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# Chapter 9 Audit Sampling

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Stratification of the population generally results in a more efficient sampling plan.
True
Discovery sampling is equivalent to an attributes sampling plan with a specified expected deviation rate of 0 percent.
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
The definition of a "deviation" for a test of a control should include only those deviations that result in misstatements in the financial statements.
False
Statistical sampling cannot be used to test all control activities.
True
Using ratio and difference estimation for a sample is an example of a dual purpose test.
False
Increases in the tolerable misstatement result in a decreased sample size when using mean-per-unit estimation.
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
When evaluating the results of a variables sampling plan, the projected misstatement is calculated and compared to the tolerable misstatement.
True
Auditors project the misstatements found in the sample to the population when using statistical sampling, but not when using nonstatistical sampling.
False
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:
\$140,000.
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:
\$144,000
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:
\$120,000.
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?
\$5.
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?
\$160,000.
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?
\$161,538.
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?
\$168,000.
If the projected misstatement in a nonstatistical sampling is \$8,000, while the tolerable misstatement is \$9,000, what would an auditor likely conclude?
The risk is high that the account is materially misstated.
A dual purpose test simultaneously:
Functions as a substantive test and as a test of controls
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?
\$19,600.
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?
\$20,600.
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?
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?
Increase.
An increase in the tolerable misstatement has what effect on the planned allowance for sampling risk?
Increase
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.
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?
This year's sample is larger than last year's sample.
The auditor using nonstatistical attributes sampling, but who nevertheless has chosen the sample in conformity with random selection procedures:
Should compare the deviation rate of the sample to the tolerable rate.
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.
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.
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.
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.
When the auditors have decided to use statistical rather than nonstatistical sampling, a disadvantage is that:
The costs of training staff may be higher.
Changing from a sampling plan using random selection with replacement to random selection without replacement has what effect on the required sample size?
Decreases
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?
Exceed
Increases in the planned allowance for sampling risk have what effect on required sample size?
Decreases
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.
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:
Attributes sampling.
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:
None, as sampling does not seem appropriate in this situation.
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.
D) Using statistical sampling techniques.
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.
The auditors' failure to recognize a misstatement in an amount or a deviation in an internal control data processing procedure is described as a:
Nonsampling error.
What effect does obtaining a sample with a standard deviation larger than that estimated during planning have on the adjusted allowance for sampling risk?
Decreases
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:
\$37,500
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:
\$38,462
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:
\$38,500
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 an overstatement of \$6,000 for the entire population. The audited value of Smith's sample is:
\$1,900
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:
\$51,000
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:
\$1,300
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.
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:
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.
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:
\$60,000
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.
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 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.
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
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 decrease in the required sample size.
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.
Statistical sampling generally may be applied to test internal control when the client's internal control procedures:
Leave an audit trail in the form of evidence of compliance.
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.
To determine sample size in an attribute sampling application, what must be specified?
Allowance for sampling risk, risk of assessing control risk too low, expected deviation rate.
The tolerable deviation rate in sampling for tests of controls is:
The rate the auditor will tolerate without modifying the planned assessment of control risk.
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:
Nonsampling error.
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:
Stratify the inventory population so that items subject to unusually large amounts of shrinkage are reviewed separately.
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:
Decrease.
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.
When using a statistical sampling plan, the auditors would probably require a smaller sample if the:
Desired risk of incorrect acceptance increases.
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.
An advantage of using statistical sampling techniques is that such techniques:
Mathematically measure risk.
In assessing sampling risk, the risk of incorrect rejection and the risk of assessing control risk too high relate to the:
Efficiency of the audit
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:
May occur in a systematic pattern and destroy the sample randomness.
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:
Incorrect rejection.
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:
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:
Variables and attributes.
Which of the following best illustrates the concept of sampling risk?
A) A randomly chosen sample may not be representative of the population as a whole on the characteristic of interest.
B) An auditor may select audit procedures that are not appropriate to achieve the specific objective.
C) An auditor may fail to recognize deviations in the documents examined for the chosen sample.
D) The documents related to the chosen sample may not be available for inspection.
A) A randomly chosen sample may not be representative of the population as a whole on the characteristic of interest.
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.
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.
An important statistic to consider when using a statistical sampling audit plan is the population variability. The population variability is measured by the:
Standard deviation.
In variables estimation sampling, the sample standard deviation is used to calculate the: