431 Chapter 9 Sampling

The 4000 accounts receivable of GHI Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,600. Using the mean-per-unit estimation technique, Smith has properly estimated a projected misstatement of a $8,000 overstatement for the entire population. The audited value of Smith's sample is: A) $1,300 B) $1,400 C) $1,600 D) $1,800

A) $1,300

Using difference estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? A) $160,000. B) $161,538. C) $168,000. D) $200,000.

A) $160,000.

The 2000 accounts receivable of ABC Company have a total book value of $40,000. Bob Rotter, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,950. The audited value of the 100 accounts in the sample is $1,875. Using the mean-per-unit estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: A) $37,500 B) $38,462 C) $38,500 D) $41,600

A) $37,500

The 3000 accounts receivable of DEF Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $2,100. Using the difference estimation technique, Smith has properly estimated a projected misstatement of a $9,000 overstatement for the entire population. The estimated total audited value of the population is: A) $51,000 B) $58,000 C) $60,000 D) $69,000

A) $51,000

The auditors expect a population deviation rate of billing errors of two percent, and have established a tolerable rate of five percent. The sampling approach most likely to be used is: A) Attributes sampling. B) Stratified sequential sampling. C) Discovery sampling. D) None, as sampling does not seem appropriate in this situation.

A) Attributes sampling.

When performing tests of controls over authorization of cash receipts, which of the following sampling methods would be most appropriate? A) Attributes. B) Ratio. C) Stratified. D) Variables.

A) Attributes.

In assessing sampling risk, the risk of incorrect rejection and the risk of assessing control risk too high relate to the: A) Efficiency of the audit. B) Effectiveness of the audit. C) Selection of the sample. D) Audit quality controls.

A) Efficiency of the audit.

In assessing sampling risk, the risk of incorrect rejection and the risk of assessing control risk too high relate to the: A) Efficiency of the audit. B) Effectiveness of the audit. C) Selection of the sample. D) Audit quality controls.

A) Efficiency of the audit. The risk of incorrect rejection and assessing control risk too high relate to the efficiency of the audit since the related errors result in additional, unneeded, audit procedures. The risks of incorrect acceptance and assessing control risk too low relate to audit effectiveness.

When the auditors have chosen to test a control, what relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample? A) Exceed. B) Equal. C) Be less than. D) Indefinite.

A) Exceed.

When using sampling for tests of controls, which of the following audit consequences may follow? A) If sample results indicate that the control is operating effectively, but in fact it is not, control risk will be assessed too low. B) If sample results indicate that the control is operating effectively, but in fact it is not, control risk will be assessed too high. C) If sample results indicate that the control is not operating effectively, but in fact it is operating effectively, the audit is likely to be faulty because of reduced substantive tests. D) If sample results indicate that the control is not operating effectively, but in fact it is operating effectively, control risk will be assessed too low.

A) If sample results indicate that the control is operating effectively, but in fact it is not, control risk will be assessed too low.

If all other factors specified in an attributes sampling plan remain constant, decreasing the tolerable rate and decreasing the risk of assessing control risk too low would have what effect on sample size? A) Increase. B) Remain the same. C) Decrease. D) Indeterminate, depends upon exact change being made.

A) Increase.

If all other factors specified in an attributes sampling plan remain constant, decreasing the tolerable rate and increasing the estimated population deviation rate would have what effect on sample size? A) Increase. B) Remain the same. C) Decrease. D) Indeterminate, depends upon exact change being made.

A) Increase.

An increase in the tolerable misstatement has what effect on the planned allowance for sampling risk? A) Increases. B) Decreases. C) No effect. D) Indeterminate.

A) Increases.

The auditors are using unstratified mean-per-unit sampling to audit accounts receivable as they did in the prior year. Which of the following changes in characteristics or specifications would result in a larger required sample size this year than that required in the prior year? A) Larger variance in the dollar value of accounts. B) Smaller population size. C) Larger tolerable misstatement. D) Higher risk of incorrect acceptance.

A) Larger variance in the dollar value of accounts. A larger variance in the dollar value of accounts (as measured by the standard deviation) results in a larger sample size because the standard deviation is in the numerator of the equation to calculate sample size—increasing the numerator increases sample size. The other factors all result in a smaller sample size.

An advantage of using statistical sampling techniques is that such techniques: A) Mathematically measure risk. B) Eliminate the need for judgmental decisions. C) Define the values of allowance for sampling risk and tolerable misstatement required to provide audit satisfaction. D) Have been established in the courts to be superior to judgmental sampling.

A) Mathematically measure risk.

An auditor needs to estimate the average highway weight of tractor-trailer trucks using a state's highway system. Which estimation method is most appropriate? A) Mean-per-unit. B) Difference. C) Ratio. D)Probability-proportional-to-size.

A) Mean-per-unit. Mean-per-unit estimation is best because no "book value" is available for the trucks. The difference, ratio, and probability-proportional-to-size methods all require the comparison of a book value to an audited value.

Which of the following is generally not true about statistical sampling as compared to nonstatistical sampling? A) Statistical samples are more representative of the population. B) Statistical sample plans involve additional costs of evaluation. C) Statistical sampling allows a more objective evaluation of sample results. D) Statistical sampling may assist the auditors in designing more efficient samples.

A) Statistical samples are more representative of the population.

The auditors have audited a sample with a standard deviation of audited values larger than they had originally estimated. In this situation, to maintain the risk of incorrect acceptance at its predetermined level without increasing the size of the sample, which of the following statements is correct? A) The adjusted allowance for sampling risk will be smaller than had been planned. B) The adjusted allowance for sampling risk will be larger than had been planned. C) The risk of incorrect rejection will necessarily decrease. D) The size of the population must be decreased.

A) The adjusted allowance for sampling risk will be smaller than had been planned.

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) The auditor should consider the tolerable rate of deviation from the controls being tested in determining sample size.

In which of the following circumstances is it least likely that tests of controls will be performed? A) The expected deviation rate exceeds the tolerable deviation rate. B) The planned assessed level of control risk is at a level slightly below the maximum. C) The risk of assessing control risk too low is less than the expected deviation rate. D) The tolerable deviation rate exceeds the risk of assessing control risk too low.

A) The expected deviation rate exceeds the tolerable deviation rate. When the expected deviation rate exceeds the tolerable deviation rate it is unlikely that tests of controls will be performed. This is because in such a situation testing is only likely to reveal to the auditors that the system is not operating effectively as they expected.

Which of the following statements is correct concerning statistical sampling in tests of controls? A) The population size has little effect on determining sample size except for very small populations. B) The expected population deviation rate has little or no effect on determining sample size except for very small populations. C) As the population size doubles, the sample size also should double. D) For a given tolerable rate, a larger sample size should be selected as the expected population deviation rate decreases.

A) The population size has little effect on determining sample size except for very small populations.

Which of the following situations will result in the auditors concluding that the risk of material misstatement is too high when using nonstatistical sampling for substantive tests? A) The projected misstatement exceeds the tolerable misstatement. B) The allowance for sampling risk exceeds the projected misstatement. C) The risk of incorrect acceptance exceeds the risk of incorrect rejection. D) The tolerable misstatement exceeds the sample net misstatement.

A) The projected misstatement exceeds the tolerable misstatement.

Which of the following types of risk is of critical importance to auditors in performing tests of controls? A) The risk of assessing control risk too low. B) The risk of assessing control risk too high. C) The risk of incorrect acceptance. D) The risk of incorrect rejection.

A) The risk of assessing control risk too low.

In performing a test of a control last year the auditors specified a tolerable deviation rate of X percent. This year the auditors have specified a tolerable rate of less than X percent. Assuming that all other factors remain the same, which of the following is true regarding the relationship between this year's sample size compared to last year's sample size? A) This year's sample is larger than last year's sample. B) This year's sample is smaller than last year's sample. C) This year's sample is equal to last year's sample. D) This year's sample is indeterminate in relation to last year's sample.

A) This year's sample is larger than last year's sample.

Which of the following is accurate regarding tolerable misstatement? A) Tolerable misstatement is directly related to materiality. B) Tolerable misstatement cannot be determined until the sample results are evaluated. C) Tolerable misstatement does not affect sample size. D) Tolerable misstatement is a measure of reliability of the sample.

A) Tolerable misstatement is directly related to materiality. Tolerable misstatement is directly related to materiality. That is, as the measure of materiality increases, the tolerable misstatement allocated to the various accounts is increased. Tolerable misstatement is materiality at the account balance level.

The 10,000 accounts receivable of DEF Company have a total book value of $120,000. A CPA has selected and audited a sample of 100 accounts with a total book value of $1,000 and an audited value of $1,200. Using the mean-per-unit estimation technique, the estimated total audited value of the population is: a) $100,000. B) $120,000. C) $140,000. D) $144,000

B) $120,000.

Using ratio estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? A) $160,000. B) $161,538. C) $168,000. D) $200,000.

B) $161,538.

The 1000 accounts receivable of Winco Company have a total book value of $20,000 (Average book value = $20). Bob Duffo, CPA, has selected and audited a sample of 50 accounts with the following mean values: 1. Book value of $19. 2. Audited value of $19.60. What is the estimated total audited value using mean-per-unit sampling? A) $19,000. B) $19,600. C) $20,000. D) $20,632.

B) $19,600.

The 2000 accounts receivable of ABC Company have a total book value of $40,000. Bob Rotter, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,950. The audited value of the 100 accounts in the sample is $1,875. Using the ratio estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: A) $37,500 B) $38,462 C) $38,500 D) $41,600

B) $38,462

Using the mean-per-unit estimation method an auditor has properly calculated the estimated total audited value of a population as $200,000. Her sample included 200 of the population's 40,000 items. She found that, in her sample the average audited value was $1 less than the average book value. What was the average audited value in the sample? A) $4. B) $5. C) $6. D) $10.

B) $5.

Use of the ratio estimation sampling technique to estimate dollar amounts is inappropriate when: A) The total book value is known and corresponds to the sum of all the individual book values. B) A book value for each sample item is unknown. C) There are some observed differences between audited values and book values. D) The audited values are nearly proportional to the book value.

B) A book value for each sample item is unknown.

Which of the following statistical sampling techniques is least desirable for use by the auditors? A) Random number table selection. B) Block selection. C) Systematic selection. D) Random number generator selection.

B) Block selection. Block sampling is least desirable. It consists of all items during a selected time period, numerical sequence, or alphabetical sequence. Due to the relatively large number of blocks needed to form a reasonable audit conclusion, block sampling cannot generally be relied upon to efficiently produce a representative sample.

Which of the following is an element of sampling risk? A) Choosing an audit procedure that is inconsistent with the audit objective. B) Concluding that no material misstatement exists in a materially misstated population based on taking a sample that includes no misstatement. C) Failing to detect an error on a document that has been inspected by an auditor. D) Failing to perform audit procedures that are required by the sampling plan.

B) Concluding that no material misstatement exists in a materially misstated population based on taking a sample that includes no misstatement. Sampling risk is the risk of making a wrong decision based on a sample result. The other choices are elements of nonsampling risk.

Changing from a sampling plan using random selection with replacement to random selection without replacement has what effect on the required sample size? A) Increases. B) Decreases. C) No effect. D) An indeterminate effect.

B) Decreases.

Increases in the planned allowance for sampling risk have what effect on required sample size? A) Increases. B) Decreases. C) No effect . D) Indeterminate.

B) Decreases.

What effect does obtaining a sample with a standard deviation larger than that estimated during planning have on the adjusted allowance for sampling risk? A) Increases. B) Decreases. C) No effect. D) Indeterminate.

B) Decreases.

While performing a substantive test of details during an audit, the 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) Incorrect acceptance. B) Incorrect rejection. C) Assessing control risk too high. D) Assessing control risk too low.

B) Incorrect rejection.

When performing a test of a control over cash disbursements, a CPA may use a systematic sampling technique with a start at any randomly selected item. The biggest disadvantage of this type of sampling is that the items in the population: A) Must be recorded in a systematic pattern before the sample can be drawn. B) May occur in a systematic pattern and destroy the sample randomness. C) May systematically occur more than once in the sample. D) Must be systematically replaced in the population after sampling.

B) May occur in a systematic pattern and destroy the sample randomness.

In the past, the auditors have found that the book value of a receivable account has been related to the amount the account is misstated (i.e., large accounts have large misstatements and small accounts have small misstatements). Which of the following techniques is most likely to be efficient? A) Mean-per-unit estimation. B) Ratio estimation. C) Difference estimation. D) Sequential sampling estimation.

B) Ratio estimation.

Which of the following statistical sampling techniques involves taking samples in a series of stages? A) Systematic sampling. B) Sequential sampling. C) Continuous sampling. D) Multiple location sampling.

B) Sequential sampling.

An important statistic to consider when using a statistical sampling audit plan is the population variability. The population variability is measured by the: A) Sample mean. B) Standard deviation. C) Standard error of the sample mean. D) Estimated population total minus the actual population total.

B) Standard deviation.

Discovery sampling is particularly effective when: A) There are a large number of errors in the population. B) The auditors are looking for critical deviations that are not expected to be frequent in number. C) The auditors know where deviations are likely to occur. D) The population is large in size.

B) The auditors are looking for critical deviations that are not expected to be frequent in number. Discovery sampling is a modified case of attributes sampling. Its purpose is to detect at least one deviation, with a predetermined risk of assessing control risk too low, if the deviation rate in the population is greater than the specified tolerable deviation rate. It is effectively used when auditors are looking for critical deviations that are not expected to be frequent in number.

Which of the following is a correct statement with respect to evaluating results when using nonstatistical sampling for substantive tests? A) When the projected misstatement exceeds the tolerable misstatement, the auditor should conclude that the population is not misstated. B) The closer the projected misstatement is to the tolerable misstatement, the higher the risk of material misstatement. C) When the projected misstatement is equal to zero, the auditors may conclude with certainty that no misstatements exist in the account. D) When the projected misstatement percentage exceeds the risk of incorrect acceptance, the auditors will generally conclude that the population is materially misstated.

B) The closer the projected misstatement is to the tolerable misstatement, the higher the risk of material misstatement.

When the auditors have decided to use statistical rather than nonstatistical sampling, a disadvantage is that: A) Designing efficient samples is more difficult. B) The costs of training staff may be higher. C) Sampling without replacement must be used. D) Objectively evaluating results is impossible.

B) The costs of training staff may be higher.

An auditor plans to examine a sample of 20 checks for counter signatures as prescribed by the client's control procedures. One of the checks in the chosen sample of 20 cannot be found. The auditor should consider the reasons for this limitation and: A) Evaluate the results as if the sample size had been 19. B) Treat the missing check as a deviation for the purpose of evaluating the sample. C) Treat the missing check in the same manner as the majority of the other 19 checks, i.e., countersigned or not. D) Choose another check to replace the missing check in the sample.

B) Treat the missing check as a deviation for the purpose of evaluating the sample.

There are many kinds of statistical estimates that an auditor may find useful, but basically every statistical estimate in auditing is of either a quantity or of an error rate. The statistical terms that roughly correspond to "quantities" and "occurrence rate," respectively, are: A) Attributes and variable. B) Variables and attributes. C) Constants and attributes. D) Constants and variables.

B) Variables and attributes.

The 3000 accounts receivable of DEF Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $2,100. Using the difference estimation technique, Smith has properly estimated a projected misstatement of an overstatement of $6,000 for the entire population. The audited value of Smith's sample is: A) $1,700 B) $1,800 C) $1,900 D) $2,300

C) $1,900

The 10,000 accounts receivable of DEF Company have a total book value of $120,000. A CPA has selected and audited a sample of 100 accounts with a total book value of $1,000 and an audited value of $1,200. Using the difference estimation technique, estimated total audited value of the population is: A) $100,000. B) $120,000. C) $140,000. D) $144,000.

C) $140,000.

Using mean-per-unit estimation, an auditor has taken a sample of 200 from a population's 40,000 items; that population has a book value of $200,000. She found that in her sample the average audited value was $4.20, while the average book value was $5.20. What is the estimated total audited value of the population? A) $160,000. B) $161,538. C) $168,000. D) $200,000.

C) $168,000.

The auditors have sampled 50 accounts from a population of 1,000 accounts receivable. The sample items have a mean book value of $200 and a mean audited value of $203. The book value in the population is $198,000. What is the estimated total audited value of the population using the difference method? A) $198,000. B) $200,000. C) $201,000. D) $203,000.

C) $201,000. When calculating the estimated audited value of the population using the difference method the average misstatement is first calculated as $203 - $200 = $3. The projected misstatement is then calculated by multiplying the average misstatement times the number of accounts in the population, or $3 x 1000 = $3000. Because the average misstatement is an understatement, the projected misstatement of $3000 is added to the population book value of $198,000 to calculate the estimated audited value of $201,000.

The 2000 accounts receivable of ABC Company have a total book value of $40,000. Bob Rotter, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,950. The audited value of the 100 accounts in the sample is $1,875. Using the difference estimation technique, Rotter's estimate (to the nearest dollar) of year-end accounts receivable balance would be: A) $37,500 B) $38,462 C) $38,500 D) $41,600

C) $38,500

Assume a mean-per-unit estimation variables sampling application with a tolerable misstatement of $70,000 and a book value of $700,000. After performing the sampling plan, the auditors calculated an adjusted allowance for sampling risk of $45,000 and a point estimate of the population's total audited value to be $640,000. The projected misstatement based on this sample is: A) $5,000 B) $45,000 C) $60,000 D) $70,000

C) $60,000

The auditors' primary objective in selecting a sample of items from an audit population is to obtain: A) A random sample. B) A stratified sample. C) A representative sample. D) A large sample.

C) A representative sample. A sample that is representative of the audit population must be obtained. The sample is "representative" in the sense that it allows the auditor to project sample results to the overall population. The sample may, but need not be random, stratified, or large.

Which of the following factors does an auditor need to consider in planning a particular audit sample for a test of control? A) Number of items in the population. B) Total dollar amount of the items to be sampled. C) Acceptable level of risk of assessing control risk too low. D) Tolerable misstatement.

C) Acceptable level of risk of assessing control risk too low.

Which of the following may be used to reduce the risk of nonsampling errors? A) Increasing the size of audit samples. B) Stratifying audit samples. C) Adequately planning audit samples. D) Using statistical sampling techniques.

C) Adequately planning audit samples.

To determine sample size in an attribute sampling application, what must be specified? A) Population mean, expected error rate, and allowance for sampling risk. B) Allowance for sampling risk, risk of assessing control risk too low, and standard deviation. C) Allowance for sampling risk, risk of assessing control risk too low, and expected deviation rate. D) Population mean, standard deviation, and allowance for sampling risk.

C) Allowance for sampling risk, risk of assessing control risk too low, and expected deviation rate.

Which of the following sampling techniques is typically used for tests of controls? A) Mean-per-unit sampling. B) Difference sampling. C) Attribute sampling. D) Probability-proportional-to-size sampling.

C) Attribute sampling. Attribute sampling is used for test of controls since it is a plan that enables auditors to estimate the rate of deviation in a population.

Which of the following statistical selection techniques is least desirable for use by an auditor? A) Systematic selection. B) Stratified selection. C) Block selection. D) Sequential selection.

C) Block selection.

If all other factors specified in an attributes sampling plan remain constant, changing the specified tolerable rate from 6% to 10%, and changing the specified risk of assessing control risk too low from 3% to 7% would cause the required sample size to: A) Increase. B) Remain the same. C) Decrease. D) Change by 4%.

C) Decrease.

When using a statistical sampling plan, the auditors would probably require a smaller sample if the: A) Population increases. B) Desired allowance for sampling risk decreases. C) Desired risk of incorrect acceptance increases. D) Expected deviation rate increases.

C) Desired risk of incorrect acceptance increases.

Statistical sampling generally may be applied to test internal control when the client's internal control procedures: A) Depend primarily on appropriate segregation of duties. B) Are carefully reduced to writing and are included in client accounting manuals. C) Leave an audit trail in the form of evidence of compliance. D) Enable the detection of material fraud in the accounting records.

C) Leave an audit trail in the form of evidence of compliance.

When using statistical sampling, which of the following need not be known to evaluate the results of an attributes sample? A) Sample size. B) Risk of assessing control risk too low. C) Number of deviations in the population. D) Number of deviations found in the sample.

C) Number of deviations in the population.

Which of the following is not generally used for selecting samples? A) Random number tables. B) Random number generators. C) Physical representation numbers. D) Systematic selection.

C) Physical representation numbers.

An auditor wishes to estimate inventory shrinkage by weighing a sample of inventory items. From experience, the auditor knows that a few specific items are subject to unusually large amounts of shrinkage. In using statistical sampling, the auditor's best course of action is to: A) Eliminate any of the items known to be subject to unusually large amounts of shrinkage. B)Increase the sample size to lessen the effect of the items subject to unusually large amounts of shrinkage. C) Stratify the inventory population so that items subject to unusually large amounts of shrinkage are reviewed separately. D) Continue to draw new samples until a sample is drawn which includes none of the items known to be subject to large amounts of shrinkage.

C) Stratify the inventory population so that items subject to unusually large amounts of shrinkage are reviewed separately.

If the projected misstatement in a nonstatistical sampling is $8,000, while the tolerable misstatement is $9,000, what would an auditor likely conclude? A) Since the projected misstatement is less than the tolerable misstatement, the account is not misstated. B) Since the projected misstatement is less than the tolerable misstatement, the account is misstated. C) The risk is high that the account is materially misstated. D) The analysis has been improperly performed since the projected misstatement is unequal to the tolerable misstatement.

C) The risk is high that the account is materially misstated.

The auditors have sampled 50 accounts from a population of 1,000 accounts receivable. The sample items have a mean book value of $200 and a mean audited value of $203. The book value in the population is $198,000. What is the estimated audited value of the population using the mean-per-unit method? A) $198,000. B) $200,000. C) $201,000. D) $203,000.

D) $203,000. The estimated total audited value of the population using the mean-per-unit method is calculated as $203 (mean audited value in sample) x 1000 accounts = $203,000.

During the final planning of the accounts receivable program, a CPA specified a tolerable misstatement of $30,000, instead of the $20,000 contained in the preliminary audit program. What would be the impact of this change? A) A decrease in population standard deviation. B) An increase in sample standard deviation. C) An increase in required sample size. D) A decrease in the required sample size.

D) A decrease in the required sample size.

In variables estimation sampling, the sample standard deviation is used to calculate the: A) Point estimate of central tendency. B) Tainting of the sample interval. C) Risk of incorrect acceptance. D) Adjusted allowance for sampling risk.

D) Adjusted allowance for sampling risk.

Assume a mean-per-unit estimation variables sampling application with a tolerable misstatement of $70,000 and a book value of $700,000. After performing the sampling plan, the auditors calculated an adjusted allowance for sampling risk of $45,000 and a point estimate of the population's total audited value to be $650,000. Based on these results, the auditor would: A) Because the tolerable misstatement exceeds the adjusted allowance for sampling risk, conclude that the population does not contain a material misstatement. B) Because the total audited value ± tolerable misstatement includes the book value, conclude that the population does not contain a material misstatement. C) Because the tolerable misstatement exceeds the adjusted allowance for sampling risk, conclude that there is too great a risk that the account balance is materially misstated. D) Because the total audited value ± adjusted allowance for sampling risk does not include the book value, conclude that there is too great a risk that the account balance is materially misstated.

D) Because the total audited value ± adjusted allowance for sampling risk does not include the book value, conclude that there is too great a risk that the account balance is materially misstated.

Which of the following is an advantage of systematic selection over random number selection? A) It provides a stronger basis for statistical conclusions. B) It enables the auditor to use the more efficient "sampling with replacement" tables. C) There may be correlation between the location of items in the population, the feature of sampling interest, and the sampling interval. D) It does not require establishment of correspondence between random numbers and items in the population.

D) It does not require establishment of correspondence between random numbers and items in the population.

The auditors expect a population deviation rate of billing errors of eight percent, and have established a tolerable rate of five percent. The sampling approach most likely to be used is: A) Attributes sampling. B) Stratified random sampling. C) Variables sampling. D) None, as sampling does not seem appropriate in this situation.

D) None, as sampling does not seem appropriate in this situation.

In testing accounts receivable, an auditor sends out positive confirmation requests to 100 randomly selected customers. A customer returns the confirmation indicating that the balance is correct when, in fact, the balance is overstated. This is an example of: A) Projected misstatement. B) Sampling error. C) Standard error. D) Nonsampling error.

D) Nonsampling error.

The auditors' failure to recognize a misstatement in an amount or a deviation in an internal control data processing procedure is described as a: A) Statistical error. B) Sampling misstatement. C)Standard error of the mean. D) Nonsampling error.

D) Nonsampling error.

Which of the following statements is correct concerning the use of nonstatistical sampling for substantive tests? A) Its use is generally acceptable only for populations with an immaterial book value. B) It requires the use of structured sample size selection techniques to be acceptable. C) It may be especially useful in circumstances in which the combination of inherent and control risk is at the maximum level. D) Results will be projected to the population.

D) Results will be projected to the population.

The auditor using nonstatistical attributes sampling, but who nevertheless has chosen the sample in conformity with random selection procedures: A) Need not consider the risk of assessing control risk too low. B) Has committed a nonsampling error. C) Will have to use discovery sampling techniques to evaluate the results. D) Should compare the deviation rate of the sample to the tolerable rate.

D) Should compare the deviation rate of the sample to the tolerable rate.

Various factors influence the sample size for a substantive test of details of an account balance. All other factors being equal, which of the following would lead to a larger sample size? A) Lower assessment of control risk. B) Greater reliance on analytical procedures. C) Smaller expected frequency of misstatements. D) Smaller measure of tolerable misstatement.

D) Smaller measure of tolerable misstatement.

The tolerable deviation rate in sampling for tests of controls is: A) Used to determine the probability of the auditor's conclusion based upon reliance factors. B) The probability that the financial statements are not materially in error. C) A measure of the reliability of substantive tests. D) The rate the auditor will tolerate without modifying the planned assessment of control risk.

D) The rate the auditor will tolerate without modifying the planned assessment of control risk.

The 10,000 accounts receivable of DEF Company have a total book value of $120,000. A CPA has selected and audited a sample of 100 accounts with a total book value of $1,000 and an audited value of $1,200. Using the ratio estimation technique, the estimated total audited value of the population is: A)$100,000. B)$120,000. C)$140,000. D)$144,000.

D)$144,000.

The 1000 accounts receivable of Winco Company have a total book value of $20,000 (Average book value = $20). Bob Duffo, CPA, has selected and audited a sample of 50 accounts with the following mean values: 1. Book value of $19. 2. Audited value of $19.60. What is the estimated total audited value using difference estimation sampling? A) $19,387. B) $19,400. C) $19,600. D)$20,600.

D)$20,600.

Auditors project the misstatements found in the sample to the population when using statistical sampling, but not when using nonstatistical sampling. True False

False

The definition of a "deviation" for a test of a control should include only those deviations that result in misstatements in the financial statements. True False

False

The larger the standard deviation of a population, the smaller the required sample size. True False

False

Unrestricted random sampling normally results in a smaller sample size than does stratified sampling. True False

False

Using ratio and difference estimation for a sample is an example of a dual purpose test. True False

False

A 100 percent sample would have to be taken to eliminate sampling risk. True False

True

Discovery sampling is equivalent to an attributes sampling plan with a specified expected deviation rate of 0 percent. True False

True

In general, all items in excess of a material misstatement need to be examined and sampling of them is inappropriate. True False

True

Increases in the number of deviations in an attributes sample results in an increase in the achieved upper deviation rate of the attributes sample. True False

True

Increases in the tolerable misstatement result in a decreased sample size when using mean-per-unit estimation. True False

True

Increasing the expected misstatement for a probability-proportional-to-size sample increases the required sample size. True False

True

It is likely that five different random samples from the same population could produce five different estimates of the true population mean. True False

True

Statistical sampling cannot be used to test all control activities. True False

True

Stratification of the population generally results in a more efficient sampling plan. True False

True

The effect of the inclusion by chance of a very large or very small item in a random sample can be lessened by increasing the size of the sample. True False

True

The mean book value of the items included in a mean-per-unit sample is not directly used in the evaluation of sample results. True False

True

The standard deviation is a measure of the variability of items in a population. True False

True

To be random, every item in the population must have an equal chance of being selected for inclusion in the sample. True False

True

Unrestricted random sampling with replacement may result in a larger sample size than unrestricted random sampling without replacement. True False

True

When evaluating the results of a variables sampling plan, the projected misstatement is calculated and compared to the tolerable misstatement. True False

True

When sampling from the population of accounts receivable for certain objectives, the auditor might sample only active accounts with balances. True False

True

A normally distributed sample is assumed when using probability-proportional-to-size sampling. True False

False

Probability-proportional-to-size sampling is especially efficient for populations with high misstatement rates. True False

False

The upper limit on misstatement in a probability-proportional-to-size sample plan consists of the total of the projected misstatement and the tolerable misstatement. True False

False

Assume the following relating to a PPS sample: • Projected Misstatement = $20,000. • Basic Precision = $16,000. • Incremental Allowance = $4,500. • Tolerable Misstatement = $34,000. The most likely amount of misstatement in the population is equal to: A) $20,000. B) $20,500. C) $40,000. D) $40,500.

A) $20,000.

For which of the following populations would probability-proportional-to-size sampling be most likely to be the most efficient technique in confirming accounts receivable? A) 2,000 accounts with a standard deviation of $650, with few misstatements expected. B) 2,000 accounts with a standard deviation of $25, with few misstatements expected. C) 6,000 accounts with a standard deviation of $650, with many misstatements expected. D) 6,000 accounts with a standard deviation of $25 with many misstatements expected.

A) 2,000 accounts with a standard deviation of $650, with few misstatements expected.

In a PPS sample, the most likely misstatement in the population is equal to the: A) Projected Misstatement. B) Upper limit on misstatement. C) Basic Precision. D) Total misstatements identified in the sample.

A) Projected Misstatement.

When using probability-proportional-to-size sampling, the actual total misstatement in a population is most likely to be closest to the: A) Projected misstatement. B) Basic precision. C) Allowance for sampling risk. D) Upper limit on misstatement.

A) Projected misstatement.

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) $2,000.

In a probability-proportional-to-size sample with a sampling interval of $10,000, an auditor discovered that a selected account with a book value of $6,000 had an audited value of $4,000. The projected misstatement is: A) $2,000. B) $3,333. C) $6,000. D) $10,000.

B) $3,333.

Assume the following relating to a PPS sample: • Projected Misstatement = $20,000. • Basic Precision = $16,000. • Incremental Allowance = $4,500. • Tolerable Misstatement = $34,000. The allowance for sampling risk is equal to: A) $20,000. B) 20,500. C) $40,500. D) $74,500.

B) 20,500.

When no misstatements are identified in a PPS sample, the upper limit on misstatement equals: A) An amount dependent upon the sample's standard deviation. B) Basic precision. C) Half of the allowance for sampling risk. D) Zero.

B) Basic precision.

In a probability-proportional-to-size sample, increasing the tolerable misstatement has what effect on sample size, when all other factors are held constant? A) Increases. B) Decreases. C) No effect. D) Indeterminate.

B) Decreases.

When using probability-proportional-to-size sampling, the allowance for sampling risk is the combination of basic precision and the: A) Projected misstatement. B) Incremental allowance. C) Upper limit on misstatements. D) Tainting.

B) Incremental allowance.

Which statement is correct with respect to the probability-proportional-to-size technique? A) The technique insures that every account in the population has an equal chance of being selected. B) The technique automatically stratifies the population. C) The technique results in a representative sample every time. D) The technique allows the auditors to measure more precisely the risk of incorrect acceptance.

B) The technique automatically stratifies the population.

Which of the following factors would indicate that probability-proportional-to-size sampling should be used rather than other statistical sampling techniques? A) There is a book value for every item in the population. B) There is a low expected misstatement rate in the population. C) The auditors wish to obtain an estimate of the amount of misstatement in the population. D) The book value of the population is large.

B) There is a low expected misstatement rate in the population.

In a probability-proportional-to-size sample with a sampling interval of $10,000, an auditor discovered that as selected account receivable with a recorded amount of $12,000 had an audited amount of $9,000. If this were the only misstatement discovered by the auditor, the projected misstatement of this sample would be: A) $2,000. B) $2,500. C) $3,000. D) $10,000.

C) $3,000.

Assume the following relating to a PPS sample: • Projected Misstatement = $20,000. • Basic Precision = $16,000. • Incremental Allowance = $4,500. • Tolerable Misstatement = $34,000. The upper limit on misstatement equals: A) $20,000. B) $20,500. C) $40,500. D) $74,500.

C) $40,500.

The use of probability-proportional-to-size sampling would be least likely to be efficient if: A) Commercial receivable accounts are being audited. B) Statistical inferences are to be made. C) Many accounts are known to be in error. D) The population has a high total dollar value.

C) Many accounts are known to be in error.

Which statement is most proper for evaluating the results of this PPS sample? A) Accept the population because the projected misstatement is less than the tolerable misstatement. B) Accept the population because the sum of the projected misstatement and the basic precision exceeds the incremental allowance. C) Reject the population because the sum of the projected misstatement, basic precision, and incremental allowance exceeds the tolerable misstatement. D) Reject the population because the tolerable misstatement exceeds the basic precision plus the incremental allowance.

C) Reject the population because the sum of the projected misstatement, basic precision, and incremental allowance exceeds the tolerable misstatement.

Which of the following statements is correct concerning probability-proportional-to-size sampling? A) The sampling distribution should approximate the normal distribution. B) The auditors control the risk of incorrect rejection by specifying that risk level for the sampling plan. C) The sampling interval is calculated by dividing the population book value by the sample size. D) The auditors control the risk of incorrect acceptance by incorporating an expected misstatement into the sample size formula.

C) The sampling interval is calculated by dividing the population book value by the sample size.

The auditors of Smith Electronics wish to limit the audit risk of material misstatement in the test of accounts receivable to 5 percent. They believe that inherent risk is 100%, there is a 40 percent risk that material misstatement could have bypassed the client's system of internal control, and a 50 percent risk that any existing material misstatement would not have been brought to light by the auditors' analytical procedures. What is the maximum risk of incorrect acceptance the auditors should specify in their substantive tests of details of accounts receivable? A) 5 percent. B) 10 percent. C) 20 percent. D) 25 percent.

D) 25 percent.

An increase in the scope of analytical procedures may result in a lower allowable risk of incorrect acceptance for a substantive test of details. True False

True