14.3 Flashcards
Which of the following statements is correct about the sample size in statistical sampling when testing internal controls?
The auditor should consider the tolerable population rate of deviation from the controls being tested in determining sample size.
A test of controls is an application of attribute sampling. The initial size for an attribute sample is based on (1) the desired assurance (complement of the risk of overreliance) that the tolerable population deviation rate is not exceeded by the actual rate, (2) the tolerable population deviation rate, (3) the expected population deviation rate, and (4) the population size. However, a change in the size of the population has a very small effect on the required sample size when the population is large. Consequently, population size is often not considered unless it is small.
Which of the following statements is true concerning the auditor’s use of statistical sampling?
An auditor needs to estimate the dollar amount of the standard deviation of the population to use classical variables sampling.
Variables sampling is used to estimate the amount of misstatement in, or the value of, a population. In auditing, this process entails estimating the monetary value of an account balance or other accounting total. The estimated population standard deviation is used in the sample size formula for variables estimation. Hence, it should be stated in dollar terms.
A CPA’s client wishes to determine inventory shrinkage by weighing a sample of inventory items. If a stratified random sample is to be drawn, the strata should be identified in such a way that
Each stratum differs as much as possible with respect to expected shrinkage, but the shrinkages expected for items within each stratum are as close as possible.
When the items in a population are heterogeneous, it may be advantageous to stratify the population into homogeneous subpopulations. Each stratum should differ from the others, but the items within each stratum should be similar.
An auditor who uses statistical sampling for attributes in testing internal controls should alter the assessed risk of material misstatement when the
Sample rate of deviation plus the allowance for sampling risk exceeds the tolerable population deviation rate.
The auditor may calculate sample size from standard tables based on the tolerable population deviation rate, the likely rate of deviations, and the risk of overreliance. Given the sample size and the sample deviation rate, another table is used to determine an upper deviation rate at the specified level of risk. The difference between the upper deviation rate and the sample rate is the allowance for sampling risk. When the upper deviation rate (sample rate + allowance for sampling risk) exceeds the tolerable population deviation rate, the sample result does not support the assessed risk of material misstatement.
When using classical variables sampling for estimation, an auditor normally evaluates the sampling results by calculating the possible misstatement in either direction. This statistical concept is known as
Precision.
The precision or confidence interval (allowance for sampling risk) is an interval around the sample statistic that is expected to include the true value of the population at the specified confidence level. When using classical variables sampling, the allowance for sampling risk is calculated based on the normal distribution.
When performing tests of controls with respect to the effectiveness of internal controls related to cash receipts, an auditor may use a systematic sampling technique with a start at any randomly selected item. The biggest disadvantage of this type of sampling is that the items in the population
May occur in a systematic pattern, thus destroying the sample randomness.
Systematic sampling is accomplished by selecting a random start and taking every nth item in the population. The value of n is computed by dividing the population by the size of the sample. The random start should be in the first interval. Because the sampling technique only requires counting in the population, no correspondence between random numbers and the items in the population is necessary as in random number sampling. 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.
In estimation sampling for variables, which of the following must be known in order to estimate the appropriate sample size required to meet the auditor’s needs in a given situation?
The acceptable level of risk.
Variables sampling is used in tests of details because it may be used to (1) estimate the amount of a variable, such as an account balance, and (2) quantify the risk that the estimate may not approximate the true value. For substantive tests of details, the sample size depends on the auditor’s desired assurance (1.0 – the risk of incorrect acceptance) that tolerable misstatement is not less than actual misstatement in the population. The desired assurance may be based on, among other things, the following: (1) the assessed risk of material misstatement, (2) the assurance provided by other substantive procedures related to the same assertion, (3) tolerable misstatement, and (4) expected misstatement for the population. Accordingly, as the acceptable risk of incorrect acceptance decreases, the desired assurance increases, and the auditor decreases the tolerable misstatement.
Which of the following statements about audit sampling risks is correct for a nonissuer?
Nonsampling risk can arise because an auditor failed to recognize misstatements.
Nonsampling risk is the risk that the auditor may draw an erroneous conclusion for any reason not related to sampling risk. Examples include the use of inappropriate audit procedures or misinterpretation of audit evidence and failure to recognize a misstatement or deviation. Nonsampling risk may be reduced to an acceptable level through such factors as adequate planning and proper conduct of a firm’s audit practice in accordance with the quality control standards (AU-C 530).
An auditor is testing a multinational corporation’s fixed asset purchases for overstatement and notices that, out of the hundreds of purchases, a significant number of large purchases were made during the year. The auditor decides to use monetary-unit sampling (MUS) to test fixed asset purchases. Which of the following would not be an advantage of using MUS in this situation?
MUS eliminates the need for auditor’s judgment.
Statistical sampling, such as MUS, allows the auditor to obtain an objective sample from an existing population. However, this method of sampling does not eliminate the need for the auditor’s judgment in evaluating the sample.
An advantage of statistical over nonstatistical sampling methods in tests of controls is that the statistical methods
Provide an objective basis for quantitatively evaluating sample risks.
The results of statistical (probability) sampling are objective and subject to the laws of probability. Hence, sampling risk can be quantified and controlled, and the degree of reliability desired (the confidence level) can be specified. Sampling risk is the risk that the sample selected does not represent the population.
Which of the following combinations results in a decrease in sample size in an attribute sample?
Allowable risk for overreliance:
Tolerable rate:
Expected population deviation rate:
Increase
Increase
Decrease
To determine the sample size for a test of controls, the auditor considers (1) the tolerable rate of deviations from the control being tested, (2) the expected actual rate of deviations, and (3) the allowable risk of overreliance. An increase in the allowable risk of overreliance, an increase in the tolerable rate, and a decrease in the expected rate each has the effect of reducing the required sample size.
An auditor is determining the sample size for an inventory observation using mean-per-unit estimation, which is a variables sampling plan. To calculate the required sample size, the auditor usually determines the
Variability in the dollar amounts of the inventory items:
Risk of incorrect rejection:
Yes
Yes
Four factors are considered in determining the sample size for mean-per-unit estimation. Those factors include (1) the population size, (2) an estimate of population variation (the standard deviation), (3) the risk of incorrect rejection (its complement is the confidence level), and (4) the tolerable misstatement (the desired allowance for sampling risk is a percentage thereof, and this percentage is a function of the risk of incorrect rejection and the allowable risk of incorrect acceptance).
An auditor initially planned to use unrestricted random sampling with replacement in the audit of accounts receivable. Later, the auditor decided to use unrestricted random sampling without replacement. As a result of this decision, the sample size should
Decrease.
Unrestricted random sampling means that each item in the population has an equal and nonzero chance of being selected. Sampling with replacement means that an item may be included more than once in the sample. Sampling without replacement removes an item from the population after selection. Thus, sampling without replacement uses information about the population more efficiently. It results in a smaller sample, if other things are held constant, because the sample size formula for sampling with replacement is multiplied by the finite population correction factor (always less than 1.0).
When an auditor uses monetary-unit sampling to examine the total value of invoices, each invoice
Has a probability proportional to its monetary value of being selected.
Monetary-unit sampling results in the selection of every nth monetary unit. Thus, a $1,000 item is 1,000 times more likely to be selected than a $1 item. The probability of selection of a sampled item is directly proportional to the size of the item.
Which of the following statements is generally correct about the sample size in statistical sampling when testing internal controls?
The population size has little or no effect on the sample size.
In an attribute sampling application, e.g., for testing internal controls, the total number of sampling units in the population should be known. However, the sample size is relatively insensitive to size changes in large populations.
