In an application of mean per unit sampling, the following information has been obtained: Reported book value $600,000 Point estimate estimated total value 591,000 Allowance for sampling
Trang 1Statistical Sampling for Substantive Testing MULTIPLE CHOICE:
1 In applying variables sampling, an auditor attempts to
a Estimate a qualitative characteristic of interest
b Determine various rates of occurrence for specified
attributes
c Discover at least one instance of a critical error
d Predict a monetary population value within a range of precision
ANSWER: D 2 The measure of variability of a statistical sample that serves as an estimate of the population variability is the
a Basic precision
b Range
c Standard deviation
d Interval
ANSWER: C 3 An auditor selects a statistical sample from a large inventory of replacement parts Which of the following audit objectives would be most appropriate if the sampling method used is probability proportional to size (PPS)?
a The auditor plans to estimate the total dollar value of the inventory when a recorded book value does not exist b The auditor plans to make a statement concerning the total dollar amount of error in the population from the recorded book value
c The auditor wishes to accept or reject the hypothesis that the proportion of defective parts in the population is less than 5%
d The auditor wishes to estimate the proportion of
defective parts in the population ANSWER: B
4 Precision is defined as the range (plus or minus) within
which the true answer most likely falls Reliability, also referred to as the confidence level, is the likelihood that the sample range contains the true value Of the following
Trang 2statements concerning precision and reliability, which one
is not true?
a Precision is set by the auditor and is a function of
materiality and risk
b The narrower the range of precision, the smaller the
sample size
c An increase in control risk, other parameters remaining
unchanged, causes a narrowing of the precision range
d Overall audit risk is the complement of reliability ANSWER: B
5 In an application of mean per unit sampling, the following
information has been obtained:
Reported book value $600,000 Point estimate (estimated total value) 591,000 Allowance for sampling risk (precision) +- 22,000 Tolerable error +- 45,000 The appropriate conclusion would be that the reported book
value is
a Acceptable only if the risk of incorrect rejection is
at least twice the risk of incorrect acceptance
b Acceptable
c Not acceptable
d Acceptable only if the risk of incorrect acceptance is
at least twice the risk of incorrect rejection ANSWER: B
6 Sampling risk refers to the possibility that:
a The auditor may use a less than optimal statistical
method for the circumstances, e.g difference estimation instead of ratio estimation
b The auditor may fail to recognize an error that is
included in the sample
c Even though a sample is properly chosen, it may not be
representative of the population
d The confidence level and/or precision established by
the auditor are not appropriate ANSWER: C
7 The primary reason for an auditor to use statistical
sampling is to
a Obtain a smaller sample than would be required by
non-statistical sampling techniques
b Obtain a sample more representative of the population
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techniques
c Allow the auditor to quantify, and therefore control, the risk of making an incorrect decision based on sample evidence
d Meet requirements of Statements on Auditing Standards ANSWER: C 8 The variability of a population, as measured by the standard deviation, is the
a Extent to which the individual values of the items in the population are spread about the mean
b Degree of asymmetry of a distribution
c Tendency of the means of large samples (at least 30
items) to be normally distributed
d Measure of the closeness of a sample estimate to a
corresponding population characteristic
ANSWER: A 9 Management has asked the internal auditing staff to evaluate the efficiency of the accounts payable system, particularly whether it would be economically feasible to reduce the number of discounts lost through slow payment The audit staff decides that it needs to determine the amount currently being lost and can do so by taking a sample from payments made in the last six months, examining each, and recording the amount, if any, of the discount lost This information can be used to project the total amount of discounts lost for the period This proposed plan is an example of
a Attribute sampling
b Acceptance sampling
c Variables sampling
d Discovery sampling
ANSWER: C 10 During an audit involving testing of accounts receivable
balances, an auditor decides to specify a precision interval of $100,000 instead of the $200,000 precision interval that was called for in the sampling plan contained in the audit program Which of the following would be a result of the auditor's decision to narrow the precision interval?
Trang 4a An increase in the required sample size
b A decrease in the required sample size
c An increase in the population standard deviation
d A decrease in the population standard deviation
ANSWER: A 11 To determine the number of items to be selected in a sample for a particular substantive test of details, the auditor should consider all of the following except
a Tolerable error
b Expected error
c Allowable risk of incorrect acceptance
d Characteristics of the population
ANSWER: D 12 Sample size
a Increases with the use of higher confidence levels
b Decreases with the use of higher confidence levels
c Remains unchanged with changes in confidence levels d Increases with the use of lower confidence levels
ANSWER: A 13 In 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?
a The total amount of the population
b The desired standard deviation
c The desired confidence level
d The estimated rate of error in the population
ANSWER: C 14 In a variables sampling application, which of the following will result when the confidence level is changed from 90% to 95%?
a Standard error of the mean will not be affected
b Non-sampling error will decrease
c Sample size will increase
d Point estimate of the arithmetic mean will increase ANSWER: C
Trang 515 An auditor wishes to estimate inventory shrinkage by
weighing a sample of inventory items From past
experience, the auditor knows that a few specific items are subject to unusually large amounts of shrinkage
In using statistical sampling, the auditor's best course of
action is to
a Eliminate any of the items known to be subject to
unusually large amounts of shrinkage
b Increase the sample size to lessen the effect of the items subject to unusually large amounts of shrinkage c Stratify the inventory population so that items subject to unusually large amounts of shrinkage are reviewed separately
d Continue to draw new samples until a sample is drawn which includes none of the items known to be subject to large amounts of shrinkage
ANSWER: C 16 In conducting a substantive test of an account balance, an auditor hypothesizes that no material error exists The risk that sample results will support the hypothesis when a material error actually does exist is the risk of
a Incorrect rejection
b Alpha error
c Incorrect acceptance
d Type I error
ANSWER: C 17 Which of the following best illustrates the concept of sampling risk?
a A randomly chosen sample may not be representative of the population as a whole on the characteristic of interest b An auditor may select audit procedures that are not
appropriate to achieve the specific objective
c An auditor may fail to recognize errors in the documents examined for the chosen sample
d The documents related to the chosen sample may not be available for inspection
ANSWER: A 18 Using the following results from a variables sample, compute the achieved precision:
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Population size = 10,000
Sample size = 144
Sample standard deviation = $24.00
Confidence level = 90% (Z = 1.65)
Mean = $84.00
a $5,702
b $33,000
c $20,000
d $16,500
ANSWER: B 19 Which of the following sampling plans would be designed to estimate a numerical measurement of a population, such as a dollar value?
a Discovery sampling
b Numerical sampling
c Sampling for variables
d Sampling for attributes
ANSWER: C 20 An auditor is using the mean-per-unit method of variables sampling to estimate the correct total value of a group of inventory items Based on the sample, the auditor estimates with precision of +-4% and confidence of 90% that the correct total is $800,000 This means that:
a There is a 4% chance that the actual correct total is less than $720,000 or more than $880,000
b There is a 10% chance that the actual correct total is less than $768,000 or more than $832,000
c The probability that the inventory is not significantly overstated is between 6% and 14% d The inventory is not likely to be overstated by more than 4.4% ($35,200) nor understated by more than 3.6% ($28,800)
ANSWER: B 21 Which of the following statements is correct concerning the auditor's use of statistical sampling?
a An auditor needs to estimate the dollar amount of the standard deviation of the population to use classical variables sampling
b An assumption of PPS sampling is that the underlying accounting population is normally distributed
c A classical variables sample needs to be designed with
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in the sample
d The selection of zero balances usually does not require special sample design considerations when using PPS
sampling
ANSWER: A 22 Which of the following statements concerning alpha and beta risk is true? a As alpha risk increases, beta risk decreases b As inherent risk and/or control risk increase, beta risk should also increase c As inherent risk and/or control risk increase, beta risk should decrease d As a "rule of thumb," the auditor generally sets beta risk equal to or less than 10%, inasmuch as it is the basis for the audit opinion ANSWER: C 23 Statistical samples as compared to non-statistical samples permit the auditor to
a Quantify and control sampling risk
b Eliminate non-sampling errors of every type
c Obtain smaller sample sizes in all cases
d Use less complex formulas than those required to
evaluate non-statistical samples
ANSWER: A 24 Probability-proportional-to-size (PPS) sampling is less
efficient if
a Computerized account balances are being audited
b Statistical inferences are to be made
c The audit objective is oriented to understatements
d The account contains a large number of transactions ANSWER: C 25 A number of factors influences the sample size for a
substantive test of details of an account balance All other factors being equal, which of the following would lead to a larger sample size?
a Lowering of assessed level of control risk
b Lowering of assessed inherent risk through use of
analytical review procedures
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c Smaller expected frequency of errors
d Smaller measure of tolerable error
ANSWER: D 26 For variables sampling purposes, changes in certain parameters affect sample size positively while changes in others have a negative effect In this regard, which of the following statements is true? a An increase in beta risk reduces sample size b Population size affects sample size inversely, i.e., as population size increases, sample size decreases c An increase in alpha risk increases sample size d As materiality (M) increases, sample size increases ANSWER: A 27 A population that is physically separated into two or more groups based on the sample variation being less than that for the entire population is called a
a Systematic sample
b Judgment sample
c Simple random sample
d Stratified sample
ANSWER: D 28 The standard deviation of a sample will usually decrease with a A decrease in sample size
b The use of stratification
c An increase in desired precision
d An increase in confidence level
ANSWER: B 29 An auditor is primarily concerned with substantial overstatements of accounts receivable balances and expects few, if any, errors In an effort to concentrate on the large dollar values, the auditor would logically employ
a Ratio estimation
b Probability proportional to size sampling
c Discovery sampling
d Mean per unit sampling ANSWER: B
Trang 930 Consider the following sampling plan: An auditor took a
sample of 30 receiving reports completed in the last 12 months The receiving reports were filed along with
the date on which the goods were moved from the receiving department to their storage area in the warehouse Sampling
and the next two digits to determine the day of the month
which corresponding dates did not exist or on which the
then took as the sample item the second report in the file for that day Can the auditor rely on the statistical
inference of this test?
a Yes, because the plan eliminated any possible deliberate or unconscious bias in the auditor's selection of the sample items
b Yes, because a random number table was used to make the selection
c No, because the auditor sampled without replacement d No, because all items do not have an equal chance of being selected
ANSWER: D 31 In testing accounts receivable, an auditor sends out positive confirmation requests to 100 randomly selected customers A customer returns the confirmation indicating that the balance is correct when, in fact, the balance is overstated This is an example of
a Tainting
b Sampling error
c Standard error
d Non-sampling error
ANSWER: D 32 An auditor wishes to use stratified sampling to estimate the book value of a large accounts receivable file The auditor has a complete listing of the file in account number order The listing is several pages long and includes the account balance of each customer Several customers have very large account balances while most balances are small Which of the following would be the most appropriate means of
Trang 10classifying members of this population into
strata?
a Account balance
b Account number
c Alphabetically by name
d Numerically by pages of the listing
ANSWER: A 33 Auditors who prefer statistical to non-statistical sampling believe that the principal advantage of statistical sampling flows from its unique ability to
a Define the precision required to provide adequate
satisfaction
b Provide a mathematical measurement of risk c Establish conclusive audit evidence with decreased audit effort
d Promote a more legally defensible procedural approach ANSWER: B 34 In a probability-proportional-to-size sample with a sampling interval of $10,000, an auditor discovered that a selected account receivable with a recorded amount of $5,000 had an audit amount of $2,000 The projected error of this sample was
a $3,000
b $4,000
c $6,000
d $8,000
ANSWER: C 35 An auditor selects a preliminary sample of 100 items out of a population of 1,000 items The sample statistics generate an arithmetic mean of $60, a standard deviation of $6, and a standard error of the mean of $.60 If the sample was
adequate for the auditor's purposes and the auditor's desired precision was plus or minus $1,000, the minimum acceptable dollar value of the population would be
a $61,000
b $60,000
c $59,000
d $58,800 ANSWER: C