Chapter 9 – Homework1.Problem 9-1Define and differentiate between, nonstatistical (judgmental) sampling and statistical sampling.Nonstatistical sampling is an audit sampling technique in which the risk of sampling error is estimated by the auditorsusing professional judgment rather than by the laws of probability. Statistical sampling involves the quantification of therisk of sampling error through the use of mathematics and laws of probability.2.Problem 9-2Describe the difference between sampling risk and nonsampling risk.Sampling risk is the possibility that the auditors will make an erroneous decision based on a sample result. To controlsampling risk the auditors increase the size of their samples. Nonsampling risk is the risk of erroneous conclusions by theauditors based on any factor other then sampling. For example, the auditors may perform inappropriate tests, or they maynot recognize errors in the sample items examined. Nonsampling risk may be controlled by adequate planning andsupervision of engagements, and the establishment of effective quality control policies and procedures.3.Problem 9-17What would be the difference between an attributes sampling plan and a variables sampling plan in a test ofinventory extensions?Attributes sampling would estimate the percentage of extensions that are in error, and variables sampling would estimatetotal dollar amount of misstatements in the schedule. In general, attributes sampling estimates the deviation rate(occurrence rate) of a characteristic, and the variables sampling estimates the dollar value of a characteristic.4.Problem 9-29CPAs may decide to apply nonstatistical or statistical techniques to audit testing.a. List and explain the advantages or applying statistical sampling techniques to audit testing.b. List and discuss the decisions involving professional judgment that must be made by the CPAs in applyingstatistical sampling techniques to test of controls.c. You have applied attributes sampling to the clients pricing to the inventory and discovered from yoursampling that the sample deviation rate exceeds your tolerable rate. Discuss the courses of action you take.
(a) Relative to nonstatistical sampling, statistical techniques may provide the auditors with the following advantages: (1) Designing efficient samples (that may avoid "overauditing"). (2) Measuring the sufficiency of the evidence obtained (this potentially could be helpful in a court proceeding or to help justify work to a client who was critical of the extent of testing). (3) Objectively evaluating sample results. (b) Decisions requiring professional judgment in performing statistical tests of controls include: (1) Identifying the controls to be tested. This involves consideration of the types of misstatements that might occur, identifying the controls that should prevent these misstatements, and deciding whether consideration of those controls to reduce the auditors assessment of control risk would sufficiently reduce the required amount of substantive procedures to justify the related tests of controls. (2) Defining a "deviation." If the test results are to be meaningful, all exceptions included in the definition of "deviation" must be similar in their potential audit significance. (3) Determining the maximum tolerable deviation rate. This involves judgment because deviations do not necessarily correspond directly with misstatements in the financial statements. A single deviation may result in material misstatement, while numerous deviations may result in no misstatement. (4) Establishing an appropriate risk of assessing control risk too low. (5) Defining the population to be tested. The auditor may want to consider stratifying the population by time period if, for example, changes in internal control may have occurred or new personnel may have been hired. (6) Evaluating the results. In addition to drawing statistical conclusions, the CPAs should evaluate the qualitative characteristics of the exceptions found in the sample. Also, if the sample results do not support the planned assessed level of control risk, the CPA must determine the required modification of substantive procedures. (c) When the CPAs have applied attributes sampling techniques and discovered that the deviation rate exceeds their stipulated maximum tolerable deviation rate, the following courses of action are available to them: (1) An investigation might be made to determine the reasons for the unexpectedly high deviation rate and to ascertain its potential effect upon the financial statements. (2) The CPAs might extend the size of their original sample to provide a more precise estimate of the population deviation rate. (3) In light of the higher than anticipated deviation rate, the auditors must increase their assessment of control risk in the related area. This may necessitate expanding the planned substantive test procedures for assertions that are potentially affected by the control weakness.5.Problem 9-38
The 10 following statements apply to unrestricted random sampling without replacement. Indicate whether eachstatement is true or false.A. TrueB. False1. When sampling from the population of accounts receivable for certain objectives, the auditor might sample only active accounts with balances.2. To be random, even item in the population must have an equal change of being selected for inclusion in the sample.3. In general, all items in excess of a material misstatement need to be examined and sampling of them is appropriate.4. It is likely that five different random samples from the sample population could produce five different estimates of the true population mean.5. A 100 percent sample would have to be taken to eliminate sampling risk.6. The effect of the inclusion by chance of a very large or very small item in a random sample can be lessened by increasing the size of the sample.7. The standard deviation of a measure of the variability of items in a population.8. The larger the standard deviation of a population, the smaller the required sample size.9. Unrestricted random sampling with replacement may result in a larger sample size than unrestricted random sampling without replacement.10. Unrestricted random sampling normally results in a smaller sample size than does stratified sampling.6.Problem 9-40
For each term in the column below, identify the definition (or partial definition). Each definition may be usedonce or not at all.A. A classical variables sampling plan enabling the auditors to estimate the average dollar value (or othervariable) of items in a population by determining the average value of items in a sample.B. A defined rate of departure from prescribed controls. Also referred to as occurrence rate or exception rate.C. A sampling plan enabling auditors to estimate the rate of deviation (occurrence) in a population.D. A sampling plan for locating at least 1 deviation, providing that the deviation occurs in the population with aspecified frequency.E. A sampling plan in which the sample is selected in stages, with the need for each subsequent stage beingconditional on the results of the previous stage.F. Also referred to as precision, an interval around the sample results in which the true population characteristicis expected to lie.G. An estimate of the most likely amount of monetary misstatement in a population.H. The complement of the risk of incorrect acceptance.I. The maximum population rate of deviations from a prescribed control that the auditors will accept withoutmodifying the planned assessment of control risk.J. The possibility that the assessed level of control risk based on the sample is less than the true operatingeffectiveness of the controls.K. The possibility that the assessed level of control risk based on the sample is greater than the true operatingeffectiveness of the control.L. The risk that sample results will indicate that a population is materially misstated when, in fact, it is not.M. The risk that sample results will indicate that a population is not materially misstated when, in fact, it ismaterially misstated.N. The risk that the auditors conclusion based on a sample might be different from the conclusion they wouldreach if the test were applied to the entire population. Allowance for sampling risk Deviation rate Discovery sampling Projected misstatement Reliability Risk of assessing control risk too low Risk of incorrect acceptance Sampling risk Tolerable deviation rate
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