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SAMPLING



1. Productivity statistics are provided quarterly to the Board of Directors. An auditor checked the ratios and other statistics in the four most recent reports. The auditor used scratch paper and copies of the board reports to verity the accuracy of computations and compared the data used in the computations with supporting documents. The auditor wrote a note describing his work for the working papers and then discarded the scratch paper and report copies. The auditors note stated: The ratios and other statistics in the quarterly board reports were checked for the last tour quarters and appropriate supporting documents were examined. All amounts appear to be appropriate. In this situation:
a. Four quarters is not a large enough sample on which to base a conclusion.
b. The auditor's working papers are not sufficient to facilitate an efficient review of the auditor's work.
c. The auditor should have included the scratch paper in the working papers.
d. The auditor did not consider whether the information in the board report was compiled efficiently.

2. An auditor prepared a working paper that consisted of a list of employee names and identification numbers as well as the following statement: By matching random numbers with employee identification numbers, 40 employee personnel files were selected to verity that they contain alt documents required by company policy 501. No exceptions were noted. The auditor did not place any tick marks on this working paper Which one of the following changes would improve the auditor's working paper the most?
a. Use of tick marks to show that each file was examined.
b. Removal of the employee names to protect their confidentiality.
c. Justification for the sample size.
d. Listing of the actual documents examined for each employee.

3 As part of an internal audit, a benchmark must be established for the defect rate for an innovative new production process. The auditor can either use a large sample that is already available from other production processes in the same plant or draw a fresh sample from the new process. However, a fresh sample would be expensive, time consuming, and much smaller in size. Which one at the following is the best course of action for the auditor?
a. The auditor should accept this large historical sample because analyses based on it will have high statistical power.
b. The auditor should draw a fresh sample and combine it with the old sample.
c. The auditor should accept the historical sample but use nonparametric statistics to analyze it.
d. The auditor should first determine how similar the review process is to the old process before deciding what to do.

4. In a large computer manufacturer there has been much concern about the consistency across departments in adhering to new and unpopular purchasing guidelines. An auditor has a list that rank-orders all departments according to the percentage of purchases that are consistent with the guidelines and indicates which division the department is from. The auditor performs a t-test for differences in means on the average rank of departments in divisions A and B to see if there is any difference in compliance with the policy and finds that division A (which has more departments) has a significantly higher (i.e., better) average rank than division B. Which one of the following conclusions should be drawn from this analysis?
a. Division A is complying better with the new policy.
b. A random sample of departments should be drawn and the analysis recalculated.
c. A t-test is not valid when the tested groups differ in size.
d. A t-test is inappropriate for this data and another type of analysis should be used-

5. An auditor is checking the accuracy of a computer-printed inventory listing to determine whether the total dollar value of inventory is significantly overstated. Because there is no time or resources to check all items in the warehouse, a sample of inventory items must be used. If the sample size is fixed, which one of the following would be the most accurate sampling approach in this case?
a. Select those items that are most easily inspected.
b. Employ simple random sampling.
c. Sample so that the probability of a given inventory item being selected is proportional to the number of units sold for that item.
d. Sample so that the probability of a given inventory item being selected is proportional to its book value.

6. After partially completing an internal control review of the accounts payable department, an auditor suspects that some type of fraud has occurred. To ascertain whether the fraud is present, the best sampling approach would be to use:
a. Simple random sampling to select a sample of vouchers processed by the department during the past year.
b. Probability-proportional-size sampling to select a sample of vouchers processed by the department during the past year.
c. Discovery sampling to select a sample of vouchers processed by the department during the past year.
d. Judgmental sampling to select a sample of vouchers processed by clerks identified by the department manager as acting suspiciously.

7. A division uses a regression in which monthly advertising expenditures are used to predict monthly product sales (both in millions of dollars). The results show a regression coefficient for the independent variable equal to 0.8. This coefficient value indicates that:
a. The average monthly advertising expenditure in the sample is $800,000.
b. When monthly advertising is at its average level, product sales will be 5800,000.
c. On average, for every additional dollar advertising you get $0.80 in additional sales.
d. Advertising is not a good predictor of sales because the coefficient is so small.

8. The current audit of disbursements activities shows a significant number of errors made during the accounts payable vouching process which have resulted in lost discounts and an extraordinary number of adjustments and credit memos. Audit hours are already over budget in this section because of the number of exceptions which had to be analyzed Audit staff has had time to observe the operations performed by each of the voucher clerks, sample and analyze transaction documents in the accounts payable, purchasing, and receiving departments, and obtain system statistics which show transaction volume, error correction transactions, and lost discount summaries. To date, the causes have not been fully identified for all types of errors noted during detail testing, observation, and analysis of exceptions, in any of the three departments. The most appropriate course of action for the lead auditor to determine the causes of these errors is to:
a. Question and get the opinions of the accounts payable clerks and those involved in processing these transactions.
b. Expand sample sizes for attributes already tested in transactions entered by accounts payable, purchasing, and receiving.
c. Concentrate on audit program requirements for cash disbursements testing to discover any related information from those tests.
d. Describe the transaction-related problems identified to date in a special report to management without expressing a cause or an auditor's conclusion about the situation-

9. During an operational audit, a department head was asked why the detect rate in his department had increased. Which one of the following potential responses would be most creditable considering how perceptions affect judgments?
a. The detect rate increased because we received unreliable information from the design department.
b. The defect rate increased because I did not adequately train the new employees.
c. The detect rate increased because some employees have developed bad attitudes over the increased workload that has resulted from downsizing.
d. The defect rate increased because of equipment malfunctions.

10. During an internal control inspection an auditor is evaluating the contents of a large warehouse that contains records from both the retail and the wholesale divisions of the client company. Upon inspecting the contents of one particular randomly selected box, the auditor discovers that the contents do not match the computer-generated label taped to the outside of the box. On average, errors of this kind have occurred in 6% of retail boxes and 2% of wholesale boxes. Unfortunately, some water has leaked onto the label and smeared the part that indicated the division of origin. The auditor does know that two-thirds of the boxes in this warehouse come from the wholesale division and one-third from the retail division. Which of the following can be concluded?
a. The box is more likely to have come from the retail division than from the wholesale. division.
b. The box is more likely to have come from the wholesale division than from the retail division.
c. The proportion of retail boxes in the warehouse is probably much larger than the auditor thought.
d. The proportion of wholesale boxes in the warehouse is probably much larger than the auditor thought.

11. Which one of the following statements about sampling is true2.
a. A larger sample is always more representative of the underlying population than a smaller sample.
b. For very large populations, the absolute size of a sample has more impact on the precision of its results than does its size relative to its population.
c. For a given sample size, a simple random sample always produces the most representative sample.
d. The limitations of an incomplete sample frame can almost always be overcome by careful sampling techniques.

12. Which one of the following is not an important consideration in determining the appropriate sample size?
a. Whether the sample is designed to estimate a mean or a proportion.
b. The amount of variability in the population under study.
c. The sensitivity of the decision using this sample to errors of estimation.
d. The cost per sample observation.

13. An auditor is considering a sample size of 50 to estimate the average amount per invoice in a large trucking company. How would the precision of the sample results be affected if the sample size was increased to 200?
a. The larger sample would be about two times as precise as the smaller sample.
b. The larger sample would be about four times as precise as the smaller sample.
c. Although precision would not be increased that much, a possible downward bias in the estimate of the average per invoice would be corrected.
d. Since both sample sizes are larger than 30, the increase would not have that much of an effect on precision.

14. Which one of the following is a correct rationale for using a nonparametric statistic rather than a more conventional statistic?
a. it is not known how the variable being tested is distributed.
b. The event or difference to be tested is fairly small I and therefore you need a more sensitive test.
c. The sample was not drawn randomly
d. The variable being tested is measured on a continuous scale.

15. A 90% confidence interval for the mean of a population based on the information in a sample always implies that there is a 90% chance that the:
a. Estimate is equal to the true population mean.
b. True population mean is no larger than the largest endpoint of the interval.
c. Standard deviation will not be any greater than 10 % of the population mean.
d. True population mean lies within the specified confidence interval.

16. Which one of the following statements is true regarding two random samples drawn in the same way from the same population, one of size 30 and one of size 300?
a. The two samples would have the same expected value.
b. The larger sample is more likely to produce a large sample mean.
c. The smaller sample will have a smaller 95% confidence interval for the mean.
d. The smaller sample will, on the average, produce a lower estimate of the variance of the population.

17. Management is legally required to prepare a shipping document for all movement of hazardous materials. The document must be tiled with bills of lading. Management expects 100% compliance with the procedure. Which of the following sampling approaches would be most appropriate?
a. Attributes sampling.
b. Discovery sampling.
c. Targeted sampling.
d. Variables sampling.

18. An auditor is conducting a survey of perceptions and beliefs of employees concerning an organization health care plan. The best approach to selecting a sample would be to:
a. Focus on people who are likely to respond so that a larger sample can be obtained.
b. Focus on managers and supervisors because they can also reflect the opinions of the people in their departments.
c. Use stratified sampling where the strata are defined by marital and family status, age, and salaried/hourly status.
d. Use monetary' unit sampling according to employee salaries.

19. An auditor asks accounting personnel how they determine the value of the organization's real estate holdings. They say that valuations are based on a regression model that uses different characteristics of the properties (square footage, proximity to downtown, age, etc) to predict value. The coefficients of this model were estimated using a random sample of 20 company properties, for which the model produced an k2 value of 0.92. Based on this information, which one of the following should the auditor conclude?
a. The model's high R1 is probably due in large Part to random chance.
b. 92% of the variables that determine value are in the model.
c. The model is very reliable.
d. This sample of properties is probably representative of the overall population of. company holdings.

lb 2c 3d 4d 5d 6c 7c 8a 9b 10 b 11 b 12 a 13 a 14 a 15 d 16 a 17 b 18 c 19a

1. A bank auditor is interested in estimating the average account balance of its depositors bard on a sample. This substantive test is an example of:
a. Attributes sampling.
b. Discovery sampling.
c. Acceptance sampling.
d. Variable sampling.

2. A bank auditor wishes to confirm liability demand deposits. The bank has excellent internal control. The auditor might efficiently use all of the following samples techniques in confirming demand deposits except:
a. Discovery sampling.
b. Monetary unit sampling probabIiity proportional to size.).
c. Cluster sampling.
d. Stratified mean per unit (variables estimation) sampling.

3 A car rental agency has branches located throughout the world that are essentially small-scale representations of the entire population. What is the appropriate sampling method for determining the average net revenue per vehicle in inventory?
a. Stratified sampling.
b. cluster sampling.
c. Attributes sampling.
d. Systematic sampling.

4. A company had two billing clerks during the year. Snow worked three months and white worked nine months. The CPA wishes to use discovery sampling to test clerical accuracy during the tenure of each clerk. If the quantity of bills per month is constant and the same specified reliability and maximum tolerable occurrence rate is specified for each population, the ratio of the sample drawn from white's bills to the sample drawn from Snow's bills would be:
a. More than 3:1.
b. 3.1.
c. More than 1:1 but less than 3:1.
d. 1:1.

5. A company prepared approximately 100,000 accounts payable vouchers in 1981. Payments are generally documented and few errors have been found in previous years. The following sampling plan has been proposed to test compliance with prescribed payment policies:
a. An appropriate sample size cannot be computed until the auditor specifies the desired precision.
b. Statistical sampling is inappropriate because the population size is not known exactly.
c. An appropriate sample size cannot be computed until the distribution of errors in the population is -fled.
d. A properly designed sample will allow the auditor to conclude, with 95 percent accuracy, that the error rate does not exceed 1 percent.

6. A confidence level of 95 percent for a variables sampling application can be interpreted as a 95 percent probability that:
a. Sample results will be free of sampling and nonsampling errors.
b. Results of repeated samples win not vary from population characteristics by more than a specified amount.
c. The tested account balance win be correct if desired precision is achieved.
d. Sample results will be within plus or minus five percent of the true population values.

7. A CPA who believes the occurrence proportion of a certain characteristic in a population being examined is 3 percent and who has established a maximum acceptable occurrence proportion at 5 percent should use (a) (an)-
a. Attribute sampling plan.
b. Discovery sampling plan.
c. Stratified sampling plan.
d. Variable sampling plan

8. A CPA's test of accuracy of inventory counts involves two storehouses. Storehouse A contains 5,000 inventory items and Storehouse B contains 10,000 items. The CPA plans to use sampling without replacement to test for an estimated 5% error rate. If the CPA's sampling plan calls for a specified reliability of 95% and a maximum tolerable error occurrence rate of 7.5% for both storehouses, the ratio of the size of the CPA's sample from Storehouse A to the size of the sample from Storehouse B should be:
a. More than 1:l
b. 2:1
c. 1:1
d. More than2:l but less than 5:l
e. None of the above answers.

9. A major distinction between statistical and judgmental sampling is that:
a. Judgmental sampling allows the quantification of sampling error.
b. Statistical sampling virtually eliminates sampling risk.
c. Statistical sampling provides an objective means of determining sample size.
d. Judgmental sampling results in smaller sample sizes.

10. A major problem in using a systematic sampling plan as opposed to random number selection plan is:
a. To develop correspondence between the population and random numbers.
b. To be stir: there is not a coinciding pattern in the population.
c. The need to stratify the population.
d. To determine the size of the sampling interval.

11. A multistage sampling plan is most appropriate for evaluating inventory when:
a. Inventory records are automated.
b. A wide range of values exists in the inventory.
c. Inventory locations are geographically -err".
d. Perpetual inventory records art maintained.
e. None of the above.

12. A population that is physically separated into two or more groups bard on the sample variation being less than that for the entire population is called:
a. Systematic sample.
b. Judgrnent sample.
c. Simple random sample.
d. Stratified sample.

13. A sample of l44 times taken from a population of 10,000 items resulted in the following: Sample mean =72.0 Sample standard deviation = 18.0 Confidence level = 95% (Z=1.96) Desired precision = 3.0
a. 1.50.
b. 2.94.
c. 4.00.
d. 5.88.

14. A sampling method that can be used to estimate overstatement error of an account balance but is not based on normal curve mathematics is:
a. Discovery sampling.
b. Mean-per-unit sampling.
c. Attributes sampling.
d. Dollar-unit sampling.

15. A simple random sample requires that:
a. The population is unbiased.
b. Every item in the population has an equal chance of being selected.
c. The distribution of original data is approximately normal.
d. The expected error rate is low (1ess than five Percent).

16. A statistical sample from an inventory containing a total of 10,000 items produced a sample mean equal to $25000, and a standard error of the mean equal to $1.00. What is the interval estimate of the total value of the inventory at the 95.5 percent confidence level (Z = 2.0)7
a. $230,000 to $270,000.
b. $240,000 to $260,000.
c. $240,450 to $259,550.
d. $250,000 to $270,000.

17. A test of 200 invoices randomly selected by the internal auditor revealed 35 which had not been approved for payment. At the 95 percent confidence level, what precision can be assigned?
a. 6.9 percent
b. 5.3pereent
c. 9.1 percent
d. 3.spereent
e. l.7percent

I8. 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.

19. An attribute sampling plan would be useful in determining an estimate of the:
a. Percentage of customers more than 30 days late in making payments.
b. Frequency of late payments and their aggregate dollar amount.
c. Audit value of inventory.
d. Total purchases from subsidiaries.

20. An auditor applying a discovery-sampling plan with a 5-percent risk of overreliance may conclude that there is:
a. A 95-peeeent probability that the actual rate of occurrence in the population is less than the critical rate if only one exception were found.
b. A 95-percent probability that the actual rate of occurrence in the population is less than the critical rate if no exceptions were found
c. A 95-percent probability that the actual rate of occurrence in the population is less than the critical rate if the occurrence rate in the sample were less than the critical rate.
d. Greater than a 95-percent probability that the actual rate of occurrence in the population is less than the critical rate if no exceptions were found.

21. An auditor desired a sample of 50 items from a population of 5,000 items. The auditor initially planned to select a random number between 1 and 100 and then to systematically sample every 1000' item from the random starting point. Later, evidence was found which led the auditor to believe that the population items were arranged in some systematic manner related to the characteristic being measured or tested. The auditor should have:
a. Proceeded according to the initial plan.
b. Drawn a judgment sample instead of following the plan.
c. Used a random-number table to select the items.
d. Changed to a single block sampling plan.
e. Selected the first item in the population and then systematically sampled every l00th item thereafter.

22. An auditor desires to select a statistically representative sample from a large population of unnumbered documents. Which sampling method would provide the best opportunity for a representative sample?
a. Cluster sampling based on random identification of the first document in each cluster.
b. Stratified sampling based on multiple random starting points in the population.
c. Systematic sampling based on multiple random starting -its in the population.
d. Multistage sampling based on random identification of the primary documents in each stage.

23. An auditor desires to use a table of random digits to select a sample from a population of documents which have the following broken number sequences: 0001-1000,2000-5000, and 8000-11000. which of the following is the most efficient approach to overcome the problem of the broken number sequences?
a. Deduct four-digit constant values from the second and third sequences, choose the appropriate random numbers, and add the constants back to the individual numbers.
b. Skip through the entire random number tables until large blocks of digits appear which will fit within the three different number sequences.
c. Choose appropriate random numbers from the tables without any modifying of the approach and recognize that a large selection of unusable numbers will occur.
d. Select three different starting points in the random tables and vary the selection pattern to obtain needed numbers in the three different sequences.

24. An auditor discovered that discounts for prompt payment were frequently not being taken. About 30 percent of the suppliers' invoices offered discounts ranging from 2 percent to 5 percent of the invoice amount. To estimate the amount lost from not taking these discounts during the year, the most efficient and effective sampling technique would be:
a. Mean-per-unit estimation.
b. Dollar-unit sampling.
c. Difference estimation.
d. Ratio estimation.

25. 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. Measures 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 the possible invoice samples of the same size.
d. Perform difference estimation and avoid a large sample.
e. Compute the results of a variable sample through the use of standard tables.

1. D 2. A 3. B 4. C 5. A 6. B 7. A 8. E 9. C 10. B 11. C 12. D 13. A 14. D 15. B 16. A 17. B 18. D 19. A 20. B 21. C 22. C 23. A 24. D 25. B,C

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