When using sampling for substantive tests of details, the auditor is required to do what?

Determine the tolerable misstatement

Project the sample misstatement to the population

Select a representative sample.

What is non sampling risk?

The risk that the auditor reaches an erroneous conclusion for any reason not related to sampling risk.

What is sampling risk?

The risk that the auditor’s conclusion based on a sample may be different from the conclusion if the entire population were subjected to the same audit procedure.

As a result of tests of controls, an auditor underrelies on controls. This incorrect assessment most likely occurred because

Operating effectiveness based on the auditor’s sample is less than the true operating effectiveness of the controls.

In attribute sampling, a 10% change in which factors normally will have the least effect on the size of a statistical sample?

Population size.

A change in the size of the population has a very small effect on the required sample size when the population is large. As the population increases, the sample size also increases but at a decreasing rate.

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

Measure the sufficiency of the evidence obtained.

Statistical sampling helps the auditor to design an efficient sample, to measure the sufficiency of the evidence obtained, and to evaluate the sample results. Auditors are required to obtain sufficient appropriate evidence. Sufficiency is the measure of the quantity of evidence. It relates to the design and size of the sample.

An auditor is concerned with two aspects of sampling risk in performing substantive tests of details: the risk of incorrect acceptance and the risk of incorrect rejection. The risk of incorrect acceptance is the risk that:

an auditor erroneously concludes that a material misstatement does not exist when, in fact, it does.

The risk of incorrect rejection is the risk that:

the sample supports the conclusion that a material misstatement does exist when, in fact, it does not.

What is attribute sampling?

refers to an audit sampling application for the purpsoe of estimating the percentage of a population that contains a characteristic (attribute) of interest to the auditor. This involves testing the operating effectiveness of internal control, where, for each transaction included in the sample, the control procedure of interest is either performed approprately or not. For each item in the sample there are only 2 outcomes. (authorized or not, signed or not)

An advantage of statistical over nonstatistical sampling methods in tests of controls is that the statistical methods

Provide an objective basis for quantitatively evaluating sample risks.

In a sampling application, the group of items about which the auditor wants to estimate some characteristic is called the

A.Attribute of interest.

B.Population.

C.Sampling unit.

D.Sample.

Population.

The population is the group of items about which an auditor wishes to draw conclusions. However, the difference between the targeted population (the population about which information is desired) and the sampled population (the population from which the sample is actually drawn) should be understood.

A principal advantage of statistical methods of attribute sampling over nonstatistical methods is that they provide a scientific basis for planning the

Sample size.

Statistical theory permits the auditor to measure sampling risk and to restrict it to an acceptable level. Statistical methods determine the sample size that will accomplish the auditor’s objectives.

Stratifying a population means:

dividing it into subpopulations, thereby permitting application of different sampling techniques to each subpopulation or stratum. Stratifying allows for greater emphasis on larger or more important items.

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

The calculated audit amounts are approximately proportional to the client’s carrying amounts.

Ratio estimation calculates the population misstatement by multiplying the carrying amount of the population by the ratio of the total audit amount of the sample items to their total carrying amount. The precision is determined by considering the variances of the ratios of carrying amount to audited amount. Thus, the more homogeneous the ratios, the smaller the precision.

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

The population has highly variable recorded amounts.

The primary objective of stratification is to reduce the effect of high variability by dividing the population into subpopulations. Reducing the effect of the variance within each subpopulation allows the auditor to sample a smaller number of items while holding precision and the confidence level constant

What is unrestricted random sampling?

Unrestricted random sampling means that each item in the population has an equal and nonzero chance of being selected. Sampling with replacement means that an item may be included more than once in the sample. Sampling without replacement removes an item from the population after selection. Thus, sampling without replacement uses information about the population more efficiently. It results in a smaller sample, if other things are held constant, because the sample size formula for sampling with replacement is multiplied by the finite population correction factor (always less than 1.0).

A CPA’s client wishes to determine inventory shrinkage by weighing a sample of inventory items. If a stratified random sample is to be drawn, the strata should be identified in such a way that

Each stratum differs as much as possible with respect to expected shrinkage, but the shrinkages expected for items within each stratum are as close as possible.

When the items in a population are heterogeneous, it may be advantageous to stratify the population into homogeneous subpopulations. Each stratum should differ from the others, but the items within each stratum should be similar.

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

Produces an estimate having a desired level of precision with a smaller sample size.

The primary objective of stratification is to reduce the effect of high variability by dividing the population into subpopulations. Reducing the variance within each subpopulation allows the auditor to sample a smaller number of items while holding precision and confidence level constant.

What is the primary objective of monetary-unit sampling (MUS)?

To identify overstatement errors.

MUS gives each monetary unit in the population an equal chance of selection. However, the auditor does not examine an individual monetary unit but uses it to identify an entire transaction or balance to audit (the logical sampling unit). MUS is useful only for tests of overstatements (e.g., of assets) because a systematic selection method is applied (every nth monetary unit is selected). Accordingly, the larger the transaction or balance, the more likely it will be selected. This method is inappropriate for testing a population (e.g., liabilities) when understatement is the primary audit consideration.

To quantify the risk that sample evidence leads to erroneous conclusions about the sampled population,

Each item in the sampled population must have an equal or known probability of being selected.

Probability (random) sampling is used in any sampling plan in which every item in the population has an equal (or known) and nonzero probability of being chosen. A probability sample permits the use of statistical methods based on the laws of probability to quantify an estimate of sampling risk.

The major reason that the difference and ratio estimation methods are expected to produce audit efficiency is that the

Variability of the populations of differences or ratios is less than that of the populations of carrying amounts or audited values.

Difference estimation approximates total misstatement in the population by calculating the mean difference between the audited and carrying amounts in the sample and then multiplying by the number of population items. Ratio estimation approximates the total population misstatement by multiplying the proportion of the sample misstatement times the population carrying amount. The variability in both of these estimates is likely to be smaller than the variability within the population. Because the sample size varies directly with the variability of the population, the use of differences or ratios will usually allow for smaller sample sizes and greater efficiency in sampling.

When assessing the tolerable population deviation rate, the auditor should consider that, although control deviations increase the risks of material misstatement, such deviations do not necessarily result in misstatements. This consideration explains why

A recorded disbursement that does not show evidence of required approval may nevertheless be a transaction that is properly authorized and recorded.

The failure to apply controls does not automatically result in a misstatement of the accounting records. But the deviation does increase the risk of material misstatement.

A test of controls is an application of attribute sampling. The initial size for an attribute sample is based on:

(1) the desired assurance (complement of the risk of overreliance) that the tolerable population deviation rate is not exceeded by the actual rate,

(2) the tolerable population deviation rate,

(3) the expected population deviation rate, and

(4) the population size. However, a change in the size of the population has a very small effect on the required sample size when the population is large. Consequently, population size is often not considered unless it is small.

Does tolerable misstatement relate to test of controls or test of details?

Tests of details.

What does an auditor usually needs to consider in planning a particular audit sample for a tests of controls?

Acceptable risk of overreliance.

A test of controls is an application of attribute sampling. The initial size for an attribute sample from a large population is based on the desired assurance (complement of the risk of overreliance) that the tolerable population deviation rate is not exceeded by the actual rate.

What kind of relationship exists between a sample size and the tolerable population deviation rate?

The relationship is inverse.

The tolerable population deviation rate is set by the auditor. The auditor seeks to obtain appropriate assurance that this rate is not exceeded by the actual rate. The sample size and the tolerable population deviation rate have an inverse relationship because the degree of assurance to be provided by the sample is higher (lower) when the tolerable population deviation rate is lower (higher).

Explain overreliance and underreliance in regards to effectiveness and efficiency?

**overreliance** on a control leads to an unjustified reduction in substantive testing, thereby decreasing the **effectiveness** of the audit. However, **underreliance** on a control results in an unneeded increase in substantive testing but most likely does not decrease ultimate audit effectiveness. (efficiency)

An auditor who uses statistical sampling for attributes in testing internal controls should reduce the planned reliance on a prescribed control when the

Sample rate of deviation plus the allowance for sampling risk exceeds the tolerable population deviation rate.

If the sample deviation rate plus the allowance for sampling risk exceeds the tolerable population deviation rate, the sample results do not support the planned risk of overreliance. Thus, the risk of overreliance should be assessed at a higher level. The result is a lower acceptable level of detection risk for a given audit risk and an increase in the assurance to be provided by substantive testing.

Attribute sampling is typically used to test controls. The factors necessary to determine sample size include:

(1) the desired assurance (complement of the risk of overreliance) that the tolerable population deviation rate is not exceeded by the actual rate,

(2) the tolerable population deviation rate, and

(3) the expected population deviation rate. The population is usually assumed to be infinite, and tables are used to identify the appropriate sample size.

Tests of controls, such as tests whether check requests have been properly authorized, are binary in nature. The auditor determines whether the control has been applied. Are dollar amount relevant in this form of testing?

Dollar amounts are irrelevant in this form of testing. However, in sampling, the auditor must consider the acceptable risk of overreliance to determine sample size. The auditor also must estimate a population deviation rate.

Attribute sampling is best for test of controls or tests of details?

Tests of controls, because attribut sampling tests binary questions, such as yes or no. It is best used to test the effectiveness of internal controls because it can estimate the rate of control deviations.

What would be a consideration in planning an auditor’s sample for a test of controls?

The auditor’s allowable risk of overreliance.

When performing tests of controls with respect to the effectiveness of internal controls related to cash receipts, an auditor 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, thus destroying the sample randomness.

Many statistical estimates may be useful to an auditor. But most are either of a quantity or a deviation rate. The statistical terms that correspond to quantities and deviation rates, respectively, are

Variables and attributes.

Variables sampling is used by auditors to estimate quantities or dollar amounts in substantive testing. Attribute sampling applies to testing of internal controls and is used to estimate a deviation rate (occurrence rate) within a population.

Statistical sampling may be used to test the effectiveness of controls. The auditor’s procedures should result in a statistical conclusion about

The relation of the population deviation rate to the tolerable rate.

The auditor uses attribute sampling to test the effectiveness of controls. The auditor is concerned with the occurrence rate of procedural deviations in the population. Attribute sampling enables the auditor to estimate the occurrence rate of deviations and to determine the relation of the estimated rate to the tolerable rate.

What is an auditor’s evaluation of a statistical sample for attributes when a test of 50 documents results in 3 deviations if the tolerable rate is 7%, the expected population deviation rate is 5%, and the allowance for sampling risk is 2%?

Modify the assessed risk of material misstatement because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable deviation rate.

The sample has a 6% (3 ÷ 50) deviation rate. The auditor’s achieved upper deviation limit is 8% (6% + the 2% allowance for sampling risk). The allowance for sampling risk may be calculated from a standard table as the difference between the upper deviation limit and the sample rate. However, the allowance is given. Thus, the true deviation rate could be as large as 8% and exceed the tolerable rate. Accordingly, the auditor should revise the assessed risk of material misstatement for the relevant assertions and possibly alter the nature, timing, and extent of substantive procedures.

Statistical sampling usually may be applied in tests of controls when the client’s internal controls

Leave an audit trail in the form of documentary evidence of their effectiveness.

Sampling is useful when a population can be identified from which to sample. When attribute sampling is applied in tests of controls, an audit trail of documents and notations on them (such as signatures) should exist to provide evidence of the effectiveness of the control.

Variables sampling samples dollar amounts or other quantities. The purpose of variables sampling is to:

is to estimate a measure of a population.

When using classical variables sampling for estimation, an auditor normally evaluates the sampling results by calculating the possible misstatement in either direction. This statistical concept is known as

Precision.

The precision or confidence interval (allowance for sampling risk) is an interval around the sample statistic that is expected to include the true value of the population at the specified confidence level. When using classical variables sampling, the allowance for sampling risk is calculated based on the normal distribution.

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 and Risk of incorrect rejection.

Four factors are considered in determining the sample size for mean-per-unit estimation. Those factors include (1) the population size, (2) an estimate of population variation (the standard deviation), (3) the risk of incorrect rejection (its complement is the confidence level), and (4) the tolerable misstatement (the desired allowance for sampling risk is a percentage thereof, and this percentage is a function of the risk of incorrect rejection and the allowable risk of incorrect acceptance).

An auditor examining inventory most likely would use variables sampling rather than attributes sampling to

Estimate whether the dollar amount of inventory is reasonable.

Variables sampling is used by auditors to estimate quantities or dollar amounts in substantive testing. Attribute sampling applies to tests of controls and is used to estimate a deviation rate (occurrence rate) for a population. Thus, an auditor who wants to estimate whether the dollar amount of inventory is reasonable uses variables sampling.

Variables sampling is used to estimate the amount of misstatement in, or the value of, a population. In auditing, this process entails:

entails estimating the monetary value of an account balance or other accounting total. The estimated population standard deviation is used in the sample size formula for variables estimation. Hence, it should be stated in dollar terms.

The size of a sample designed for dual-purpose testing should be

The larger of the samples that would otherwise have been designed for the two separate purposes.