CIA - Sampling Methods

1. The internal auditor suspects that the invoices from a small number of vendors contain serious errors and therefore limits the sample to those vendors only. A major disadvantage of selecting such a directed sample of items to examine is the
a. Difficulty in obtaining sample items
b. Inability to quantify the sampling error related to the total population of vendor invoices
c. Absence of a normal distribution
d. Tendency to sample a greater number of units

2. When sampling is used, sufficiency of audit evidence is achieved when
a. Each item in the population has a chance of being selected
b. The standard deviation in the sample is less than or equal to the corresponding statistic for the population
c. The evidence gathered is directly related to the assertion the auditor is attempting to verify
d. There is reasonable assurance that the items selected are representative of the sampled population

3. In order to quantify the risk that sample evidence leads to erroneous conclusions about the sampled population,
a. Each item in the sampled population must have an equal chance of being selected
b. Each item in the sampled population must have a chance of being selected that is proportional to its book value
c. Each item in the sampled population must have an equal or known probability of being selected
d. The precise number of items in the population must be known

4. Each time an internal auditor draws a conclusion based on evidence from a sample, an additional risk, sampling risk, is introduced. An example of sampling risk is
a. Projecting the results of sampling beyond the population tested
b. Using an improper audit procedure with a sample
c. Incorrectly applying an audit procedure to sample data
d. Drawing an erroneous conclusion from sample data

5. Several risks are inherent in the evaluation of audit evidence that has been obtained through the use of statistical sampling. an example of a beta or Type II error related to sampling risk is the failure to
a. Properly define the population to be sampled
b. Draw a random sample from the population
c. Reject the statistical hypothesis that a book value is not materially misstated when the true book value is materially misstated
d. Accept the statistical hypothesis that a book value is not materially misstated when the true book value is not materially misstated

6. A confidence level of 90% means that
a. The expected error rate is equal to 10%
b. The point estimate obtained is within 10% of the true population value
c. There are 90 chances out of 100 that the sample results will not vary from the true characteristics of the population by more than a specified amount
d. A larger sample size is required than if the desired confidence level were equal to 95%

7. In statistical sampling, setting the appropriate confidence level and desired sample precision are decisions made by the auditor that will affect sample size for a substantive test. Which of the following should not be a factor in the choice of desired precision?
a. The sampling risk
b. The size of an account balance misstatement considered material
c. The audit resources available for execution of the sampling plan
d. The objectives of the audit test being conducted

8. An auditor's statistical sample drawn from a population of invoices indicates a mean value of $150 and sampling precision of +/- $30 at a 95% confidence level. Which of the following statements correctly interprets these sample data?
a. In repeated sampling, the point estimate of the true population mean will be $150 about 95% of the time
b. The probability is 95% that the true population mean is $150
c. In repeated sampling, intervals with precision +/- $30 around the sample mean will always contain the true population mean
d. The probability is 95% that the range $120 to $180 contains the true population mean

9. An auditor draws a random sample of 225 items from a population of 10,000 and calculates the sample standard deviation at $386. Sampling precision is calculated as +/- $50.40 with a confidence level of 95%. If a sample of 900 items had been drawn and if the same sample standard deviation of $386 had been calculated, the sample precision would have been approximately
a. $200
b. $100
c. $25
d. $13

10. The accounting department reports the accounts payable balance as $175,000. You are willing to accept that balance if it is within $15,000 of the actual balance. Using a variables sampling plan, you compute a 95% confidence interval of $173,000 to $190,000. You would therefore
a. Find it impossible to determine the acceptability of the balance
b. Accept the balance but with a lower level of confidence
c. Take a larger sample before totally rejecting the balance and requiring adjustments
d. Accept the $175,000 balance because the confidence interval is within the materiality limits 11. 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. Confidence interval

12. 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

13. The auditor can change the standard error of the mean for a statistical sample by
a. Stratifying the population
b. Increasing the size of the sample
c. Decreasing the size of the sample
d. All of the above

14. An auditor draws a random sample of invoices and computes the mean invoice amount. The auditor then computes the standard error of the mean. This information can be used to
a. Measure the variability of a specific item within the sample
b. Determine the standard deviation of the sample
c. Measure the variability that exists among all possible invoice samples of the same size
d. Perform difference estimation and avoid a large sample

15. In conducting a substantive test of an account balance, an auditor hypothesizes that no material misstatement exists. The risk that sample results will support the hypothesis when a material misstatement actually does exist is the risk of
a. Incorrect rejection
b. Alpha error
c. Incorrect acceptance
d. Type I error

16. In appraising the results of a statistical sample, the finite population correction factor
a. Can be greater than one
b. Has less effect as the sample becomes a larger proportion of the population
c. Is needed when sampling is performed with replacement
d. Is applied to reduce the size of the sample

17. An internal auditor of a manufacturing company analyzes cost variances incurred in the manufacturing process to determine their statistical significance. Which of the following techniques is most likely to be used for this purpose?
a. Markov chains
b. Monte Carlo method
c. Application of probability theory
d. Sensitivity analysis

18. In the audit of a health insureance claims processing department, a sample is taken to test for the presence of fictitious payees, though none are suspected. The most appropriate sampling plan is
a. Attiribute sampling
b. Discovery sampling
c. Variables sampling
d. Stop or go sampling

19. An auditor for the state highway and safety department needs to estimate the average highway weight of tractor trailer trucks using the state's highway system. Which estimation method must be used?
a. Mean per unit
b. Difference
c. Ratio
d. Probability proportional to size

20. When would difference estimation of ratio estimation methods be inappropriate?
a. If differences between the book values and audit values of a population are rare
b. If the average difference between the audit value and book value of a population is small
c. If differences between the book value and audit value of a population are numerous
d. If the average difference between the audit value and book value of a population is large

21. An internal auditor is preparing to sample accounts receivable for overstatement. A statistical sampling method that automatically provides stratification when using systematic selection is
a. Attribute sampling
b. Ratio-estimation sampling
c. Dollar-unit sampling
d. Mean-per-unit sampling

22. Which of the following best describes an inherent limitation of the probability proportional to size sampling method?
a. It can only be used for substantive testing of asset accounts
b. It is complicated and always requires the use of a computer system to perform the calculations
c. Misstatement rates must be large and the misstatements must be overstatements
d. Misstatement rates must be small and the misstatements must be overstatements

23. An internal auditor plans to test the accuracy of recorded quantities on hand in an inventory file against the actual quantities on hand. Under which of the following conditions would the auditor be least likely to use a stop or go sampling plan?
a. The population to be sampled is very large
b. The auditor expects the population to contain a high rate of deviations
c. The auditor plans to draw a relatively small sample size
d. The auditor plans to determine an upper precision limit for the estimated percentage of deviations contained in the population

24. A statistical sampling technique that will minimize sample size whenever a low rate of noncompliance is expected is
a. Ratio estimation sampling
b. Difference estimation sampling
c. Stratified mean per unit sampling
d. Stop or go sampling

25. An auditor planning an attribute sample from a large number of invoice items intends to estimate the actual rate of deviations. Which factor below is the most important for the auditor to consider?
a. Audit objective
b. Population size
c. Desired confidence level
d. Population variance

26. When planning an attribute sampling application, the difference between the expected deviation rate and the maximum tolerable rate is the planned
a. Precision
b. Reliability
c. Dispersion
d. Skewness

27. A test of 200 invoices randomly selected by the auditor revealed that 35 had not been approved for payment. At the 95% confidence level, what precision can be assigned?
a. 6.9%
b. 5.3%
c. 9.1%
d. 3.5%

28. Very small random samples (fewer than 30) should normally be avoided when using a variables sampling plan because
a. The estimated standard deviation of the population will increase disproportionately
b. The skew of the distribution of sample means cannot be determined
c. The estimated population mean value will increase disproportionately
d. The size of the sampling risk will increase disproportionately

29. In applying variables sampling, an auditor attempts to
a. Estimate a qualitative charactristic of interest
b. Determine various rates of occurrence for specified attributes
c. Discover at least one instance of a critical deviation
d. Predict a monetary population value within a range of precision

30. An internal auditor is using variables estimation as the statistical sampling technique to estimate the monetary value of a large inventory of parts. Given a sample standard deviation of $400, a sample size of 400, and a 95% two-tail confidence interval, what precision can the auditor assign to the estimate of the mean dollar value of a part?
a. +/- $39
b. +/- $2
c +/- $52
d. +/- $20

31. 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 misstatement: +/- 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.

32. A statistical sample from an inventory containing a total of 10,000 items produced a sample mean equal to $25 and a standard error of the mean equal to $1. What is the interval estimate of the total value of the inventory at the 95.5% confidence level (C=2.0)?
a. $230,000 to $270,000
b. $240,000 to $260,000
c. $240,450 to $259, 550
d. $250,000 to $270,000

33. An auditor's finding was stated as follows: "Twenty of one hundred randomly selected items tested revealed that $200 of cash discounts on purchases were lost." This variables sampling finding is deficient because the
a. Recommendation specifies no action
b. Sampling methodology is not defined
c. Amount is not material
d. Probable effect on the entire population is not provided

34. Sample selection using dollar unit sampling for inventory valuation will most likely result in selectgion of a sample with characteristics roughly equivalent to one provided by
a. Mean per unit or direct extenstion unstratified sampling plans
b. Variables sampling plans with substantial stratification by dollar amount
c. Selection of inventory records using a random starting point for the record selection
d. Difference or ratio estimation plans applied on an unstratified basis

35. When an internal auditor uses dollar unit statistical sampling to examine the total value of invoices, each invoice
a. Has an equal probability of being selected
b. Can be represented by no more than one dollar unit
c. Has an unknown probability of being selected
d. Has a probability proportional to its dollar value of being selected

36. Which of the following would be an improper technique when using dollar unit statistical sampling in an audit of accounts receivable?
a. Combining negative and positive dollar error item amounts in the appraisal of a sample
b. Using a sampling technique in which the same account balance could be selected more than once
c. Selecting a random starting point and then sampling every nth dollar unit (systematic sampling)
d. Defining the sampling unit in the population as an individual dollar value and not as an individual account balance

37. The use of probability proportional to size sampling is inefficient if
a. Bank accounts are being audited
b. Statistical inferences are to be made
c. Each account is of equal importance
d. The number of sampling units is large

1. B
2. D
3. C
4. D
5. C
6. C
7. C
8. D
9. C
10. D
11. C
12. A
13. D
14. C
15. C
16. D
17. C
18. B
19. A
20. A
21. C
22. D
23. B
24. D
25. A
26. A
27. B
28. D
29. D
30. A
31. B
32. A
33. D
34. B
35. D
36. A
37. C