CHAPTER 17 BASIC AUDIT SAMPLING CONCEPTS I Review Questions Refer to page 638, 3rd paragraph of the textbook Refer to page 638, 4th paragraph of the textbook Refer to page 640 of the textbook Audit conclusions can be made only about the population from which the sample was drawn, and a conclusion can only be valid if the sample on which it is based actually shows the characteristics of the population Auditors can attempt to achieve representativeness, but they cannot guarantee it Sampling risk – the probability that the sample does not adequately reflect the population – always exists Refer to page 646, 2nd paragraph; page 647, 1st paragraph of the textbook Refer to page 647, 6th paragraph of the textbook Refer to page 652, paragraphs to of the textbook Refer to page 652, paragraphs and of the textbook Refer to page 653, 4th paragraph & page 654, 1st to 3rd paragraph of the textbook 10 Sampling risk is the probability that the auditor’s conclusions concerning the population will be in error In terms of conclusions regarding internal control, sampling risk consists of two subsets: Alpha risk, the risk that the auditor will assess control risk too high and perform more substantive testing than is necessary under the circumstances; and Beta risk, the risk that the auditor will assess control risk too low and perform less substantive testing than is necessary For control testing purposes, the auditor is more concerned with beta risk than alpha risk, because beta risk poses the threat of underauditing and is therefore the basis for the audit opinion The auditor controls this risk by setting beta risk 17-2 Solutions Manual - Assurance Principles, Professional Ethics… sufficiently low as to maintain overall audit risk at a level less than or equal to 10% 11 Refer to pages 661 to 663 of the textbook 12 Refer to pages 655 to 660 of the textbook II Multiple Choice Questions b c d c d b a d a 10 c III Comprehensive Cases Case a Areas requiring the auditors to make judgment decisions when statistical sampling techniques are employed (only four required): (1) Defining population, characteristics to be tested, and deviations Unless a relationship is defined between the occurrence rate of deviations in the population and either the validity of the client’s financial statement or the strength of internal control, little useful information is gained by estimating the occurrence rate (2) Determining the appropriate statistical selection techniques for drawing a random sample The auditors must recognize the advantages and disadvantages of stratified selection, unstratified selection, and systematic selection, and determine which technique is appropriate for selecting an economical random sample (3) Establishing the required maximum tolerable deviation rate and the risk of assessing control risk too low for the procedure This requires judgment decisions regarding materiality, time, cost, and the planned assessed level of control risk (4) Interpreting sample results This requires a decision as to whether the results support the auditors’ planned assessed level of control risk, or whether additional sampling is necessary to reach a conclusion (5) Following up on the discovery of critical errors or unacceptable deviation rates (6) Determining the circumstances under which statistical sampling is appropriate, and those in which other techniques should be used in lieu, of or to supplement, the statistical sampling techniques This is an open-ended question The student may identify numerous other areas in which the auditors must make judgment decisions b If the CPAs’ sample shows an unacceptable deviation rate, they may take the following actions: Basic Audit Sampling Concepts 17-3 (1) They may enlarge their sample to increase the precision of their estimate (2) They may isolate the type of deviation and expand examination as it relates to the transactions that give rise to that type of misstatement (3) The auditors’ usual response to an unacceptably high deviation rate is to increase their assessed level of control risk Accordingly, the auditors would increase the intensity of their substantive tests c Techniques for selecting an unstratified random sample of accounts payable vouchers include the following: Random Sample A random sample is a sample of a given size drawn from a population in a manner such that every possible sample of that size is equally likely to be drawn Items may be selected randomly by: (1) Table of Random Numbers Use one of a number of published tables Using four columns in the table, select the first 80 numbers which fall within the range of to 3,200 The starting point in the table should be selected randomly and the path to be followed through the table should be set in advance and followed consistently (2) Random Number Generator: Using generalized audit software, generate a list of 80 random numbers Systematic Sample A systematic sample is drawn by selecting every n th item beginning with a random start (1) Every nth item Select every 40th voucher after selecting the initial voucher (from to 40) randomly (2) Several random starting points For example, use two random starting points and select 40 of the 80 vouchers from each of the two sequences Select every 80th voucher (3,200/40) after each of the two random starting points between and 80 for each of the two sequences Case a (1) Since the results of tests of controls typically play a significant role in determining the nature, timing, and extent of other audit procedures, the auditors usually specify a low level of risk of assessing control risk too low It is usually set at or 10 percent (2) In determining the tolerable deviation rate, an auditor should consider the planned assessed level of control risk and the extent of assurance desired from the evidential matter included in the sample (3) In determining the expected population deviation rate, an auditor should consider the results of prior years’ tests, the overall control environment, or utilize a preliminary sample 17-4 Solutions Manual - Assurance Principles, Professional Ethics… b (1) There is a decrease in sample size if the acceptable level of the risk of assessing control risk too low is increased (2) There is a decrease in sample size if the tolerable deviation is increased (3) There is an increase in sample size if the population deviation rate is increased c Using a statistical sampling approach, Figure 18.4 reveals that deviations in a sample of size 100 results in an achieved upper deviation rate of 12.8%, well in excess of the tolerable deviation rate (8%) The sample results should thus be interpreted as not supporting the planned assessed level of control risk Using a nonstatistical sampling approach, the 7% estimated population deviation rate identified in the sample (7 deviations / 100 sample items) approaches the tolerable deviation rate of 8% Therefore, using a nonstatistical approach, the sample result would also be interpreted as not supporting the planned assessed level of control risk d Statistical sampling allows the auditors to quantify sampling risk As described in part (c), only when statistical sampling is used the auditors know that the achieved upper deviation rate is 12.8%  ...17-2 Solutions Manual - Assurance Principles, Professional Ethics… sufficiently low as to maintain overall... prior years’ tests, the overall control environment, or utilize a preliminary sample 17-4 Solutions Manual - Assurance Principles, Professional Ethics… b (1) There is a decrease in sample size... every possible sample of that size is equally likely to be drawn Items may be selected randomly by: (1) Table of Random Numbers Use one of a number of published tables Using four columns in the