CIA Exam Part 1: Study Unit 6

To use stratified variables sampling to evaluate a large, heterogeneous inventory, an appropriate criterion for classifying inventory items into strata is A. Monetary values. B. Number of items. C. Turnover volume. D. Storage locations.

Answer (A) is correct. In variables sampling, the objective is to estimate the dollar value of the population, in this case, inventory. Strata based on dollar values are the usual population characteristic.

If an internal auditor is sampling to test compliance with a particular company policy, which of the following factors should not affect the allowable level of sampling risk? A. The experience and knowledge of the auditor. B. The adverse consequences of noncompliance. C. The acceptable level of risk of making an incorrect audit conclusion. D. The cost of performing auditing procedures on sample selections.

Answer (A) is correct. Sampling risk is the possibility that engagement conclusions based on a sample may differ from those reached if the test were applied to all items in the population. The experience and knowledge of the auditor are elements of nonsampling risk.

The most appropriate methodology for drawing a sample from 3,000 time cards to check for signatures would be A. Interval sampling. B. Cluster sampling. C. Stratified sampling. D. Variables sampling.

Answer (A) is correct. Systematic (interval) sampling is accomplished by selecting a random start and taking every nth item in the population, if n is the sampling interval, computed by dividing the population by the size of the sample. The random start should be within the first interval. A systematic sampling plan assumes the items are arranged randomly in the population. If the auditor discovers that this is not true, a random selection method should be used. The population of time cards may be in random order.

An auditor is using the mean-per-unit method of variables sampling to estimate the correct total value of a group of inventory items. Based on the sample, the auditor estimates, with precision of ±4% and confidence of 90%, that the correct total is US $800,000. Accordingly, A. There is a 4% chance that the actual correct total is less than US $720,000 or more than US $880,000. B. The chance that the actual correct total is less than US $768,000 or more than US $832,000 is 10%. C. The probability that the inventory is not significantly overstated is between 6% and 14%. D. The inventory is not likely to be overstated by more than 4.4% (US $35,200) or understated by more than 3.6% (US $28,800).

Answer (B) is correct. A 90% confidence level implies that 10% of the time the true population total will be outside the computed range. Precision of ±4% gives the boundaries of the computed range: US $800,000 × 4% = US $32,000. Hence, the range is US $768,000 to US $832,000.

Which form of sampling is most likely to be used in a fraud investigation? A. Stop-or-go sampling. B. Discovery sampling. C. Acceptance sampling for attributes. D. Probability-proportional-to-size (PPS) sampling.

Answer (B) is correct. Attribute sampling tests the effectiveness of controls because it can estimate a rate of occurrence of control deviations in a population. Discovery sampling is a form of attribute sampling that is appropriate when only a single deviation might be critical, such as when an auditor investigates fraud. The sample size is calculated so that the sample includes at least one example of a deviation if it occurs in the population at a given rate.

In an attribute sampling application, holding other factors constant, sample size will increase as which of the following becomes smaller? A. Confidence coefficient. B. Population. C. Planned precision. D. Expected rate of occurrence.

Answer (C) is correct. In an attribute test, planned precision is inversely related to sample size; its decrease (tightening) will increase sample size.

The use of probability-proportional-to-size sampling is inefficient if A. Bank accounts are being examined. B. Statistical inferences are to be made. C. Each account is of equal importance. D. The number of sampling units is large.

Answer (C) is correct. Probability-proportional-to-size sampling, also called monetary-unit sampling, gives greater weight to larger, more significant items. If all items are of the same importance, PPS is inappropriate.

An auditor is conducting a survey of perceptions and beliefs of employees concerning an organization health care plan. The best approach to selecting a sample is to A. Focus on people who are likely to respond so that a larger sample can be obtained. B. Focus on managers and supervisors because they can also reflect the opinions of the people in their departments. C. Use stratified sampling where the strata are defined by marital and family status, age, and salaried/hourly status. D. Use monetary-unit sampling according to employee salaries.

Answer (C) is correct. Stratified sampling divides a population into subpopulations, thereby permitting the application of different techniques to each stratum. This approach reduces the effect of high variability if the strata are selected so that variability among the strata is greater than variability within each stratum. For example, one expects to find greater similarities among married people than between married people and unmarried people.

The degree to which the auditor is justified in believing that the estimate based on a random sample will fall within a specified range is called A. Sampling risk. B. Non-sampling risk. C. Confidence level. D. Precision.

Answer (C) is correct. The confidence level is the percentage of times that one would expect the sample to adequately represent the population. Thus, a confidence level of 90% should result in samples that adequately represent the population 90% of the time. In other words, given repeated random sampling from a normally distributed population, 90% of the confidence intervals that may be constructed from simple random samples will contain the population mean.

Fact Pattern: An auditor is testing on a company's large, normally distributed accounts receivable file. The objectives of the audit are to test end-of-period monetary balances and accounts receivable posting exception (error) rates. Question: 66 To test the accounts receivable file to compute an estimated monetary total, the auditor could use any one of the following sampling techniques except A. Difference or ratio estimation. B. Unstratified mean-per-unit estimation. C. Probability-proportional-to-size sampling. D. Attribute sampling.

Answer (D) is correct. Attribute sampling is used for applications involving binary (yes/no or right/wrong) propositions. Attribute sampling does not involve estimation of monetary amounts.

Which sampling plan requires no additional sampling once the first error is found? A. Stratified sampling. B. Attribute sampling. C. Stop-or-go sampling. D. Discovery sampling.

Answer (D) is correct. Discovery sampling is a form of attribute sampling used to identify critical deviations in a population. The occurrence rate is assumed to be at or near 0%, and the method cannot be used to evaluate results statistically if deviations are found in the sample. Hence, discovery sampling is used for tests of controls, but it is appropriate only when one deviation is critical. The sample size is calculated so that the sample will contain at least one example of a deviation if it occurs in the population at a given rate.

Monetary-unit sampling (MUS) is most useful when the internal auditor A. Is testing the accounts payable balance. B. Cannot cumulatively arrange the population items. C. Expects to find several material misstatements in the sample. D. Is concerned with overstatements.

Answer (D) is correct. MUS, also called probability-proportional-to-size (PPS) sampling, is a modified version of attribute sampling that relates deviation rates to monetary amounts. It uses the monetary unit as the sampling unit. MUS is appropriate for testing account balances, such as those for inventory and receivables, in which some items may be far larger than others in the population. In effect, MUS stratifies the population because the larger account balances have a greater chance of being selected.

When relatively few items of high monetary value constitute a large proportion of an account balance, stratified sampling techniques and complete testing of the high monetary-value items will generally result in a A. Simplified evaluation of sample results. B. Smaller nonsampling error. C. Larger estimate of population variability. D. Reduction in sample size.

Answer (D) is correct. Stratifying a population means dividing it into subpopulations, thereby reducing sample size. Stratifying allows for greater emphasis on larger or more important items.

Fact Pattern: An auditor is testing on a company's large, normally distributed accounts receivable file. The objectives of the audit are to test end-of-period monetary balances and accounts receivable posting exception (error) rates. Question: 65 The expected population exception rate is 3% for the accounts receivable posting processes. If the auditor has established a 5% tolerable rate, the auditor would use which sampling plan for testing the actual exception rate? A. Difference or mean-per-unit estimation. B. Discovery. C. Stratified. D. Attribute.

Answer (D) is correct. The accounts receivable posting exception rate would be determined using attribute sampling. Attribute sampling is used for applications involving binary (yes/no or right/wrong) propositions. Whether an item has been posted requires a yes/no answer.

An automobile parts manufacturer has received complaints from customers about declining quality. After a quick review, management realizes the problem has no single source. To perform a thorough process of problem identification, the most appropriate tool is a(n) A. Fishbone (Ishikawa) diagram. B. Histogram. C. Pareto diagram. D. ISO 9000 audit.

Answer (A) is correct. A fishbone diagram (also called a cause-and-effect diagram or an Ishikawa diagram) is a total quality management process improvement technique. It is useful in studying causation (why the actual and desired situations differ). This format organizes the analysis of causation and helps to identify possible interactions among causes.

In sampling applications, the standard deviation represents a measure of the A. Expected error rate. B. Level of confidence desired. C. Degree of data variability. D. Extent of precision achieved.

Answer (C) is correct. The standard deviation measures the variability within a population.

Fact Pattern: An individual is an internal auditor for a car rental agency that operates a fleet of 75,000 vehicles in 1,000 cities throughout North America. As a part of an operational audit, the auditor tested the impact of vehicle age on the incidence of major repairs. A computer program showed that 20% of the fleet has been in service for more than 12 months. A sample of 375 is drawn based on Confidence level = 95% Expected rate of occurrence = 10% Precision = ±3% The records related to repairs completed after 12 months of service for the selected vehicles were reviewed to determine if major repairs were needed. Question: 38 Assuming that all other factors remain constant, how would sample size and achieved precision be affected by a change in confidence level from 95% to 90%? A. Sample size would be smaller; achieved precision would be larger. B. Both sample size and achieved precision would be larger. C. Both sample size and achieved precision would be smaller. D. Sample size would be larger; achieved precision would be smaller.

Answer (A) is correct. Because the confidence coefficient of an attribute test is directly related to the sample size, a smaller coefficient would result in a smaller sample. Also, since sample size is inversely related to precision, a larger precision would result from using a smaller sample.

Which one of the following is not an important consideration in determining the appropriate sample size? A. Whether the sample is designed to estimate a mean or a proportion. B. The amount of variability in the population under study. C. The sensitivity of the decision using this sample to errors of estimation. D. The cost per sample observation.

Answer (A) is correct. Difference and ratio estimation use the same variables sampling formula. Hence, sample size considerations are the same for both.

Fact Pattern: An auditor is testing on a company's large, normally distributed accounts receivable file. The objectives of the audit are to test end-of-period monetary balances and accounts receivable posting exception (error) rates. Question: 64 The accounts receivable file contains a large number of small monetary balances and a small number of large monetary balances, and the auditor expects to find numerous errors in the account balances. The most appropriate sampling technique to estimate the monetary amount of errors is A. Difference or ratio estimation. B. Unstratified mean-per-unit. C. Probability-proportional-to-size. D. Attribute.

Answer (A) is correct. Difference estimation calculates the average difference between the audit and recorded amounts of sample items and multiplies by the number of items in the population. Ratio estimation multiplies the recorded amount of the population by the ratio of the observed amount of the sample to its total recorded amount. These methods are useful when small errors predominate and the errors are not skewed. If the number of errors is small, a very large sample is required to provide a representative difference between audit and recorded amounts.

A bank's internal auditor wishes to determine whether all loans are supported by sufficient collateral, properly aged regarding current payments, and accurately categorized as current or noncurrent. The best audit procedure to accomplish these objectives would be to A. Use generalized audit software to read the total loan file, age the file by last payment due, and extract a statistical sample stratified by the current and aged population. Examine each loan selected for proper collateralization and aging. B. Select a block sample of all loans in excess of a specified monetary limit and determine if they are current and properly categorized. For each loan approved, verify aging and categorization. C. Select a discovery sample of all loan applications to determine whether each application contains a statement of collateral. D. Select a sample of payments made on the loan portfolio and trace them to loans to see if the payments are properly applied. For each loan identified, examine the loan application to determine that the loan has proper collateralization.

Answer (A) is correct. In some cases, stratifying the population is done 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. This procedure is the most appropriate in this situation because it takes a sample from the total loan file and tests to determine that each sampling unit is properly categorized as well as properly collateralized and aged.

The internal auditor for an insurance company is conducting an audit of claims processing and wants to assess the average length of time taken to process automobile claims to determine whether processing is being completed within standards set by company policy. The auditor plans to take a sample of claims made during the year and perform the needed analysis. The most appropriate sampling method is A. Mean-per-unit variables sampling. B. Probability-proportional-to-size sampling. C. Attribute sampling. D. Discovery sampling.

Answer (A) is correct. Mean-per-unit (MPU) variables sampling averages audit values in the sample and multiplies by the number of items in the population to estimate the population value. This is the most appropriate sampling procedure because it allows the auditor to calculate the mean for the processing time and construct a confidence interval around the mean.

An auditor for the state highway and safety department needs to estimate the average highway weight of tractor-trailer trucks using the state's highway system. Which estimation method must be used? A. Mean-per-unit. B. Difference. C. Ratio. D. Probability-proportional-to-size.

Answer (A) is correct. Mean-per-unit sampling estimates the average value of population items, in this case, truck weight.

Fact Pattern: Using mean-per-unit sampling to estimate the value of inventory, an internal auditor had the following results: Projected inventory value US $3,000,000 Confidence level 95% Confidence interval $2,800,000 to $3,200,000 Standard error $100,000 Z-value (approximate) 2.0 Precision $200,000 The recorded value of inventory was US $3,075,000. Question: 45 If the internal auditor had used nonstatistical sampling instead of statistical sampling, which of the following would be true? A. The confidence level could not be quantified. B. The precision would be larger. C. The projected value of inventory would be less reliable. D. The risk of incorrect acceptance would be higher.

Answer (A) is correct. One advantage of statistical sampling is that it allows the auditor to quantify sampling risk and the confidence level. An auditor should never attempt to quantify the sampling risk or confidence level of a nonstatistically drawn sample.

When sampling methods are used, the concept of sufficiency of information means that the samples selected provide A. Reasonable assurance that they are representative of the sampled population. B. The best information that is reasonably obtainable. C. Reasonable assurance that the information has a logical relationship to the engagement objective. D. Absolute assurance that a sample is representative of the population.

Answer (A) is correct. Sufficient information is factual, adequate, and convincing so that a prudent, informed person would reach the same conclusions as the auditor (Inter. Std. 2310). If properly designed and executed, a statistical sample is representative of the sampled population.

An auditor tested a population by examining 60 items selected judgmentally and found one error. The main limitation of the auditor's sample is the inability to A. Quantify sampling risk. B. Quantify the acceptable error rate. C. Project the population's error rate. D. Determine whether the sample is random.

Answer (A) is correct. The limitation of all nonstatistical sampling techniques is the auditor's inability to quantify sampling risk. Based on past experience and intuition, the auditor may conclude that the sampling risk is acceptable, but the auditor is not able to quantify this risk.

In a sampling application, the group of items about which the auditor wants to estimate some characteristic is called the A. Population. B. Attribute of interest. C. Sample. D. Sampling unit.

Answer (A) is correct. The population is the group of items about which an auditor wishes to draw conclusions.

When planning an attribute sampling application, the difference between the expected error rate and the maximum tolerable error rate is the planned A. Precision. B. Reliability. C. Dispersion. D. Skewness.

Answer (A) is correct. The precision of an attribute sample (also called the confidence interval or allowance for sampling risk) is an interval around the sample statistic that the auditor expects to contain the true value of the population. In attribute sampling (used for tests of controls), the achieved precision is the difference between the sample deviation rate and the achieved upper deviation limit (customarily determined from a standard table given the sample deviation rate and the sample size).

Statistical sampling is appropriate to estimate the value of an auto dealer's 3,000 line-item inventory because statistical sampling is A. Reliable and objective. B. Thorough and complete. C. Thorough and accurate. D. Complete and precise.

Answer (A) is correct. The results of statistical (probability) sampling are objective and subject to the laws of probability. Hence, sampling risk can be quantified and controlled at a specified level of confidence (reliability). Sampling risk is the risk that the sample selected does not represent the population.

The variability of a population, as measured by the standard deviation, is the A. Extent to which the individual values of the items in the population are spread about the mean. B. Degree of asymmetry of a distribution. C. Tendency of the means of large samples (at least 30 items) to be normally distributed. D. Measure of the closeness of a sample estimate to a corresponding population characteristic.

Answer (A) is correct. The standard deviation measures the degree of dispersion of items in a population about its mean.

One standard deviation corresponds to what approximate percentage of the area under a bell curve? A. 34% B. 68% C. 90% D. 95.5%

Answer (B) is correct. A person selecting an item at random from a normally distributed population (one with a bell curve) can be 68% confident that the value of the item is within 1.0 standard deviation of the mean. Thus, that area under the curve corresponds to the 68% confidence level.

To project the frequency of shipments to wrong addresses, an internal auditor chose a random sample from the busiest month of each of the four quarters of the most recent year. What underlying concept of statistical sampling did the auditor violate? A. Attempting to project a rate of occurrence rather than an error rate. B. Failing to give each item in the population an equal chance of selection. C. Failing to adequately describe the population. D. Using multistage sampling in conjunction with attributes.

Answer (B) is correct. A random sample is one in which every item in the population has an equal and nonzero chance of being selected for the sample. Here, the auditor deliberately excluded shipments from the slower months.

Systematic selection can be expected to produce a representative sample when A. Random number tables are used to determine the items included in the sample. B. The population is arranged randomly with respect to the audit objective. C. The sample is determined using multiple random starts and includes more items than required. D. Judgmental sampling is used by the auditor to offset any sampling bias.

Answer (B) is correct. A sample selected using a systematic sampling procedure and a random start will behave as if it were a random sample when the population is randomly ordered with respect to the audit objective. Sampling bias due to systematic selection will be small when the population items are not arranged in a pattern.

Which of the following techniques could be used to estimate the standard deviation for a sampling plan? A. Difference estimation. B. Pilot sample. C. Regression. D. Discovery sampling.

Answer (B) is correct. Auditors may use the standard deviation of a pilot sample to estimate the standard deviation of a population.

Fact Pattern: Using mean-per-unit sampling to estimate the value of inventory, an internal auditor had the following results: Projected inventory value US $3,000,000 Confidence level 95% Confidence interval $2,800,000 to $3,200,000 Standard error $100,000 Z-value (approximate) 2.0 Precision $200,000 The recorded value of inventory was US $3,075,000. Question: 44 Which of the following changes will result in a narrower confidence interval? A. An increase in the confidence level from 95% to 99%. B. A decrease in the confidence level from 95% to 90%. C. A decrease in the allowable risk of incorrect rejection. D. An increase in the precision.

Answer (B) is correct. Decreasing the confidence level of any variables sample allows the auditor to narrow the confidence interval.

If all other factors in a sampling plan are held constant, changing the measure of tolerable misstatement to a smaller value will cause the sample size to be A. Smaller. B. Larger. C. Unchanged. D. Indeterminate.

Answer (B) is correct. The size of the precision interval in a variables test is based upon the tolerable misstatement that is determined by materiality judgments. As this value decreases, for example, because of a decrease in tolerable misstatement, the size of the required sample increases accordingly, and vice versa. Hence, tolerable misstatement (precision) and sample size are inversely related.

The appropriate sampling plan to use to identify at least one irregularity, assuming some number of such irregularities exist in a population, and then to discontinue sampling when one irregularity is observed is A. Stop-or-go sampling. B. Discovery sampling. C. Variables sampling. D. Attribute sampling.

Answer (B) is correct. Discovery sampling is a form of attribute sampling applied when a control is critical and a single deviation is important, for example, commission of a material fraud. The expected deviation rate should be at or near zero, and the sample size is calculated so that the sample will include at least one example of a deviation if it occurs in the population at a given rate.

An auditor applying a discovery-sampling plan with a 5% risk of overreliance may conclude that there is A. A 95% probability that the actual rate of occurrence in the population is less than the critical rate if only one exception is found. B. A 95% probability that the actual rate of occurrence in the population is less than the critical rate if no exceptions are found. C. A 95% probability that the actual rate of occurrence in the population is less than the critical rate if the occurrence rate in the sample is less than the critical rate. D. Greater than a 95% probability that the actual rate of occurrence in the population is less than the critical rate if no exceptions are found.

Answer (B) is correct. Discovery sampling is a form of attribute sampling that is appropriate when even a single deviation would be critical. The sample size is calculated so that it will include at least one instance of a deviation if deviations occur in the population at a given rate. If no exceptions are found, the correct conclusion is that the probability is 95% that the occurrence rate is less than the critical rate.

When an internal auditor's sampling objective is to obtain a measurable assurance that a sample will contain at least one occurrence of a specific critical exception existing in a population, the sampling approach to use is A. Random. B. Discovery. C. Probability-proportional-to-size. D. Variables.

Answer (B) is correct. Discovery sampling is a form of attribute sampling used to identify critical deviations in a population. The occurrence rate is assumed to be at or near 0%, and the method cannot be used to evaluate results statistically if deviations are found in the sample. Hence, discovery sampling is used for tests of controls, but it is appropriate only when one deviation is critical. The sample size is calculated so that the sample will contain at least one example of a deviation if it occurs in the population at a given rate.

Management is legally required to prepare a shipping document for all movement of hazardous materials. The document must be filed with bills of lading. Management expects 100% compliance with the procedure. Which of the following sampling approaches is most appropriate? A. Attribute sampling. B. Discovery sampling. C. Targeted sampling. D. Variables sampling.

Answer (B) is correct. Discovery sampling is a form of attribute sampling used to identify critical errors or irregularities, i.e., when the occurrence rate is assumed to be 0%.

In selecting a sample of items for variables testing, an auditor must consider the desired precision, the standard deviation, and the A. Recorded monetary amount of the population. B. Acceptable risk level. C. Expected occurrence rate. D. Sampling interval.

Answer (B) is correct. Four factors determine the size of a classical variables sample: the confidence coefficient, the estimated standard deviation of the population, the population size, and the tolerable misstatement (desired precision).

If all other factors specified in an attribute sampling plan remain constant, decreasing the confidence level from 95% to 90% would cause the required sample size to A. Increase. B. Decrease. C. Change by 5%. D. Remain the same.

Answer (B) is correct. In an attribute test, the confidence level is directly related to sample size. Hence, decreasing the confidence level permits a smaller sample size to be used.

If all other sample size planning factors were exactly the same in attribute sampling, changing the confidence level from 95% to 90% and changing the desired precision from 2% to 5% would result in a revised sample size that would be A. Larger. B. Smaller. C. Unchanged. D. Indeterminate.

Answer (B) is correct. In an attribute test, the confidence level is directly related, and the precision is inversely related, to sample size. Thus, if the confidence level is reduced and precision is widened, sample size will be smaller.

An internal auditor is planning to use attribute sampling to test the effectiveness of a specific internal control related to approvals for cash disbursements. In attribute sampling, decreasing the estimated occurrence rate from 5% to 4% while keeping all other sample size planning factors exactly the same would result in a revised sample size that would be A. Larger. B. Smaller. C. Unchanged. D. Indeterminate.

Answer (B) is correct. In an attribute test, the expected deviation rate is directly related to sample size. If it is decreased, sample size will decrease.

Which of the following factors would most likely prevent the auditor from using monetary-unit sampling? A. The auditor expects to find a limited number of understatements of individual account balances. B. The auditor expects to find that a large percentage of items sampled have misstatements. C. Individual accounts are not assigned a number, but are listed only alphabetically. D. The auditor expects to find more errors in the larger dollar value items than in the smaller dollar value items.

Answer (B) is correct. Monetary-unit sampling, also called probability-proportional-to-size sampling, combines attribute and variables sampling techniques. It uses the monetary unit as the sampling unit and effectively stratifies the population because larger items are more likely to be selected. Monetary-unit sampling is most useful when few misstatements are expected and overstatements are more likely than understatements.

In which of the following situations will monetary-unit sampling be more effective and efficient than ratio estimation? A. The population contains a large number of differences between the recorded amount and the actual amount. B. The population is expected to contain few differences between the recorded amount and the actual amount. C. The population has a high degree of variability in monetary amount. D. The population has a low degree of variability in monetary amount.

Answer (B) is correct. Monetary-unit sampling, also called probability-proportional-to-size sampling, is especially efficient and effective when the population contains few differences. However, variables sampling approaches (e.g., ratio estimation) tend to be more efficient (samples are smaller) as the amount of misstatement increases. Monetary-unit sampling is also inefficient when understatements and negative amounts are expected.

The auditor wishes to sample the perpetual inventory records to develop an estimate of the monetary amount of misstatement, if any, in the account balance. The account balance is made up of a large number of small-value items and a small number of large-value items. The auditor has decided to audit all items over US $50,000 plus a random selection of others. This audit decision is made because the auditor expects to find a large amount of errors in the perpetual inventory records but is not sure that it will be enough to justify taking a complete physical inventory. The auditor expects the errors to vary directly with the value recorded in the perpetual records. The most efficient sampling procedure to accomplish the auditor's objectives is A. Monetary-unit sampling. B. Ratio estimation. C. Attribute sampling. D. Stratified mean-per-unit sampling.

Answer (B) is correct. Ratio estimation estimates the population misstatement by multiplying the recorded amount of the population by the ratio of the total audit amount of the sample to its total recorded amount. It is reliable and efficient when small errors predominate and are not skewed. Thus, ratio estimation should be used in this situation because the auditor is not sampling the very large items and the errors are not skewed (they vary directly with the size of the recorded values).

In preparing a sampling plan for an inventory pricing test, which of the following describes an advantage of statistical sampling over nonstatistical sampling? A. Requires nonquantitative expression of sample results. B. Provides a quantitative measure of sampling risk. C. Minimizes nonsampling risk. D. Reduces the level of tolerable error.

Answer (B) is correct. Statistical and nonstatistical sampling are both used to project the characteristics of a population. However, statistical sampling permits the internal auditor to make a quantitative assessment of how closely the sample represents the population for a given level of reliability.

Question: 82 A health insurer uses a computer application to monitor physician bill amounts for various surgical procedures. This program allows the organization to better control reimbursement rates. The X-bar chart below is an example of the output from this application. Select the interpretation that best explains the data plotted on the chart. A. Random variation. B. Abnormal variation. C. Normal variation. D. Cyclic variation.

Answer (B) is correct. Statistical quality control charts are graphic aids for monitoring the status of any process subject to random variations. The X-bar chart presented here depicts the sample means for a variable. If the values fall within the upper and lower control limits, no action is taken. Accordingly, values outside these limits are abnormal and should be investigated for possible corrective action.

An auditor is designing a sampling plan to test the accuracy of daily production reports over the past 3 years. All of the reports contain the same information except that Friday reports also contain weekly totals and are prepared by managers rather than by supervisors. Production normally peaks near the end of a month. If the auditor wants to select two reports per month using an interval sampling plan, which of the following techniques reduces the likelihood of bias in the sample? A. Estimating the error rate in the population. B. Using multiple random starts. C. Increasing the confidence level. D. Increasing the precision.

Answer (B) is correct. Systematic (interval) sampling involves choosing a random start and then selecting subsequent items at fixed intervals. However, if the population is not random, for example, because it exhibits cyclical variation, the results will be biased. This bias may be overcome by taking repeated systematic samples, each with a random start. In effect, each possible systematic sample in the population is a cluster. Thus, the repeated systematic samples, each with a random start, constitute a random sample of clusters.

A random attribute sample taken from a large population should be representative. However, a random sample may not detect fraud. For this reason, the size of a random sample is most dependent on which of the following factors? A. The size of the population. B. The level of risk that the organization has accepted. C. The comprehensive basis of accounting used to prepare the organization's financial statements. D. The size of the internal audit function.

Answer (B) is correct. The confidence interval is the allowance for sampling risk. It is based on the confidence level, i.e., the percentage of times that a sample is expected to represent the population. The greater the desired confidence level, the larger the sample should be. Thus, the size of a random sample is related to the level of risk the organization is willing to accept.

How does stop-or-go attribute sampling differ from fixed-sample-size attribute sampling? A. Nonsampling error is smaller. B. Total expected sample size will always be smaller. C. Desired reliability does not have to be specified in advance. D. It cannot be used to determine the assessed level of control risk.

Answer (B) is correct. The objective of stop-or-go sampling, sometimes called sequential sampling, is to reduce the sample size when the auditor believes the error rate in the population is low. Thus, total expected sample size is always lower for stop-or-go sampling.

In evaluating an attribute sample, the range within which the estimate of the population characteristic is expected to fall is called A. Confidence level. B. Precision. C. Upper error limit. D. Expected error rate.

Answer (B) is correct. The precision of an attribute sample (also called the confidence interval or allowance for sampling risk) is an interval around the sample statistic that the auditor expects to contain the true value of the population. In attribute sampling (used in tests of controls), precision is determined by subtracting the expected error rate from the tolerable error rate in the population.

Using random numbers to select a sample A. Is required for a variables sampling plan. B. Is likely to result in an unbiased sample. C. Results in a representative sample. D. Allows auditors to use smaller samples.

Answer (B) is correct. The principal issue in statistical sampling is selecting a sample that is representative of the population, i.e., unbiased. This can be achieved by ensuring the sample is drawn randomly.

The statistical quality control department prepares a control chart showing the percentages of defective production. Simple statistical calculations provide control limits that indicate whether assignable causes of variation are explainable on chance grounds. The chart is particularly valuable in determining whether the quality of materials received from outside vendors is consistent from month to month. What is the best term for this chart? A. C chart. B. P chart. C. R chart. D. X-bar chart.

Answer (B) is correct. The question states that "the statistical quality control department prepares a control chart showing the percentages of defective production." P charts show the percentage of defects in a sample.

Which one of the following statements about sampling is true? A. A larger sample is always more representative of the underlying population than a smaller sample. B. For very large populations, the absolute size of the sample has more impact on the precision of its results than does its size relative to its population. C. For a given sample size, a simple random sample always produces the most representative sample. D. The limitations of an incomplete sample frame can almost always be overcome by careful sampling techniques.

Answer (B) is correct. When the size of the population is very large, the absolute size of the sample may vary considerably even though its size relative to the population does not.

Random numbers can be used to select a sample only when each item in the population A. Can be assigned to a specific stratum. B. Is independent of outside influence. C. Can be identified with a unique number. D. Is expected to be within plus or minus three standard deviations of the population mean.

Answer (C) is correct. A random sample is one in which every item in the population has an equal and nonzero chance of being selected and that selection is not influenced by whether any other item is selected.

A distinguishing characteristic of random number sample selection is that each A. Item is selected from a stratum having minimum variability. B. Item's chance for selection is proportional to its dollar value. C. Item in the population has an equal chance of being selected. D. Stratum in the population has an equal number of items selected.

Answer (C) is correct. A random sample is one in which every item in the population has an equal and nonzero chance of being selected.

Which of the following is(are) true when using cluster sampling? 1.Sampling units are groups of items. 2. Sample items within clusters need not be assigned random numbers. 3.The auditor selects every nth item after a random start. 4.The auditor uses cluster sampling when random sampling is not cost-effective. A. 1 only. B. 1 and 2 only. C. 1, 2, and 4 only. D. 1, 2, 3, and 4.

Answer (C) is correct. Cluster sampling is a sample selection method. Groups of items are randomly selected as the sampling units. For example, these groups (clusters) may consist of file drawers. From this sample, another sample may include all or some of the documents in the drawers. An advantage of cluster sampling is that individual items need not be assigned random numbers. Instead, clusters are randomly selected. Moreover, cluster sampling may be more cost-effective than random sampling.

Fact Pattern: An organization has collected data on the complaints made by personal computer users and has categorized the complaints. Question: 83 Using the information collected, the organization should focus on A. The total number of personal computer complaints that occurred. B. The number of computer complaints associated with CD-ROM problems and new software usage. C. The number of computer complaints associated with the lack of user knowledge and hardware problems. D. The cost to alleviate all computer complaints.

Answer (C) is correct. Complaints based on lack of user knowledge and hardware problems are by far the most frequent according to this chart. Consequently, the company should devote its resources primarily to these issues.

Difference estimation sampling would be appropriate to use to project the monetary error in a population if A. Subsidiary ledger book balances for some individual inventory items are unknown. B. Virtually no differences between the individual carrying amounts and the audited amounts exist. C. A number of nonproportional differences between carrying amounts and audited amounts exist. D. Observed differences between carrying amounts and audited amounts are proportional to carrying amounts.

Answer (C) is correct. Difference estimation of population error entails determining the differences between the audit and carrying amounts for items in the sample, calculating the mean difference, and multiplying the mean by the number of items in the population. This method is used when the population contains sufficient misstatements to provide a reliable sample and when differences between carrying and audit amounts are not proportional. If differences are proportional, ratio estimation is used. A sufficient number of nonproportional errors must exist to generate a reliable sample estimate.

An auditor has to make a number of decisions when using attribute sampling. The term efficiency is used to describe anything that affects sample size. The term effectiveness is used to describe the likelihood that the statistical sample result will be a more accurate estimate of the true population error rate. Assume an auditor expects a control procedure failure rate of 0.5%. The auditor is making a decision on whether to use a 90% or a 95% confidence level and whether to set the tolerable control failure rate at 3% or 4%. Which of the following statements regarding efficiency and effectiveness of an attribute sample is true? A. Decreasing the confidence level to 90% and decreasing the tolerable control failure rate to 3% will result in both increased efficiency and effectiveness. B. Decreasing the tolerable failure rate from 4% to 3% will increase audit efficiency. C. Increasing the confidence level to 95% and decreasing the tolerable control failure rate to 3% will increase audit effectiveness. D. Increasing the confidence level to 95% will increase audit efficiency.

Answer (C) is correct. In an attribute test, confidence level and expected deviation rate are in the numerator, while the tolerable deviation rate is in the denominator. Hence, increasing the confidence level increases the sample size, and decreasing the tolerable rate also increases the sample size. A larger sample increases audit effectiveness.

The size of a given sample is jointly a result of characteristics of the population of interest and decisions made by the internal auditor. Everything else being equal, sample size will A. Increase if the internal auditor decides to accept more risk of incorrectly concluding that controls are effective when they are in fact ineffective. B. Double if the internal auditor finds that the variance of the population is twice as large as was indicated in the pilot sample. C. Decrease if the internal auditor increases the tolerable rate of deviation. D. Increase as sampling risk increases.

Answer (C) is correct. In an attribute test, the tolerable deviation rate is inversely related to sample size. If it is increased, sample size will decrease.

In a variables sampling application, which of the following will result when confidence level is changed from 90% to 95%? A. Standard error of the mean will not be affected. B. Nonsampling error will decrease. C. Sample size will increase. D. Point estimate of the arithmetic mean will increase.

Answer (C) is correct. In any sampling application (attribute or variables), an increase in the confidence level requires a larger sample.

A specified range is based on an estimate of a population characteristic calculated from a random sample. The probability that the range contains the true population value is the A. Error rate. B. Lower precision limit. C. Confidence level. D. Standard error of the mean.

Answer (C) is correct. In principle, given repeated sampling and a normally distributed population, the confidence level is the percentage of all the precision intervals that may be constructed from simple random samples that will include the population value. In practice, the confidence level is regarded as the probability that a precision interval calculated from a simple random sample drawn from a normally distributed population will contain the population value.

An auditor was presented with a population of 1,253 invoices for the period under audit. The auditor selected every 60th invoice for testing. This is an example of A. Stop-or-go sampling. B. Cluster sampling. C. Interval sampling. D. Probability sampling.

Answer (C) is correct. Interval sampling selects every nth item after a random start. The value of n equals the population divided by the number of sampling units. The random start should be in the first interval. Because the sampling method requires only counting in the population, no correspondence between random numbers and sampled items is necessary. An interval sampling plan assumes the items are arranged randomly.

An internal auditor uses a number of techniques to select samples. A frequently, and appropriately, used technique is random selection. In which of the following situations would random selection be least justified? The auditor needs to A. Test sales transactions to determine that they were properly authorized and are supported by shipping documents. B. Confirm accounts receivable and has already selected the 10 largest accounts for confirmation. The remaining accounts are not numbered. The auditor only has a computer listing of the accounts in alphabetical order approximately 250 pages long with 50 account balances on every page. C. Obtain evidence on the proper sales cut-off by sampling items from the monthly sales journal to determine if the items were recorded in the correct time period. D. Test the perpetual inventory records to ensure that the sample covers the largest monetary value items in the account.

Answer (C) is correct. Random selection is the least justified for a sales cutoff test because the auditor is concerned that the monthly sales journal has been held open to record the next month's sales. The auditor should select transactions from the latter part of the month and examine supporting evidence to determine whether they were recorded in the proper period.

Which of the following must be known to evaluate the results of an attribute sample? A. Estimated dollar value of the population. B. Standard deviation of the sample values. C. Actual size of the sample selected. D. Finite population correction factor.

Answer (C) is correct. Sample size is used to evaluate the actual occurrence rate (number of a particular attribute identified ÷ actual sample size) of the attribute of interest, such as a control deviation.

Statistical quality control often involves the use of control charts whose basic purpose is to A. Determine when accounting control procedures are not working. B. Control labor costs in production operations. C. Detect performance trends away from normal operations. D. Monitor internal control applications of information technology.

Answer (C) is correct. Statistical control charts are graphic aids for monitoring the status of any process subject to random variations. The chart consists of three horizontal lines plotted on a horizontal time scale. The vertical scale represents the appropriate quantitative measure. The center line represents the average range or overall mean for the process being controlled. The other two lines are the upper control limit and the lower control limit. The processes are measured periodically, and the values are plotted on the chart. If the value falls within the control limits, no action is taken. If the value falls outside the limits, the process is considered "out of control," and an investigation is made for possible corrective action. Another advantage of the chart is that it makes trends visible.

In selecting a sample of items for attributes testing, an auditor must consider the confidence level factor, the desired precision, and the A. Recorded monetary amount of the population. B. Sampling interval. C. Expected occurrence rate. D. Standard deviation in the population.

Answer (C) is correct. The expected occurrence rate, also called the expected deviation rate, is one of the three necessary factors in determining sample size for an attribute test.

After partially completing an internal control review of the accounts payable department, an auditor suspects that some type of fraud has occurred. To ascertain whether the fraud is present, the best sampling approach is to use A. Simple random sampling to select a sample of vouchers processed by the department during the past year. B. Probability-proportional-to-size sampling to select a sample of vouchers processed by the department during the past year. C. Discovery sampling to select a sample of vouchers processed by the department during the past year. D. Judgmental sampling to select a sample of vouchers processed by clerks identified by the department manager as acting suspiciously.

Answer (C) is correct. The purpose is to determine whether fraud has occurred rather than to estimate its overall frequency. Discovery sampling is a method designed specifically for this purpose. It is a form of attribute sampling used to identify critical deviations in a population. The occurrence rate is assumed to be 0%, and statistical evaluation of results is impossible if deviations are found. Thus, discovery sampling is only appropriate when one deviation is critical.

Variability of the monetary amount of individual items in a population affects sample size in which of the following sampling plans? A. Attribute sampling. B. Monetary-unit sampling. C. Mean-per-unit sampling. D. Discovery sampling.

Answer (C) is correct. The sample size for a variable test depends on confidence level, population size, precision, and variability of the population. The standard deviation measures variability. The larger the standard deviation, the larger the sample size that is required to achieve specified levels of precision and confidence.

The measure of variability most useful in variables sampling is the A. Median. B. Range. C. Standard deviation. D. Mean.

Answer (C) is correct. The standard deviation is a mathematical measure of the variability of items in a population about its mean.

The measure of variability of a statistical sample that serves as an estimate of the population variability is the A. Basic precision. B. Range. C. Standard deviation. D. Confidence interval.

Answer (C) is correct. The standard deviation is a measure of variability. If the sample is representative, its standard deviation will approximate that of the population.

The standard error of a sample reflects A. The projected population error based on errors in the sample. B. The average rate of error in the sample. C. The degree of variation in sample items. D. The error in the population that the auditor can accept.

Answer (C) is correct. The standard error of the sample enables the auditor to assess the precision (confidence interval) used to describe the population. The greater the standard error, the higher the precision the auditor must use.

The director of sales asks for a count of customers grouped in descending numerical rank by (1) the number of orders they place during a single year and (2) the dollar amounts of the average order. The visual format of these two pieces of information is most likely to be a A. Fishbone (Ishikawa) diagram. B. Cost of quality report. C. Kaizen diagram. D. Pareto diagram.

Answer (D) is correct. A Pareto diagram (also known as 80:20 analysis) displays the values of an independent variable such that managers can quickly identify the areas most in need of attention.

Assume the internal auditor becomes concerned that significant fraud may be taking place by dentists who are billing the health care processor for services that were not provided. For example, employees may have their teeth cleaned, but the dentist charges the processor for pulling teeth and developing dentures. The most effective procedure to determine whether such a fraud exists is to A. Develop a schedule of payments made to individual dentists. Verify that payments were made to the dentists by confirming the payments with the health care processor. B. Take a random sample of payments made to dentists and confirm the amounts paid with the dentists' offices to determine that the amounts agree with the amounts billed by the dentists. C. Take a random sample of claims submitted by dentists and trace through the system to determine whether the claims were paid at the amounts billed. D. Take a discovery sample of employee claims that were submitted through dentist offices, and confirm the type of service performed by the dentist through direct correspondence with the employee who had the service performed.

Answer (D) is correct. A discovery sample is used to identify critical errors or irregularities, that is, when a single deviation is critical. This method cannot be used to evaluate the results statistically if deviations are found. Because dentists are suspected of filing fraudulent claims, the auditor should take a discovery sample of employee claims. The internal auditor should then confirm the work done by the dentist according to the claim with the employee. The employee is the best source of information as to whether the service was provided.

As part of an internal audit, a benchmark must be established for the defect rate for an innovative new production process. The auditor can either use a large sample that is already available from other production processes in the same plant or draw a fresh sample from the new process. However, a fresh sample would be expensive, time consuming, and much smaller in size. Which one of the following is the best course of action for the auditor? A. The auditor should accept this large historical sample because analyses based on it will have high statistical power. B. The auditor should draw a fresh sample and combine it with the old sample. C. The auditor should accept the historical sample but use nonparametric statistics to analyze it. D. The auditor should first determine how similar the new process is to the old process before deciding what to do.

Answer (D) is correct. If the old and new processes are not substantially similar, the existing sample will not be representative.

An internal auditor is planning to use monetary-unit sampling for testing the monetary value of a large accounts receivable population. The advantages of using monetary-unit sampling (MUS) include all of the following except that it A. Is an efficient model for establishing that a low error rate population is not materially misstated. B. Does not require the normal distribution approximation required by variables sampling. C. Can be applied to a group of accounts because the sampling units are homogenous. D. Results in a smaller sample size than classical variables sampling for larger numbers of misstatements.

Answer (D) is correct. MUS, also called probability-proportional-to-size (PPS) sampling, is a modified version of attribute sampling that relates deviation rates to monetary amounts. It uses a monetary unit as the sampling unit. In effect, MUS stratifies the population because the larger account balances have a greater chance of being selected. However, as the number of expected misstatements increases, MUS requires a larger sample size than classical variables sampling.

An internal auditor is performing a test to determine whether a gas and electric appliance manufacturer should move its service center from one location to another. The service center houses the service trucks that are used to drive to the customers' locations to service their appliances. The internal auditor wants to determine the reduction in average miles driven as a result of moving to the other location. Which of the following statistical sampling methods would be most appropriate for this test? A. Attribute sampling. B. Discovery sampling. C. Probability-proportional-to-size (monetary-unit) sampling. D. Mean-per-unit sampling.

Answer (D) is correct. Mean-per-unit sampling is the only variables sampling method designed to estimate a variable for which individual carrying amounts of items in a population are not available.

When an internal auditor uses monetary-unit statistical sampling to examine the total value of invoices, each invoice A. Has an equal probability of being selected. B. Can be represented by no more than one monetary unit. C. Has an unknown probability of being selected. D. Has a probability proportional to its monetary value of being selected.

Answer (D) is correct. Monetary-unit sampling, also called probability-proportional-to-size sampling, results in the selection of every nth monetary unit. Thus, a US $1,000 item is 1,000 times more likely to be selected than a US $1 monetary unit item. The probability of selection of a sampled item is directly proportional to the size of the item.

Ratio estimation sampling would be inappropriate to use to project the monetary error in a population if A. The recorded carrying amounts and audited amounts are approximately proportional. B. A number of observed differences exist between carrying amounts and audited amounts. C. Observed differences between carrying amounts and audited amounts are proportional to carrying amounts. D. Subsidiary ledger book balances for some inventory items are unknown.

Answer (D) is correct. Ratio estimation is similar to difference estimation except that it estimates the population error 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. It has been demonstrated that both ratio and difference estimation are reliable and efficient when small errors predominate and the errors are not skewed. Moreover, audit amounts should be proportional to carrying amounts. Consequently, ratio estimation requires that carrying amounts be known.

A manufacturer mass produces nuts and bolts on its assembly line. The line supervisors sample every nth unit for conformance with specifications. Once a nonconforming part is detected, the machinery is shut down and adjusted. The most appropriate tool for this process is a A. Fishbone (Ishikawa) diagram. B. Cost of quality report. C. ISO 9000 audit. D. Statistical quality control chart.

Answer (D) is correct. Statistical quality control is a method of determining whether the shipment or production run of units lies within acceptable limits. It is also used to determine whether production processes are out of control. Statistical control charts are graphic aids for monitoring the status of any process subject to random variations.

An auditor is checking the accuracy of a computer-printed inventory listing to determine whether the total monetary value of inventory is significantly overstated. Because there is not adequate time or resources to check all items in the warehouse, a sample of inventory items must be used. If the sample size is fixed, which one of the following would be the most accurate sampling approach in this case? A. Select those items that are most easily inspected. B. Employ simple random sampling. C. Sample so that the probability of a given inventory item being selected is proportional to the number of units sold for that item. D. Sample so that the probability of a given inventory item being selected is proportional to its book value.

Answer (D) is correct. The audit objective is to determine whether the total monetary amount of inventory is significantly overstated. Hence, monetary-unit (probability-proportional-to-size) sampling is appropriate. It increases the likelihood that a sample of a given size will include high monetary-value inventory items.

The supervisor of claims processing for a health insurance firm selects all claims processed in the past 2 days by a particular employee for audit. From this sample, the supervisor can develop A. An overall representative view of employee work for the year. B. A quantification of sampling error. C. Conclusions about the correctness of processing for the department. D. An understanding of the details contained in the processing task.

Answer (D) is correct. The auditor has used judgment sampling, not statistical sampling. Thus, (s)he cannot quantitatively assess precision and confidence level and therefore is precluded from drawing valid statistical inferences about the population. However, this sample should assist the auditor in obtaining a preliminary understanding of the system and in determining whether a statistical sample will be needed.

A 90% confidence interval for the mean of a population based on the information in a sample always implies that there is a 90% chance that the A. Estimate is equal to the true population mean. B. True population mean is no larger than the largest endpoint of the interval. C. Standard deviation will not be any greater than 10% of the population mean. D. True population mean lies within the specified confidence interval.

Answer (D) is correct. The confidence level, e.g., 90%, is specified by the auditor. A confidence interval based on the specified confidence level, also called precision, is the range around a sample value that is expected to contain the true population value. In this situation, if the population is normally distributed and repeated simple random samples are taken, the probability is that 90% of the confidence intervals constructed around the sample results will contain the population value.

An important difference between a statistical and a judgmental sample is that with a statistical sample, A. No judgment is required because everything is computed according to a formula. B. A smaller sample can be used. C. More accurate results are obtained. D. Population estimates with measurable reliability can be made.

Answer (D) is correct. The principal benefit of statistical sampling is that it permits the auditor to make a quantitative assessment of how closely the sample represents the population for a given level of reliability, i.e., how unbiased the sample is.

Fact Pattern: An organization has collected data on the complaints made by personal computer users and has categorized the complaints. Question: 84 The chart displays the

Answer (D) is correct. This Pareto diagram depicts the frequencies of complaints in absolute terms. It displays the actual number of each type of complaint. The chart does not display arithmetic means, relative frequencies, or medians of each type of complaint.