Sampling

Question 1

An advantage that using statistical sampling has over nonstatistical sampling is that statistical sampling helps an auditor to

Answer 1

Measure the sufficiency of the evidential matter obtained.
Statistical sampling allows an auditor to:
1) design an efficient sample;
2) measure the sufficiency of the evidential matter obtained; and
3) evaluate the sample results.

Question 2

The risk of incorrect acceptance and the likelihood of assessing control risk too low relate to the

Answer 2

Effectiveness of the audit.
The risk of incorrect acceptance and the likelihood of assessing control risk too low both relate to the effectiveness of the audit. The risk of incorrect acceptance is the risk that the auditor will accept a balance as fairly stated when it really isn’t. The risk of assessing control risk too low is the risk that the auditor will conclude that the controls are effective when they are not effective.
In either case, the auditor has made an erroneous judgment that could result in the failure to detect a material misstatement and the issuance of an incorrect opinion.

Question 3

An auditor may decide to increase the risk of incorrect rejection when

Answer 3

The cost and effort of selecting additional sample items are low.
The risk of incorrect rejection relates to the efficiency of the audit. If the auditor incorrectly believes that a material misstatement exists, the auditor will perform extra auditing procedures to try to find the material misstatement. After performing the extra work, the auditor will then reach the correct conclusion that the balance is fairly stated.
When the auditor decides to increase the risk of incorrect rejection, the auditor is increasing the risk of audit inefficiency, i.e., of doing too much work. This decision might seem appropriate if the cost and effort of selecting additional sample items are low.

Question 4

For which of the following audit tests would an auditor most likely use attribute sampling?

Answer 4

Inspecting employee time cards for proper approval by supervisors.
Attribute sampling is used to estimate the maximum rate of occurrence in the population of an attribute or characteristic. As a result, it is frequently used for testing controls. The only test listed that is a test of controls is D, inspecting employee time cards for proper approval by supervisors.

Question 5

As a result of sampling procedures applied as tests of controls, an auditor incorrectly assesses control risk lower than appropriate.
The most likely explanation for this situation is that

Answer 5

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.
If the auditor has incorrectly assessed control risk lower than appropriate, the sample deviation rate must have been less than the actual rate and the actual population rate exceeds the tolerable rate. This would cause the auditor to accept the control as effective when it really was not and, thus, to assess control risk lower than appropriate.

Question 6

The sample size of a test of controls varies inversely with

Answer 6

The sample size of a test of controls varies inversely with the tolerable deviation rate. It varies directly with the expected population rate.

Question 7

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 the
I. Likely rate of deviations.

II. Allowable risk of assessing control risk too high.

Answer 7

This is an audit sampling question for a test of controls. In order to correctly answer it, you must know the definitions for tolerable rate of deviation, likely rate of deviations, and allowable risk of assessing control risk too high. The tolerable rate of deviation is the “maximum rate of deviations from prescribed controls that would support (the auditor’s) planned assessed level of control risk.” In other words, this is the rate at which the control procedure was NOT applied.
The likely rate of deviations is the expected population error rate. The allowable 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 auditor considers the tolerable rate of deviation, the likely rate of deviation, and the allowable risk of assessing control risk too LOW in determining sample size for a test of controls.

Question 8

Which of the following most likely would be an advantage in using classical variables sampling rather than probability-proportional-to-size (PPS) sampling?

Answer 8

Inclusion of zero and negative balances generally does not require special design considerations.
Because PPS sampling utilizes dollar units for sampling, the inclusion of zero and negative balances requires special design considerations. This would be an advantage for classical variables sampling, rather than PPS sampling.

Question 9

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

Answer 9

Precision.
Classical sampling methods are based on the normal curve distribution. They calculate a “best estimate” of a population value and then provide confidence intervals around that estimate. The width of the confidence interval is the precision of the estimate, or the possible error in either direction.

Question 10

In a PPS sampling application, the sampling interval was $6,000. The auditor discovered that a selected account receivable having a recorded amount of $5,000 had an audit amount of $1,000. What was the projected error associated with this sample?

Answer 10

$ 4,800
When the recorded balance of the account involved is less than the sampling interval, the auditor must determine the “tainting” percentage and apply that percentage to the sampling interval. In this case the tainting percentage = [($5,000 − $1,000)/$5,000] = 80%. Accordingly, the projected misstatement is $6,000 × 80% = $4,800.

Question 11

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?

Answer 11

Reevaluate the risk of fraud and design alternate tests for the related transactions.
Fraud risk increases when copies of documents are provided instead of originals and more so when they are related to a single vendor, rather than multiple vendors. The auditor will need to obtain other evidence to support the transactions in question.

Question 12

Which of the following statements is correct concerning statistical sampling in tests of controls?

Answer 12

Deviations from specific internal control procedures at a given rate ordinarily result in misstatements at a lower rate.
Deviations from specific control activities at a given rate ordinarily result in misstatements at a lower rate because each failure to apply a control does not necessarily result in a misstatement.

Question 13

As a result of sampling procedures applied as tests of controls, an auditor incorrectly assesses control risk lower than appropriate.
The most likely explanation for this situation is that

Answer 13

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.
If the auditor has incorrectly assessed control risk lower than appropriate, the sample deviation rate must have been less than the actual rate and the actual population rate exceeds the tolerable rate. This would cause the auditor to accept the control as effective when it really was not and, thus, to assess control risk lower than appropriate.

Question 14

The use of the ratio estimation sampling technique is most effective when

Answer 14

The calculated audit amounts are approximately proportional to the client’s book amounts.
Ratio estimation is most efficient when the differences are proportional to book values. If the calculated audit amounts are approximately proportional to the book amounts, a correlation exists between book values and the individual differences, and ratio estimation will be effective.

Question 15

Stratified mean per unit (MPU) sampling is a statistical technique that may be more efficient than unstratified MPU because it usually

Answer 15

Produces an estimate that has a desired level of precision with a smaller sample size.
Stratification of the population enables the auditor to separate the population into size-related classes. For example, all transactions over $50,000 may be grouped into a class.
Applying MPU sampling to these strata or classes will then result in a higher level of precision for a smaller sample size.

Question 16

In statistical sampling methods used in substantive testing, an auditor most likely would stratify a population into meaningful groups if

Answer 16

The population has highly variable recorded amounts.
A population with highly variable recorded amounts will have amounts that cover a wide range. Stratifying such a population would involve separating the population into homogeneous groups based on size or other factors. In this manner, the auditor could select transactions to meet specific audit objectives and perform substantive procedures more efficiently. For example, the auditor could select all of the larger transactions over a specific dollar amount and a portion of the smaller transactions.

Question 17

Which of the following is the primary objective of probability proportional to sample size?

Answer 17

To identify overstatement errors.
PPS sampling is most effective in detecting overstatements, since the likelihood of an item’s selection increases with the recorded magnitude of the item.