accepts an account as being materially accurate or incorrectly concludes that control risk is below the maximum, additional procedures that may detect this incorrect conclusion are either eliminated or reduced and the audit would prove ineffective in detecting misstatements. Answers (a) and (b) are incorrect because of an inappropriate combination of terms. In (a), risk should relate to exceeding tolerable misstatement levels. In (b), materiality is judged, not estimated and related to tolerable misstatement. Audit efficiency is related to the risk of incorrect rejection or the risk of assessing control risk as too high.
The risk of incorrect acceptance is the
risk that the sample supports the conclusion that the recorded account balance is not materially misstated when it is materially misstated
The risk of incorrect rejection is
the risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not materially misstated. These are sampling risks related to substantive tests of details.
The sampling unit in a test of controls pertaining to the existence of payroll transactions ordinarily is a(an) A. Clock card or time ticket B. Employee Form W-2 C. Employee personnel record D. Payroll register entry
D. Assertions about existence deal with whether assets or liabilities of the entity exist at a given date. In this case, the auditor would consider the recorded transactions in the payroll register. The clock card or time ticket would provide evidence for the completeness assertion, not whether payroll transactions recorded actually occurred (the existence assertion). The employee personnel record would not provide evidence on whether payroll transactions recorded actually occurred, but only provide a summary of those transactions recorded.
The use of the ratio estimation sampling technique is most effective when A. The calculated audit amounts are approximately proportional to the client's book amounts. B. A relatively small number of differences exist in the population. C. Estimating populations whose records consist of quantities, but not book values. D. Large overstatement differences and large understatement differences exist in the population.
A. The use of the ratio estimation sampling technique is most effective when the calculated audit amounts are approximately proportional to the client's book amounts. The auditor uses sample results to estimate the ratio of audited value to book value, which is then applied to the population to estimate the actual value. Ratio estimation should be used when each population item has a book value, an audited value may be ascertained for each sample item, and differences occur frequently. Large overstatement or understatement differences would reduce the effectiveness of this technique.
Using statistical sampling to assist in verifying the year-end accounts payable balance, an auditor has accumulated the following data: Number of accounts Population:4,000 Sample: 200 Book balance Population: $5,000,000 Sample: $125,000 Balance determined by the auditor Population: ? Sample: $150,000 Using the difference estimation technique, the auditor's estimate of year-end accounts payable balance would be A. $5,500,000 B. $6,000,000 C. $4,500,000 D. $3,000,000
The correct answer is (A). Using the difference estimation technique, the auditor's will estimate year-end accounts payable balance as follows: Determine the average dollar value difference between the audited value and book value of the sample. Multiply this average value of difference by the no. of items in the population. Add (or subtract) the result to the book value of the population. We will first determine the total misstatement i.e. the total balance of sample determined by auditor subtracted from the book balance of the sample i.e. $150,000 – $125,000 = $25,000. This $25,000 variance is for 200 items in sample. Hence, average variation in each item is $25,000/200 = $125 and then calculate the total variation in the population by extrapolating it to 4000 items = $125 x 4,000 = $500,000. Add the $500,000 to total book balance of $5,000,000 = $5,500,000. Note: Since, in this case, the sample was understated we added the difference per sample to book value. If the sample was overstated we would subtract the adjustment from book value.
Using statistical sampling to assist in verifying the year-end accounts payable balance, an auditor has accumulated the following data: Number of accounts Population:4,000 Sample: 200 Book balance Population: $5,000,000 Sample: $125,000 Balance determined by the auditor Population: ? Sample: $150,000 Using the MPU technique, the auditor's estimate of year-end accounts payable balance would be A. $5,500,000 B. $6,000,000 C. $4,500,000 D. $3,000,000
D. Take the total balance determined by the auditor $150,000 and divide by the number of accounts in the sample 200 to get the Mean Per Unit of the sample $750. Multiply the Mean Per Unit of the sample $750 by the total population 4,000 to get the estimate of year-end accounts payable $3,000,000.
Using statistical sampling to assist in verifying the year-end accounts payable balance, an auditor has accumulated the following data: Number of accounts Population:4,100 Sample: 200 Book balance Population: $5,000,000 Sample: $125,000 Balance determined by the auditor Population: ? Sample: $150,000 Using the ratio estimation technique, the auditor's estimate of year-end accounts payable balance would be Number of accounts Population:4,100 Sample: 200 Book balance Population: $5,000,000 Sample: $125,000 Balance determined by the auditor Population: ? Sample: $150,000 Using the difference estimation technique, the auditor's estimate of year-end accounts payable balance would be A. $6,150,000 B. $6,000,000 C. $5,125,000 D. $5,050,000
B. Under the ratio estimation technique, the auditor uses sample results to estimate the ratio of audited value to book value. The ratio is then applied to the population book value to estimate the audited value of the population. The sample 'audited value/book value' ratio equals 1.2:1 ($150,000 / $125,000). When this ratio is applied to the population book balance of $5,000,000, an estimated $6,000,000 audited value results.
What is an auditor's evaluation of a statistical sample for attributes when a test of 50 documents results in 3 deviations if tolerable rate is 7%, the expected population deviation rate is 5%, and the allowance for sampling risk is 2%? A. Modify the planned assessed level of control risk because the tolerable rate plus the allowance for sampling risk exceeds the expected population deviation rate. B. Accept the sample results as support for the planned assessed level of control risk because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate. C. Accept the sample results as support for the planned assessed level of control risk because the tolerable rate less the allowance for sampling risk equals the expected population deviation rate. D. Modify the planned assessed level of control risk because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate.
D. The auditor should modify his or her planned assessed level of control risk when the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate. In this question, the deviation rate of 6% (3 deviations among 50 documents) plus the allowance for sampling risk of 2% is greater than the given tolerable rate of 7%.
What is the primary objective of using stratification as a sampling method in auditing? A. To increase the confidence level at which a decision will be reached from the results of the sample selected. B. To determine the occurrence rate for a given characteristic in the population being studied. C. To decrease the effect of variance in the total population D. To determine the precision range of the sample selected
C. The primary objective of using stratification as a sampling method in auditing is to decrease the effect of variance in the total population.
When performing a substantive test of a random sample of cash disbursements, an auditor is supplied with a photocopy of vendor invoices supporting the disbursements for one particular vendor rather than the original invoices. The auditor is told that the vendor's original invoices have been misplaced. What should the auditor do in response to this situation? A. Increase randomly the number of items in the substantive test to increase the reliance that may be placed on the overall test B. Reevaluate the risk of fraud, and design alternate tests for the related transactions C. Increase testing by agreeing more of the payments to this particular vendor to the photocopies of its invoices D. Count the missing original documents as misstatements, and project the total amount of the error based on the size of the population and the dollar amount of the errors
B. When an auditor is supplied with copies of vendor invoices instead of originals and told the originals have been misplaced, the auditor should reevaluate the risk of fraud and design alternate tests for the related transactions. Audit procedures that are appropriate to the particular audit objective should be applied to each sample item. If considering those unexamined items [the originals] to be misstated would lead to a conclusion that the balance or class contains material misstatement, the auditor should consider alternative audit procedures that would provide sufficient appropriate audit evidence to form a conclusion. The auditor should also consider whether the reasons for the lack of availability of the items have implications in relation to assessing risks of material misstatement due to fraud, the assessed level of control risk that the auditor expects to be supported, or the degree of reliance on management representations.
Which of the following would be a consideration in planning an auditor's sample for a test of controls? A. Preliminary judgments about materiality levels. B. The auditor's allowable risk of assessing control risk too high C. The level of detection risk for the account D. The auditor's allowable risk of assessing control risk too low
D. When planning an audit sample for a test of controls, the auditor should consider the auditor's allowable risk of assessing control risk too low; not too high. The auditor also should consider the relationship of the sample to the objective of the test of controls; the maximum rate of deviations from prescribed controls that would support the planned assessed level of control risk; and characteristics of the population, i.e., the items comprising the account balance or class of transactions of interest. Preliminary judgments about material levels and the level of detection risk are considerations for planning a sample for a substantive test of details.
When planning a sample for a substantive test of details, an auditor should consider tolerable misstatement for the sample. This consideration should A. Be related to the auditor's business risk B. Not be adjusted for qualitative factors C. Be related to preliminary judgments about materiality levels D. Not be changed during the audit process
C. Tolerable misstatement is a planning concept and is related to the auditor's determination of materiality for planning the financial statement audit in such a way that tolerable misstatement, combined for all of the tests in the entire audit, does not exceed materiality for the financial statements. Materiality judgments (tolerable misstatements) are not affected by the auditor's business risk. Judgments about materiality (tolerable misstatements) are subjective and do involve consideration of qualitative as well as quantitative factors and ordinarily will change during the process of conducting an audit as the auditor develops new evidence.
When using classical variables sampling for estimation, an auditor normally evaluates the sampling results by calculating the possible error in either direction. This statistical concept is known as A. Precision B. Reliability C. Projected error D. Standard deviation
A. In classical variables sampling for estimation, precision represents the range within which the sample result is expected to be accurate. Hence, it provides a calculation of the maximum acceptable error in either direction. Reliability varies inversely with the assessed level of control risk and is a measure of the probability that the sample result will fall within the precision range mentioned above. Projected error is the anticipated deviation rate, based on the sample, in the entire population. The standard deviation is a measure of the dispersion among the relative values of a particular characteristic.
Which of the following audit procedures most likely will involve sampling? A. Risk assessment procedures performed to obtain an understanding of internal control. B. Tests of automated application controls when effective information technology general controls are present. C. Analysis of controls to determine the appropriate segregation of duties. D. Testing of process for approval of credit to customers for sales on account.
The correct answer is (D). Testing of process for approval of credit to customers for sales on account will most likely involve sampling. The credit has to be approved by appropriate authority after following prescribed procedures. The procedures can be looking at the credit reports, financial statements, payment history or references for the customers. An auditor would normally pull some customers from accounts receivable balances on a sample basis and trace for each of the customer, the credit approval process followed.
Which of the following characteristics most likely would be an advantage of using classical variables sampling rather than probability-proportional-to-size (PPS) sampling? A. The selection of negative balances requires no special design considerations. B. The sampling process can begin before the complete population is available. C. The auditor need not consider the preliminary judgments about materiality. D. The sample will result in a smaller sample size if few errors are expected.
A. Special consideration must be given to zero and negative balance accounts which usually are excluded from a probability proportional to size (PPS) sample. For both classical variables sampling and PPS sampling, the sampling process may begin before the complete population is available and the auditor must consider the preliminary judgments about materiality. If few errors are expected, the sample will result in a smaller sample size using PPS sampling than if classical variables sampling is used.
Which of the following combinations results in a decrease in sample size in a sample for attributes? Allowed Risk of Assessing Control Risk Too Low Expected Tolerable Rate Population Deviation Rule A. Increase Decrease Increase B. Decrease Increase Decrease C. Increase Increase Decrease D. Increase Increase Increase
The correct answer is (C). Increase in Risk of Assessing Control Risk Too Low results in a decrease in sample size. Increase in Expected Tolerable Rate results in a decrease in sample size. Decrease in Population Deviation Rate results in a decrease in sample size.
Which of the following courses of action would an auditor most likely follow in planning a sample of cash disbursements if the auditor is aware of several unusually large cash disbursements? A. Set the tolerable rate of deviation at a lower level than originally planned. B. Stratify the cash disbursements population so that the unusually large disbursements are selected. C. Increase the sample size to reduce the effect of the unusually large disbursements. D. Continue to draw new samples until all the unusually large disbursements appear in the sample.
B. In planning a sample of cash disbursements if the auditor is aware of several unusually large cash disbursements, the auditor will most likely stratify the sample to include the unusually large disbursements. By stratifying the sample, the auditor will decrease the effect of the variances in the total population, and therefore be able to reduce the number of items in the sample.
Which of the following factors is(are) considered in determining the sample size for a test of controls? Expected deviation rate Tolerable deviation rate A. Yes Yes B. No No C. No Yes D. Yes No
A. Both the expected (likely) deviation rate and the tolerable deviation rate are considerations in determining the sample size for a test of controls.
Which of the following is a sampling risk that is associated with the efficiency of an audit? A. Risk of assessing control risk too high B. Risk of incorrect acceptance C. Inherent risk D. Detection risk
The correct answer is (A). Sampling risk or the risk of drawing an erroneous conclusion from the sample because the sample is not representative of the population contains 2 types of sampling errors. Type 1 is associated with the efficiency of an audit and occurs when the sample selected indicates an error, but the population is not misstated. In the context of tests of controls, this occurs when the auditor under-relies on the entity’s internal control when the auditor assesses the control risk as too high, and consequently, assesses the risk of material misstatement too high and ends up applying extra substantive procedures which hamper the efficiency of the audit. Risk of incorrect acceptance impacts the effectiveness of the audit. Inherent Risk and Detection Risk are separate components of audit risk and are not a sampling risk.
Which of the following is the primary objective of probability-proportional-to-size (PPS) sample? A. To identify overstatement errors B. To increase the proportion of smaller-value items in the sample C. To identify items where controls were not properly applied D. To identify zero and negative balances
A. In PPS sampling, because the sample is selected proportional to size, larger dollar amounts have a higher probability of being selected, thus overstatements (errors) are more likely to be selected than understatements. An auditor will normally use PPS sampling when testing for material overstatements. For the reason just stated, PPS sampling is unlikely to select smaller-value items and these amounts may be significantly understated in the sample, not increased. PPS sampling is a form of variables sampling which is normally used in substantive testing where the auditor is usually interested in the selection of dollar amounts, not attributes as is usually the case in tests of controls. Additionally, samples taken to test the operating effectiveness of controls (to provide a basis for the auditor to conclude whether the controls are being properly applied) should be selected in a manner such that the sample is representative of the population, thus all items in the population should have an opportunity to be selected which is not the case with PPS sampling. Zero balances are not subject to PPS selection and negative balances would have to be segregated into a separate population for testing.
Which of the following objectives is achieved when an auditor decides to employ classical variable sampling? A. To determine the reliability of voucher processing. B. To determine the completeness of billing transactions. C. To determine the inventory quantities on hand. D. To determine the efficiency of the payroll system.
The correct answer is (C). Classical variable sampling is used when performing a test of details for substantive testing to determine if individual account balances stated in dollars or other numerical values (Example: units) are materially correct. Classical variable sampling is used to evaluate the entire population based on the sample data. The auditor can use variable sampling to determine the units of inventory in hand based on the sample of inventory tested. Reliability of voucher processing, Completeness of billing transactions and Efficiency of the payroll system are all attributes and will not be tested through dollar or numerical values as per classical variable sampling but attribute sampling.
Which of the following sampling methods would be used to estimate a numerical measurement of a population, such as a dollar value? A. Attributes sampling B. Stop-or-go sampling C. Variables sampling D. Random-number sampling
C. Substantive tests of details are performed by the auditor to either detect misstatements or obtain evidence about the validity and propriety of the accounting treatment of transactions and balances. In substantive testing, the auditor is primarily interested in dollar amounts, and the traditional method of performing substantive tests is by variables sampling.
Which of the following statements about audit sampling risks is correct for a nonissuer? A. Nonsampling risk arises from the possibility that, when a substantive test is restricted to a sample, conclusions might be different than if the auditor had tested each item in the population. B. Nonsampling risk can arise because an auditor failed to recognize misstatements. C. Sampling risk is derived from the uncertainty in applying audit procedures to specific risks. D. Sampling risk includes the possibility of selecting audit procedures that are not appropriate to achieve the specific objective.
B. Nonsampling risk arises from issues unconnected with sampling, such as failing to recognize misstatements. Sampling risk arises from the possibility that, when a substantive test is restricted to a sample, conclusions might be different than if the auditor had tested each item in the population. The risk derived from the uncertainty in applying audit procedures to specific risks and the possibility of selecting audit procedures that are not appropriate to achieve the specific objective are unconnected with sampling. Nonsampling risk includes all the aspects of audit risk that are not due to sampling. Examples of nonsampling risk include failure to properly define the audit population, failure to define clearly the nature of an audit exception, failure to recognize an error when one exists in the sample, and failure to evaluate sample findings properly. Sampling risk arises from the possibility that, when a substantive test is restricted to a sample, conclusions might be different than if the auditor had tested each item in the population. Audit risk is derived from the uncertainty in applying audit procedures to specific risks. Nonsampling risk includes the possibility of selecting audit procedures that are not appropriate to achieve the specific objective.
Which of the following statements is correct about the sample size in statistical sampling when testing internal controls? A. The auditor should consider the tolerable rate of deviation from the controls being tested in determining sample size. B. As the likely rate of deviation decreases, the auditor should increase the planned sample size. C. The allowable risk of assessing control risk too low has no effect on the planned sample size. D. Of all the factors to be considered, the population size has the greatest effect on the sample size.
A. An increase in the tolerable rate of deviation would allow a reduction in sample size. As the likely deviation rate decreases, the auditor may decrease the planned sample size. The allowable risk of assessing control risk too low has an inverse effect on the sample size. Of all the factors to be considered, the population size has the least effect on the sample size.
Which of the following statements is correct concerning probability-proportional-to-size (PPS) sampling, also known as dollarunit sampling? A. The sampling distribution should approximate the normal distribution. B. Overstated units have a lower probability of sample selection than units that are understated. C. The auditor controls the risk of incorrect acceptance by specifying that risk level for the sampling plan. D. The sampling interval is calculated by dividing the number of physical units in the population by the sample size.
C. In PPS sampling, the auditor achieves control over the risk of incorrect acceptance by specifying the level of risk the auditor is willing to assume. PPS sampling does not require direct consideration of the standard deviation of dollar amounts to determine the appropriate sample. The book value of the unit determines how probable it is that it will be included in the sample, not whether it is over or understated. The sampling interval is calculated by dividing the book value of the population by the sample size.
Which of the following statements is correct concerning the auditor's use of statistical sampling? A. An auditor needs to estimate the dollar amount of the standard deviation of the population to use classical variables sampling. B. The selection of zero balances usually does not require special sample design considerations when using PPS sampling. C. A classical variables sample needs to be designed with special considerations to include negative balances in the sample. D. An assumption of PPS sampling is that the underlying accounting population is normally distributed.
A. The factors affecting sample size when using classical variables sampling are (1) desired precision, (2) desired sample reliability, (3) variability among item values in the population (the estimate of the population's standard deviation) and (4) population size. PPS is a non-parametric method that does not assume a normal distribution. PPS plans require special design to deal with negative balances and zero balances because sample selection is based on the cumulative sum of dollars of the population. Negative figures distort the cumulative sum and zero balances would not be considered without special adjustments in a PPS plan. Classical variables techniques are unaffected by either zero balances or negative balances.
Which of the following statements is generally correct about the sample size in statistical sampling when testing internal controls? A. As the population size doubles, the sample size should increase by about 67%. B. The sample size is inversely proportional to the expected error rate. C. There is no relationship between the tolerable error rate and the sample size. D. The population size has little or no effect on the sample size.
D. When a sample is small in relation to the population, the population size has little or no effect on the determination of an appropriate sample size.
Which of the following statements is ordinarily correct about the sample size in statistical sampling when testing controls? A. The expected population deviation rate has little effect on determining the sample size. B. As the population size doubles, the sample size should also double. C. As the tolerable deviation rate increases, the sample size should also increase. D. The population size has little effect on the sample size.
D. The population size has little effect on the sample size. To determine the number of items to be selected for a particular sample for a test of controls, the auditor should consider the tolerable rate of deviation from the controls being tested, the likely rate of deviations, and the allowable risk of assessing control risk too low. An auditor applies professional judgment to relate these factors in determining the appropriate sample size. As the tolerable deviation rate increases, the sample size can be decreased, not increased.
Which of the following types of sampling allows an auditor to quantify sampling risk? A. Stratified nonstatistical B. Haphazard C. Attribute D. Block
The correct answer is (C). Attribute sampling is a statistical approach used to test controls. Statistical approaches allow auditors to quantify sampling risk. Attribute sampling involves statistical sample selection, which often includes random sampling or systematic sampling Stratified nonstatistical, Haphazard and Block are all non-statistical sampling which does not allow the auditor to quantify sampling risk.
Which of the following would be a consideration in planning an auditor's sample for a test of controls? A. Preliminary judgments about materiality levels. B. The auditor's allowable risk of assessing control risk too high C. The level of detection risk for the account D. The auditor's allowable risk of assessing control risk too low
D. When planning an audit sample for a test of controls, the auditor should consider the auditor's allowable risk of assessing control risk too low; not too high. The auditor also should consider the relationship of the sample to the objective of the test of controls; the maximum rate of deviations from prescribed controls that would support the planned assessed level of control risk; and characteristics of the population, i.e., the items comprising the account balance or class of transactions of interest. Preliminary judgments about material levels and the level of detection risk are considerations for planning a sample for a substantive test of details.
Which of the following would be a consideration in planning a sample for a test of subsequent cash receipts? A. Preliminary judgments about materiality levels B. The amount of bad debt write-offs in the prior year C. The size of the intercompany receivable balance D. The auditor’s allowable risk of assessing control risk is too low
A. When planning a particular sample for a substantive test of details, such as subsequent cash receipts, the auditor should consider (1) the relationship of the sample to the relevant audit objective; (2) preliminary judgments about materiality levels; (3) the auditor's allowable risk of incorrect acceptance; and (4) characteristics of the population, that is, the items comprising the account balance or class of transactions of interest. The amount of bad debt write-offs from the prior year would not be appropriate to consider to detect information about subsequent cash receipts. The size of the intercompany receivable balance is not related to subsequent cash receipts. The risk of assessing control risk too low (the risk that the assessed level of control risk based on the sample is less than the true operating effectiveness of the control) relates to sampling risk in performing tests of controls rather than a substantive test of details as described in this question.
While performing a test of details during an audit, an auditor determined that the sample results supported the conclusion that the recorded account balance was materially misstated. It was, in fact, not materially misstated. This situation illustrates the risk of A. Assessing control risk too high B. Assessing control risk too low C. Incorrect rejection D. Incorrect acceptance
C. The risk of incorrect rejection is the risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not materially misstated. 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. The risk of assessing control risk too low is just the opposite. The risk of incorrect acceptance is the risk that the sample supports the conclusion that the recorded account balance is not materially misstated when it is materially misstated.
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%. In the evaluation of this sample, the auditor decided to increase the level of the preliminary assessment of control risk because the A. Tolerable rate (7%) was less than the achieved upper precision limit (8%). B. Expected deviation rate (7%) was more than the percentage of errors in the sample (3.5%). C. Achieved upper precision limit (8%) was more than the percentage of errors in the sample (3.5%). D. Expected deviation rate (2.5%) was less than the tolerable rate (7%).
A. The auditor would increase the preliminary assessment of control risk because the achieved upper precision limit of 8% (sample error rate plus an allowance for sampling risk) exceeded the tolerable error rate of 7% (determined by professional judgment). Therefore, the results of the test did not allow the auditor to conclude with 99% confidence that the error rate in the population did not exceed 7%. All other answers describe comparisons that are meaningless |
When testing automated IT controls the auditor is most likely?
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