MODULE EOverview of SamplingLEARNING OBJECTIVESReview Checkpoints MultipleChoiceExercises andProblems1. Understand the basic principles ofsampling, including the differencesbetween statistical and nonstatisticalsampling and sampling andnonsampling risk. 1, 2, 3, 4, 5, 6 26, 27, 28, 29, 30,31, 33, 34, 35, 36,37, 38, 44, 46, 4751, 52, 53, 54, 55,56, 63, 66, 672. Understand the basic steps andprocedures used in conducting asampling plan. 7, 8, 9, 10, 11, 12,1332, 39, 48, 49 55, 57, 58, 59, 60,61, 62, 63, 64, 65,68, 703. Identify the two situations in whichsampling is used in an auditexamination. 14, 15, 16, 17, 18,19, 20, 2140, 41, 42, 43, 45,50714. Understand how the basic steps andprocedures used in a sampling planapply to an audit examination.22, 23, 24 25 69,72, 73, 74SOLUTIONS FOR REVIEW CHECKPOINTSE.1 Sampling can be used by the auditor during the study and evaluation of a client’s internal contsubstantive procedures.E.2 Sampling risk is the likelihood that the decision made based on the sample will differ from the decisionthat would have been made if the entire population had been examined, which is a sampling error.Sampling error arises when the sample drawn from the population does not appropriately represent thatpopulation.E.3 Nonsampling risk is the likelihood that an incorrect conclusion will be reached because of reasonsunrelated to sampling, which is a nonsampling error. Nonsampling error arises because of errors injudgment or execution of the sampling plan.E.4 Sampling risk is controlled by the auditor by (1) determining an appropriate sample size and (2) evaluatingsample results to consider the possibility that the sample does not appropriately represent the population.E.5 Statistical sampling is a plan that applies the laws of probability to select items for examination andevaluates the results. Statistical sampling plans differ from nonstatistical sampling plans in terms of themethods used to determine the appropriate sample size and evaluate the sample results. In a statisticalsampling plan, these methods control exposure to sampling risk, whereas they do not do so in anonstatistical sampling plan.E.6 Both statistical sampling and nonstatistical sampling can be used under generally accepted auditingstandards. Nonstatistical sampling should not be used solely to reduce sample size.E.7 1. Determine the objective of sampling.2. Define the characteristic of interest.3.Define the population.4.Determine the sample size.5.Select sample items.6.Measure sample items.7.Evaluate the sample results.E.8 It is important to carefully define the population of interest because the results of the entire samplingapplication will be based on the population from which the sample is drawn.E.9 Sampling risk has an inverse relationship with sample size; that is, as a lower level of sampling risk isnecessary, the individual needs to select a larger sample (and vice versa).E.10 Four methods commonly used to select sample items are (a) unrestricted random selection, (b) systematicrandom selection, (c) haphazard selection, and (d) block selection.When using unrestricted random selection, a series of random numbers is identified and the randomnumbers are matched to numbered items in the corresponding population.When using systematic random selection, a random starting point is selected within the population. A fixednumber of items are bypassed and the corresponding item in the population is selected. This process iscontinued until the number of items equal to the appropriate sample size is selected.Haphazard selection identifies sample items in a nonsystematic manner with no deliberate effort to matchrandom numbers to sample items. When using this selection method, care should be taken to eliminate anybias.Block selection identifies a series of contiguous (adjacent) units for selection.E.11 Unrestricted random selection and systematic random selection can be used with statistical samplingbecause these methods (a) provide a reasonable likelihood of selecting a representative sample, (b) allowthe probability of selecting sample items to be determined, and (c) allow the sample selection process to bereplicated.E.12 The precision (or allowance for sampling risk) is the numeric distance from the estimated populationvalue in which the true (but unknown) population value may lie with a given probability.Reliability (or confidence) is the likelihood that the true population value lies within the precision interval.The precision interval is a range around the sample estimate that has a likelihood (equal to reliability, or100 percent minus the sampling risk) of including the true population value.E.13 The following are the basic steps in evaluating sample results:a.Select and measure sample items to determine the sample estimate.b.Based on the acceptable sampling risk, determine the reliability and related precision.c.Form the precision interval by adding and subtracting the precision from the sample estimate.d.Determine whether the hypothesized (or acceptable) value falls within the precision interval.E.14 Attributes sampling is a method used to determine the extent to which a particular characteristic (orattribute) exists within a population. In an audit examination, attributes sampling is used in the study andevaluation of internal control and subsequent assessment of control risk.E.15 The tolerable rate of deviation is the maximum rate of deviations from a control that an audit teampermits without reducing the planned reliance on internal control. The audit team compares an “adjusted” sample deviation rate (upper limit rate of deviation) to the tolerable rate of deviation to determine the extentto which the auditor can rely on internal control.E.16 The risk of underreliance (risk of assessing control risk too high) occurs when the auditor’s sampleindicates that the control is not functioning effectively when, in fact, it is doing so. When this risk occurs,upper limit rate of deviation exceeds the tolerable rate of deviation. However, unknown to the the auditor’sauditor, the true population deviation rate is less than the tolerable rate of deviation.The risk of overreliance (risk of assessing control risk too low) occurs when the auditor’s sampleindicates that the control is functioning effectively when, in fact, it is not. When this risk occurs, theauditor’s upper limit rate of deviation is less than the tolerable rate of deviation. However, unknown to theauditor, the true population deviation rate exceeds the tolerable rate of deviation.The risk of underreliance results in an efficiency loss for the auditor because she or he performs moreextensive substantive procedures than are necessary. The risk of overreliance exposes the auditor to aneffectiveness loss because the auditor’s substantive procedures will not reduce audit risk to the acceptablelevel.E.17 The risk of overreliance is of more concern to the audit team because it may eventually result in theissuance of an unmodified opinion on financial statements that are materially misstated.E.18 Variables sampling is used to examine a population when the auditor wants to estimate the amount (orvalue) of some characteristic of that population. The auditor uses variables sampling when performingsubstantive procedures to evaluate the fairness of an account balance or class of transactions.E.19 Tolerable misstatement is the maximum amount by which an account balance or class of transactions canbe misstated and be accepted by the audit team as being fairly presented. The auditors compare anupper limit on misstatement) to the tolerable misstatement to determine “adjusted” sample misstatement (whether the account balance is materially misstated.E.20 The two sampling risks associated with variables sampling are (a) the risk of incorrect acceptance and (b)the risk of incorrect rejection. The risk of incorrect acceptance is the likelihood that the sample resultsindicate the account balance is fairly stated when, in fact, it is materially misstated. The risk of incorrectrejection is the likelihood that the sample results indicate that the account balance is materially misstatedwhen, in fact, it is fairly stated.Incorrect acceptance exposes the auditor to an effectiveness loss because the auditor will make an incorrect conclusion and issue an inappropriate opinion on the financial statements.Incorrect rejection exposes the auditor to an efficiency loss because additional transactions or components will be examined prior to proposin g an adjustment to the client’s account balance.E.21 Auditors are more concerned with the risk of incorrect acceptance because it may result in issuing anunmodified opinion on financial statements that are materially misstated.E.22 The objective of attributes sampling is to assess the operating effectiveness of a key control. The objectiveof variables sampling is to estimate the amount of misstatement in or the value of an account balance orclass of transactions.E.23 The factors that affect the sample size in an attributes sampling application (as well as their relationship tosample size) are:Population size (direct relationship).Expected rate of deviation (direct relationship).Tolerable rate of deviation (inverse relationship).Sampling risk (inverse relationship).E.24 The factors that affect the sample size in a variables sampling application (as well as their relationship tosample size) are:Population size (direct relationship).Expected misstatement (direct relationship).Tolerable misstatement (inverse relationship).Sampling risk (inverse relationship).Population variability (direct relationship).SOLUTIONS FOR MULTIPLE-CHOICE QUESTIONSE.25 a. Incorrect When sampling, the auditor performs procedures on less than 100 percent of theitems in a balance.b.Correct When sampling, the auditor performs procedures on less than 100 percent of theitems in a balance to form a conclusion about the entire balance.c.Incorrect Becoming familiar with an accounting system is not an application of auditsampling.d.Incorrect Performing analytical procedures is not an application of audit sampling.E.26 a. Incorrect Statistical sampling is characterized by mathematical evaluation of the results.b.Incorrect Statistical sampling is characterized by representative sample selection.c.Correct Statistical sampling is characterized by both representative sample selection andmathematical evaluation of the results.d.Incorrect Statistical sampling is characterized by both representative sample selection andmathematical evaluation of the results.E.27 a. Incorrect Sampling is typically most appropriate for populations consisting of a largenumber of items.b. Correct Sampling is appropriate when the need for precise information about thepopulation is not important.c. Incorrect More critical decisions would typically increase the need to examine the entirepopulation.d. Incorrect Sampling is not appropriate when the costs of an incorrect decision areextremely high.E.28 a. Incorrect Audit risk is the likelihood that auditors will unknowingly fail to modify theiropinion on financial statements that are materially misstated.b. Incorrect There is no term examination risk.c.Correct This response represents the correct definition of sampling risk.d.Incorrect Nonsampling risk is related to errors in judgment and execution, not to thenature of the sample.E.29 Note to instructor: Because this question asks students to identify the statement that is not a method thatauditors use to control their exposure to sampling risk during the examination, the response labeledis the one that will not assist in controlling the auditor’s exposure to sampling risk and the those “correct” labeled “incorrect” will assist.a. Incorrect This method assists in controlling the au ditor’s exposure to sampling risk.b. Correct Performing the appropriate audit procedure is related to nonsampling risk, notsampling risk.c. Incorrect This method assists in controlling the auditor’s exposure to sampling risk.d. Incorrect This method assists in controlling the auditor’s exposure to sampling risk.E.30 a. Incorrect Only statistical sampling methods measure the auditor’s exposure to samplingrisk.b. Incorrect Generally accepted auditing standards permit the use of either statisticalsampling or nonstatistical sampling methods.c. Incorrect Samples can be selected either randomly or judgmentally under nonstatisticalsampling methods.d. Correct Nonstatistical sampling is typically less complex than statistical sampling.E.31 a. Incorrect Block selection identifies a series of contiguous units for examination.selection of sample itemsb. Incorrect Haphazard selection is characterized by the auditor’ｓin an unstructured manner but without any intentional bias.c. Incorrect Systematic random selection uses a random starting point and then bypasses afixed number of items in selecting sample items.d. Correct Unrestricted random selection uses a series of random numbers to identifysample items.E.32 a. Incorrect The random starting point (10) is the first item selected. The sampling intervalwould be calculated as 5 (100 20 = 5). Adding the sampling interval to therandom starting point would result in item 15 being selected (10 + 5 = 15),followed by item 20 (15 + 5 = 20).b. Incorrect The random starting point (10) is the first item selected. The sampling intervalwould be calculated as 5 (100 20 = 5). Adding the sampling interval to therandom starting point would result in item 15 being selected (10 + 5 = 15),followed by item 20 (15 + 5 = 20).c. Correct The random starting point (10) is the first item selected. The sampling intervalwould be calculated as 5 (100 20 = 5). Adding the sampling interval to therandom starting point would result in item 15 being selected (10 + 5 = 15),followed by item 20 (15 + 5 = 20).d. Incorrect The random starting point (10) is the first item selected. The sampling intervalwould be calculated as 5 (100 20 = 5). Adding the sampling interval to therandom starting point would result in item 15 being selected (10 + 5 = 15),followed by item 20 (15 + 5 = 20).E.33 a. Incorrect Systematic random selection provides a relatively high likelihood of yielding arepresentative sample.b. Incorrect There is no difference in the sample size provided by systematic randomselection and other selection methods.c. Correct Because systematic random selection bypasses items between selections, alimitation may occur if the population is not randomly ordered.d. Incorrect Systematic random selection can be used with statistical sampling plans.E.34 a. Incorrect Block selection cannot be used with statistical sampling applications.b. Correct Of these two methods, only unrestricted random selection can be used withstatistical sampling applications.c. Incorrect Unrestricted random selection can be used with statistical sampling plans; blockselection cannot be used with statistical sampling applications.d. Incorrect Unrestricted random selection can be used with statistical sampling applications.E.35 a. Incorrect Block selection cannot be used with statistical sampling applications.b. Incorrect Neither block selection nor haphazard selection can be used with statisticalsampling applications.c. Incorrect Haphazard selection cannot be used with statistical sampling applications.d. Correct Unrestricted random selection and systematic random selection can be used withstatistical sampling applications.E.36 a. Incorrect The confidence is the likelihood that the precision interval contains the true (butunknown) population value.b. Incorrect The mean is the average of the observations in the sample.c. Correct The precision represents a range around the sample estimate that has a certainlikelihood (equal to reliability) of including the true population value.d. Incorrect The precision interval is the sample estimate plus and minus the precision.E.37 a. Correct The confidence is the likelihood that the precision interval contains the true (butunknown) population value.b. Incorrect The mean is the average of the observations in the sample.c. Incorrect The precision represents the closeness of a sample estimate to the truepopulation value.d. Incorrect The likelihood that the interval contains the true population value is confidence,or 1 minus sampling risk.E.38 Note to instructor: Because this question asks students to identify the statement that is not true, theresponse labeled “correct” is not true and those labeled “incorrect” are true.a. Incorrect Because there is a 90 percent (1 minus sampling risk) probability that theinterval contains the true population value, there is a 10 percent probability thatthe true population value lies outside this interval.b. Correct There is a 10 percent probability (sampling risk) that the true population value isless than 60 or more than 70.c. Incorrect Reliability equals 1 minus sampling risk, or 90 percent (1 minus 10 percent = 90percent).d. Incorrect Because the precision interval is symmetrical around the sample estimate, thesample estimate is the average of the precision interval, or 65 [(60 + 70) 2 =65)]. The precision can be determined as the distance between either bound ofthe precision interval and the sample estimate, or 5 (65 – 60 = 5).E.39 a. Incorrect Sampling risk is a characteristic of both statistical and nonstatistical samplingapplications.b.Incorrect This response is the definition of nonsampling risk.c.Incorrect This response is the definition of inherent risk.d.Correct This response is the definition of sampling risk.E.40 a. Correct Both the risk of incorrect acceptance and risk of assessing control risk too lowrelate to the effectiveness of an audit.b.Incorrect The risk of incorrect rejection and the risk of assessing control risk too highrelate to the efficiency of the audit.c.Incorrect Only the risk of assessing control risk too low is related to control riskassessments.d.Incorrect Only the risk of incorrect acceptance is related to evidence about assertions infinancial statements.E.41 a. Correct Attributes sampling is most frequently used during the auditor’s study ofinternal control.b. Incorrect Control sampling is not a type of sampling.c. Incorrect Monetary unit sampling is a form of variables sampling, which is used in thestantive procedures.auditor’s subd. Incorrect Variables sampling is used in the auditor’s substantive procedures.E.42 a. Incorrect Although attributes sampling occurs as part of the use of the audit risk model, itis most closely associated with the assessment of control risk.b. Correct Attributes sampling is most closely associated with the assessment of controlrisk.c. Incorrect Although attributes sampling allows the auditor to determine the acceptablelevel of detection risk, it is most closely associated with the assessment ofcontrol risk.d. Incorrect Attributes sampling is unrelated to inherent risk.E.43 a. Incorrect If the upper limit rate of deviation exceeds the tolerable rate of deviation,auditors reduce their reliance on controls. These responses are reversed.b. Correct If the upper limit rate of deviation exceeds the tolerable rate of deviation,auditors reduce their reliance on controls.c. Incorrect Auditors’ evaluation of controls is not related to the expected rate of deviation.evaluation of controls is not related to the expected rate of deviation.d. Incorrect Auditors’E.44 a. Incorrect Statistical sampling methods do not necessarily provide more assurance.b.Correct Statistical sampling methods allow the auditor to quantitatively measure theexposure to sampling risk.c.Incorrect Both statistical and nonstatistical sampling methods can convert samples intodual-purpose tests for substantive procedures.d.Incorrect Judgments are required to assess various factors that affect sample size underboth statistical and nonstatistical sampling.E.45 a. Incorrect The auditor would compare the upper limit rate of deviation to the tolerable rateof deviation (and not the expected rate of deviation) when using sampling in thestudy of internal control.b. Incorrect The auditor would compare the upper limit rate of deviation to the tolerable rateof deviation (and not the sample rate of deviation) when using sampling in thestudy of internal control.c. Incorrect The auditor would compare the upper limit rate of deviation to the tolerable rateof deviation (and not the statistical rate of deviation) when using sampling in thestudy of internal control.d. Correct The auditor would compare the upper limit rate of deviation to the tolerable rateof deviation when using sampling in the study of internal control.E.46 Note to instructor: Because this question asks students to identify the item that would not expose annot expose an individual toindividual to nonsampling risk, the response labeled “correct” wouldnonsampling risk, and the responses labeled “incorrect” would expose the individual to nonsampling risk.a. Incorrect Measuring the characteristic in an inappropriate manner would result inexposure to nonsampling risk.b. Correct If items selected are not representative of the population, this representssampling risk, not nonsampling risk.c. Incorrect A mistake in measurement (whether intentional or unintentional) would result inexposure to nonsampling risk.d. Incorrect Because (b) would not result in exposure to nonsampling risk, this choice wouldnot be appropriate.E.47 Note to instructor: Because this question asks students to identify the statement that is not true with respectnot true and those labeled “incorrect” are true to nonstatistical sampling, the response labeled “correct” isa. Correct Either statistical or nonstatistical sampling can be used in an audit conducted inaccordance with generally accepted auditing standards.b. Incorrect Nonstatistical sampling considers various factors in determining sample size.c. Incorrect Nonstatistical sampling does provide an estimate of the characteristic of interest.d. Incorrect Nonstatistical sampling requires the use of judgment in establishing factors thatwill be used to determine sample size among other areas.E.48 a. Incorrect Because a 90 percent probability exists that the average weight is between 110and 130 pounds, the likelihood that the average weight is more than 130 poundsis less than 10 percent because the average weight could be less than 110 pounds.b. Incorrect Because a 90 percent probability exists that the average weight is between 110and 130 pounds, the likelihood that the average weight is less than 110 pounds isless than 10 percent because the average weight could be more than 130 pounds.c. Incorrect The likelihood that the average weight is less than 110 pounds or more than 130pounds is 1 minus reliability, or 10 percent (not 90 percent).d. Correct A reliability (90 percent) probability exists that the average weight is in theprecision (in this case, 120 pounds ±interval bounded by the sample estimate ±10 pounds, or 110 pounds to 130 pounds).E.49 a. Correct The audit team would examine sample items and determine the sample estimateafter it determines the objective of the sampling application, the level ofreliability, and the appropriate sample size.b. Incorrect The desired level of reliability must be determined prior to selecting the sample,which precedes examining sample items.c. Incorrect Determining the objective of the sampling application is the first step in thesampling application.d. Incorrect Determining the appropriate sample size would occur prior to examining sampleitems.E.50 a. Incorrect In both cases, the auditor should ultimately make the correct decision withrespect to the client’s internal control or account balances.performing more extensive substantiveb.Correct Both risks may result in the auditor’ｓprocedures than necessary to control audit risk to acceptable levels.c.Incorrect Only the risk of incorrect rejection is related to preliminary estimates ofmateriality.d.Incorrect Only the risk of incorrect rejection is related to tolerable misstatement.SOLUTIONS FOR EXERCISES AND PROBLEMSE.51 Sampling Riska.Sampling risk is the likelihood that the decision made based on the sample will differ from thedecision that would have been made if the entire population had been examined.The two types of sampling risk are concluding that (1) the temperature will be above 50 degreeswhen it will be below 50 degrees and (2) the temperature will be below 50 degrees when it will beabove 50 degrees.b.The costs of sampling risk if you conclude that the temperature will be above 50 degrees but it isnot is that you will not pack heavy clothing and will be uncomfortable or forced to purchase heavyclothing during your trip.The cost of sampling risk if you conclude that the temperature will be below 50 degrees but it isnot is that you will unnecessarily pack heavy clothing.c.If you use statistical sampling, your sampling plan would calculate the effect of the acceptablelevel of sampling risk in determining the appropriate sample size and evaluating sample results.Nonstatistical sampling methods would not calculate the effect of sampling risk in determiningsample size or evaluating sample results.d.The primary advantage of statistical sampling is that it allows you to explicitly control yourexposure to sampling risk. The primary disadvantage of using statistical sampling is that it istypically more complex and time consuming than nonstatistical sampling.E.52 Sampling and Nonsampling Riska.NS (misplaced distance markers would result in the failure to accurately record yardage).b.S (golfers playing in a club championship would typically have a higher skill level than those notplaying in a club championship).c.NS (because a 3-wood will not hit the ball as long as a driver, your conclusion may be affected bythe club used, not the golf ball).d.S (a sample of golfers that includes only females will not be representative of the population).e.NS (the conclusions may be affected by the fact that the comparison golf balls are older, notinferior in quality to the Wilson golf balls).f.NS (failure to accurately record yardage may influence your conclusions).Note to instructor: Some students might classify items (c) and (e) as neither sampling risk nor nonsampling risk because they do not apparently relate to an error made in recording results. However, one couldcontend that the failure to ensure that the proper golf club or a new golf ball is being used is a form of error.The important point to make is that these issues do not relate to the representativeness of the samplealthough items (b) and (d) do relate to the representativeness of the sample.。
