14.5 Flashcards
As a result of tests of controls, an auditor overrelied on controls and decreased substantive testing. This assessment occurred because the true deviation rate in the population was
More than the deviation rate in the auditor’s sample.
In the case of a test of controls, overreliance is the erroneous conclusion that controls are more effective than they actually are. Overreliance occurs if the sample has fewer observed deviations than the true deviation rate in the population.
In a sampling application, the group of items about which the auditor wants to estimate some characteristic is called the
Population.
The population is the group of items about which an auditor wishes to draw conclusions. However, the difference between the targeted population (the population about which information is desired) and the sampled population (the population from which the sample is actually drawn) should be understood.
In estimating the total value of supplies on repair trucks, Baker Company draws random samples from two equal-sized strata of trucks. The mean value of the inventory stored on the larger trucks (stratum 1) was computed at $1,500, with a standard deviation of $250. On the smaller trucks (stratum 2), the mean value of inventory was computed as $500, with a standard deviation of $45. If Baker had drawn an unstratified sample from the entire population of trucks, the expected mean value of inventory per truck would be $1,000, and the expected standard deviation would be
Greater than $250.
The standard deviation is a measure of variability within a population. That the population was stratified indicates that each stratum has a smaller standard deviation than the population as a whole. If the two diverse populations are combined, the resulting standard deviation is likely to be larger than that of either of the separate strata. Because the standard deviations of the two strata were $250 and $45, the expected standard deviation is likely to be greater than $250.
As a result of control testing, a CPA has decided to reduce control risk. What is the impact on substantive testing sample size if all other factors remain constant?
The sample size would be lower.
As the assessed level of control risk decreases, the auditor’s allowable risk of incorrect acceptance for the substantive tests of details increases. Thus, the required sample size decreases.
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).
The risk of incorrect acceptance and the risk of overreliance relate to the
Effectiveness of the audit.
If a financial statement amount is erroneously accepted as fairly stated based upon a sample, additional audit work and the chances of exposing the mistake will probably be minimal. However, rejection of a fairly stated amount typically results in further audit investigation and ultimately the acceptance of the amount. Similarly, overreliance on a control leads to an unjustified reduction in substantive testing, thereby decreasing the effectiveness of the audit. However, underreliance on a control results in an unneeded increase in substantive testing but most likely does not decrease ultimate audit effectiveness.
Which of the following is the primary objective of monetary-unit sampling (MUS)?
To identify overstatement errors.
MUS gives each monetary unit in the population an equal chance of selection. However, the auditor does not examine an individual monetary unit but uses it to identify an entire transaction or balance to audit (the logical sampling unit). MUS is useful only for tests of overstatements (e.g., of assets) because a systematic selection method is applied (every nth monetary unit is selected). Accordingly, the larger the transaction or balance, the more likely it will be selected. This method is inappropriate for testing a population (e.g., liabilities) when understatement is the primary audit consideration.
While performing a test of details during an audit, the auditor determined that the sample results supported the conclusion that the recorded account balance was materially misstated. It was, in fact, not materially misstated. This situation illustrates the risk of
Incorrect rejection.
An auditor is concerned with two aspects of sampling risk in performing substantive tests of details: the risk of incorrect acceptance and the risk of incorrect rejection. The second is the risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not materially misstated.
An auditor has determined the recorded amount of a population of accounts receivable to be $1,638,000 and has set the level of tolerable misstatement (TM) at $46,800. No errors were expected to be found in the population. Based upon a risk of incorrect acceptance of 5% and a reliability factor (RF) of 3, what is the sample size to be used for testing?
105.
The sample size for accounts receivable testing is 105. The sampling interval is calculated as SI = TM ÷ RF [15,600 = 46,800 ÷ 3], if SI is the sampling interval. The recorded amount of the population then is divided by the sampling interval to obtain the sample size. The sample size to be tested is 105 (1,638,000 ÷ 15,600).
The use of the ratio estimation sampling technique is most effective when
The calculated audit amounts are approximately proportional to the client’s carrying amounts.
Ratio estimation calculates the population misstatement 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. The precision is determined by considering the variances of the ratios of carrying amount to audited amount. Thus, the more homogeneous the ratios, the smaller the precision.
Which of the following statements is true concerning statistical sampling in tests of controls?
The population size has little or no effect on determining sample size except for very small populations.
A change in the size of the population has a very small effect on the required sample size when the population is large. Tables are available for smaller population sizes providing appropriate smaller sample sizes.
Which of the following would be designed to estimate a numerical measurement of a population, such as a dollar value?
Sampling of variables.
Variables sampling is used to estimate the amount of misstatement in or the amount of a population. In auditing, this process involves estimating the monetary value of an account balance or other accounting totals. The result is often stated in terms of a point estimate plus or minus a stated dollar amount (the precision at the desired level of confidence).
An auditor has been assigned to take a monetary-unit sample of a population of vouchers in the purchasing department. The population has a total recorded amount of $300,000. The auditor believes that a maximum misstatement of $900 is acceptable and would like to have 95% confidence in the results. (The confidence factor at 95% and zero misstatements = 3.00.) Additional information is provided in the opposite column.
In examining the sample, one overstatement was detected causing an extension of $270 to the tolerable misstatement. Assuming a sample size of 1,000 and assuming that the maximum dollar amount of overstatement, if no misstatements were found, was established to be $900 before the sampling analysis, what conclusion can the auditor now make from the sampling evidence?
(S)he is 95% confident that the dollar amount of overstatement in the population of vouchers is less than $1,170.
Had the auditor detected no misstatements in the sample, (s)he could have been 95% confident that the dollar amount of overstatement in the balance was less than $900. Given discovery of an overstatement causing an extension to the tolerable misstatement of $270, the auditor can conclude with 95% confidence that the overstatement is less than $1,170 ($900 + $270).
An auditor may decide to increase the risk of incorrect rejection when
The cost and effort of selecting additional sample items are low.
The risk of incorrect rejection is the risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not. This risk relates to the efficiency, not the effectiveness, of the audit. Incorrect rejection ordinarily results in the application of additional procedures that finally lead the auditor to the proper conclusion. If the cost and effort of selecting additional sample items are low, a higher risk of incorrect rejection may be acceptable.
Which of the following factors is(are) considered in determining the sample size for a test of controls?
Expected population of deviation rate:
Tolerable population deviation rate:
Yes
Yes
Attribute sampling is typically used to test controls. The factors necessary to determine sample size include (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, and (3) the expected population deviation rate. The population is usually assumed to be infinite, and tables are used to identify the appropriate sample size.
