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1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review Audit Sampling Chapter Seven ©Black CPA Review www.BlackCPAreview.com Chapter 7 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review Objectives: Objective 1: Understand sampling basics Objective 2: Understand sampling risk Objective 3: Understand attribute sampling Objective 4: Understand classical variable sampling and probability-‐proportional-‐to-‐size sampling Objective 5: Know what affects sampling size Objective 6: Know the basic steps for audit sampling Objective 7: Know the sampling methodologies ©Black CPA Review www.BlackCPAreview.com Chapter 7 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review Objective 1: Audit sampling basics A. According to AU 350, audit sampling is the application of an audit procedure to less than 100% of the items within an account balance or class of transactions, and the application of the results to the entire population. An auditor uses audit sampling because it is neither time or cost effective to look at every piece of data B. There are two types of sampling: a. Non-‐statistical sampling i. This is based on human decisions b. Statistical sampling i. This is based on formula ii. The formula helps the auditor determine the appropriate sample size that gives the auditor enough evidence to form an opinion during the audit iii. This type of sampling helps the auditor to evaluate and understand the data collected during the audit iv. This type of sampling helps the auditor to evaluate the results and determine sampling risk v. There are two types of statistical sampling: 1. Variable sampling – This type of sampling is used when doing substantive testing. The results are presented in dollars or units. 2. Attributes sampling – This type of sampling is used during a test of controls. The results are presented as a rate of occurrence. Objective 2: Understand sampling risk A. Non-‐sampling risk a. These are the risks associated with sampling that are based on human error B. Sampling Risk a. There are two types of sampling risks i. Type I error (a.k.a. alpha risk) – This is the risk of incorrectly assessing control risk too high 1. This type of error would lead the auditor to incorrectly reject an account balance 2. This type of error relates to the efficiency of the audit because the auditor would do more procedures than necessary to make up for the high risk which was incorrectly assessed ii. Type II error (a.k.a. beta risk) – This is the risk of incorrectly assessing control risk too low ©Black CPA Review www.BlackCPAreview.com Page 7 -‐ 1 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review 1. This type of error would lead the auditor to incorrectly accept an account balance when in fact the auditor should perform more tests on the account 2. This type of error relates to the effectiveness of the audit as the auditor is accepting accounts that may be materially misstated by over relying on internal control. Objective 3: Understand attribute sampling A. Attribute sampling is used when testing controls B. The results are given as a rate of occurrence a. Example: The auditor is using attribute sampling to test 200 purchase orders. The auditor finds that 20 out of the 200 were improperly approved. The error rate is 10%. The auditor has to determine if this is an acceptable rate. C. The acceptable rate of error is known as the tolerable rate a. The tolerable rate has an inverse relationship to sample size i. The higher the tolerable rate the smaller the audit sample has to be ii. The lower the tolerable rate the larger the sample has to be D. When the auditor evaluates the sample results they take the sample deviation rate (number of deviations divided by the sample size) plus the allowance for sampling risk and compare it to the tolerable rate. If the results from the sampling plus the allowance for sampling risk is greater than the tolerable rate, then the auditor must do additional tests. a. Example: An auditor determines that the tolerable rate of error is 8% and that there is an audit risk of 2%. After doing an audit using attribute sampling, the auditor determines that the sample error rate is 5%. Because the sample rate of 5% plus the risk rate of 2% is less than the tolerable rate of error, the auditor does not need to do additional tests. E. The desired level of reliability or the level of confidence determines Sample Risk. If the auditor decides that the level of reliability needs to be 97% it means they are willing to accept a 3% sample risk. F. When using attribute sampling the auditor may choose either the sequential sampling method or the discovery sampling method a. Sequential sampling – In this process the sample is selected over several steps. The auditor chooses a sample and, based on the results from that sample, chooses another sample. b. Discovery sampling – In this process the auditor can ascertain the sample size that is required to determine that an error rate within the population is not in excess of a given percentage. ©Black CPA Review www.BlackCPAreview.com Page 7 -‐ 2 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review Objective 4: Understand classical variable sampling and probability-‐ proportional-‐to-‐size sampling A. Classical variable sampling – This is a type of variable sampling used when doing a test of details that compares samples to a calculated standard deviation a. There are three types of classical variable sampling one needs to know for the CPA exam i. Mean-‐per-‐unit estimation – This type of sampling projects the sample average to the total population. This is done by taking the sample average and multiplying it by the number of units in the total population 1. Example: You have a total population of 4,000 items in accounts payable, and your sample size is 100. Adding up the individual values of the 100 items, you get a total of $6,000; therefore, your mean is $60 (6,000/100). Your mean estimate of the true value of accounts payable is $240,000 ($60 x 4,000). Now consider this data and your sampling risk, confidence level, and error rate. If your confidence level is 98% and your error rate is 10 percent, you can say that you’re 98% confident that the total value of accounts receivable is $240,000, plus or minus $24,000 ($240,000 times your error rate of 10 percent). ii. Difference estimation – This type of sampling allows the auditor to estimate the amount of misstatement within a population and determine the allowance for sampling risk. This is done by taking the average amount of error per sample unit and applying it to the total population 1. Example: The total population has 7,500 units and the sample has 2,500 units. Within the sample there are errors totaling $1,500. The auditor takes the average number of errors per sample unit and applies it to the total: The total projected misstatement is $4,500 [($1,500/2,500) x 7,500)] iii. Ratio estimation – This type of sampling is like difference estimation but it does not include the items in the sample population in the final calculations 1. Example: The sample population of 5,000 has $25,000 in errors giving a misstatement ratio of 20%. The total population has $150,000 in the account and, based on the sample misstatement ratio, has $30,000 (20% x $150,000) of misstatements b. It is common to stratify the samples taken during classical variable sampling. This means that the samples are broken down into groups of similar transactions. This cuts down on the variation of items allowing the auditor to take smaller samples. B. Probability-‐proportional-‐to-‐size (PPS) sampling (a.k.a. dollar-‐unit sampling or cumulative monetary amount sampling) – this is a type of variable sampling used when doing a test of details that allows larger or more valuable items in a population to be included more often in the sample population. ©Black CPA Review www.BlackCPAreview.com Page 7 -‐ 3 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review a. PPS is typically easier to apply then the classical variable sampling and uses a series of calculations to determine the projected misstatements. Once the auditor determines the error rate of the sample it must be projected to the total population. i. Step 1 – Calculate the sampling interval (SI): 1. SI = Tolerable misstatement/Reliability factor (given) Or 2. SI = Population amount/sample size ii. Step 2 – Determine sample size 1. SS = Population amount/ SI iii. Step 3 – Determine the projected misstatement 1. Misstatement amount of sample = Book amount – audited amount 2. Error rate or tainting factor = Misstatement / Book amount 3. Projected misstatement (PM)= a. If SI < book amount then the PM = the amount of misstatement from part 1 of step 3. b. If SI > book amount then PM = Error rate X SI PPS Examples Book Amount Audited amount Misstatement Error rate SI PM SI < book amount $3,000 $2,600 400 13% $2,000 $400 SI > book amount $1,000 700 300 30% $2,000 $600 C. Classical variable sampling (CVS) compared to PPS a. PPS i. Easier to use ii. Allows for a smaller sample size iii. Gives a stratified sample automatically iv. Zero and negative balances require special consideration b. CVS i. Easy to increase sampling size ii. Zero and negative balances are easy to handle iii. Better at detecting understatements than PPS Objective 5: Know what affects sampling size A. The following will cause an auditor to increase sample size: ©Black CPA Review www.BlackCPAreview.com Page 7 -‐ 4 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review a. A larger deviation rate b. The need for more precise results c. The need for a higher confidence level d. The higher the expected error rate the larger the sample needs to be B. The following will cause an auditor to decrease a sample size a. The higher the tolerable rate the smaller the sample needs to be b. The lower the expected error rate the smaller the sample needs to be Objective 6: Know the basic steps for audit sampling A. Step 1 –Determine the test objective or audit objective B. Step 2-‐ Define the population and tolerable deviation rate C. Step 3 – Determine sample size based on: a. Expected population error rate b. Tolerable rate of error c. Risk of assessing control risk too low D. Step 4 – Select the sampling methodology E. Step 5 -‐ Perform the sample plan F. Step 6 -‐ Evaluate the results Objective 7: Know the sampling methodologies A. Haphazard Sampling – This method for selecting which transactions are included in the sample is based on no defined characteristics. There is no specific reason for including or discarding certain transactions. Every transaction has the same probability of being included in the sample B. Block sampling – This type of methodology is done by selecting transactions from varying transaction “blocks” or sections. For example, the auditor may choose to sample invoices #1-‐10, #50-‐60 and #100-‐110. This type of sampling is generally not a good representation of the total population. C. Random-‐number sampling – This is done by selecting a random number and then picking the transaction that corresponds with that number. So if the number 10 is randomly chosen then invoice #10 is included. Every transaction has the same probability of being chosen D. Systematic sampling – This is done by selecting a number at random as a starting point then picking every “nth” item from that starting point. For example if the number 11 is picked at random as the starting point and the auditor is going to include every 5th transaction, then the #11, #16, #21 and so forth would be included ©Black CPA Review www.BlackCPAreview.com Page 7 -‐ 5 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review Questions Objective 1: Question 1: An advantage of statistical sampling over nonstatistical sampling is that statistical sampling helps an auditor to A. Eliminate the risk of nonsampling errors B. Reduce the level of audit risk and materiality to a relatively low amount C. Measure the sufficiency of the evidential matter obtained D. Minimize the failure to detect errors and fraud Question 2: Which of the following is not true of statistical sampling A. It is based on a formula B. It helps the auditor to evaluate the results and determine sampling risk C. It is based on human decisions D. There are two types of statistical sampling Objective 2: Question 3: The risk of incorrect acceptance and the likelihood of assessing control risk too low relate to the: A. Allowable risk of tolerable misstatement B. Preliminary estimates of materiality levels C. Efficiency of the audit D. Effectiveness of the audit Question 4: Which type of error would lead an auditor to incorrectly reject an account balance? A. Type I error B. Type II error C. Type III error D. All of the above Objective 3: Question 5: What is the term used to refer to the acceptable rate of error? A. Standard rate B. Allowable rate C. Sample rate D. Tolerable rate Objective 4: Question 6: An auditor uses difference estimation to sample a company’s receivables. The total population has 14,500 units and the sample has 4,250 units. Within the sample there are errors totaling $8,500. What is the projected misstatement? A. $2,491 B. $18,750 ©Black CPA Review www.BlackCPAreview.com Page 7 -‐6 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review C. $29,000 D. $7,250 Question 7: This type of classical variable sampling projects the sample average to the total population. A. Difference estimation B. Ratio estimation C. Mean-‐per-‐unit estimation D. Probability-‐proportional-‐to-‐size estimation Objective 5: Question 8: Which of the following will cause an auditor to increase their sample size? A. The need for a higher confidence level B. The need for more precise results C. A larger deviation rate D. All of the above Objective 6: No questions Objective 7: Question 9: This method for selecting which transactions are included in a sample is based on no defined characteristics. A. Haphazard sampling B. Block sampling C. Random-‐number sampling D. Systematic sampling Question 10: This method for selecting which transactions are included in a sample is done by selecting a number at random as a starting point then picking every “nth” item from that starting point. A. Haphazard sampling B. Block sampling C. Random-‐number sampling D. Systematic sampling ©Black CPA Review www.BlackCPAreview.com Page 7 -‐7 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review Answers Objective 1: Question 1: C Statistical sampling A. This is based on formula B. The formula helps the auditor determine the appropriate sample size that gives the auditor enough evidence to form an opinion during the audit C. This type of sampling helps the auditor to evaluate and understand the data collected during the audit D. This type of sampling helps the auditor to evaluate the results and determine sampling risk Question 2: C Non-‐statistical sampling -‐ This is based on human decisions Objective 2: Question 3: D Type II error (a.k.a. beta risk) – This is the risk of incorrectly assessing control risk too low -‐ This type of error would lead the auditor to incorrectly accept an account balance when in fact the auditor should perform more tests on the account -‐ This type of error relates to the effectiveness of the audit as the auditor is accepting accounts that may be materially misstated by over relying on internal control Question 4: A Type I error (a.k.a. alpha risk) – This is the risk of incorrectly assessing control risk too high -‐ This type of error would lead the auditor to incorrectly reject an account balance Objective 3: Question 5: D The acceptable rate of error is known as the tolerable rate Objective 4: Question 6: C (Sample errors ÷ Sample size) x Total population = Projected misstatement ($8,500 ÷ 4,250) x 14,500 = $29,000 Question 7: C Mean-‐per-‐unit estimation – This type of sampling projects the sample average to the total population. This is done by taking the sample average and multiplying it by the number of units in the total population Objective 5: Question 8: D ©Black CPA Review www.BlackCPAreview.com Page 7 -‐8 1-‐855-‐75-‐BLACK Auditing and Attestation Exam Review The following will cause an auditor to increase sample size: a. A larger deviation rate b. The need for more precise results c. The need for a higher confidence level d. The higher the expected error rate the larger the sample needs to be Objective 6: No questions Objective 7: Question 9: A Haphazard Sampling – This method for selecting which transactions are included in the sample is based on no defined characteristics. There is no specific reason for including or discarding certain transactions. Every transaction has the same probability of being included in the sample Question 10: D Systematic sampling – This is done by selecting a number at random as a starting point then picking every “nth” item from that starting point. For example if the number 11 is picked at random as the starting point and the auditor is going to include every 5th transaction, then the #11, #16, #21 and so forth would be included ©Black CPA Review www.BlackCPAreview.com Page 7 -‐9