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statistical sampling to auditing

Applications Of Statistical Sampling To Auditing 1st Edition Alvin A. Arens, James K. Loebbecke - Solutions

What is meant by the precision interval for ratio estimation? Calculate the precision interval for the errors in question 6-3 at a confidence level of 90%. Compare your answer to the one for question 5-11, where the same errors were used to determine the precision interval for difference
Calculate the confidence interval and confidence limits for the errors in question 6-3 using ratio estimation. Compare your answer to the one for question 5-12 where the same errors were used to determine the confidence interval and confidence limits for difference estimation.Question
When difference estimation is used for calculating confidence intervals in a hypothesis test, the auditor must know the population size, sample size, value of each individual error in the sample, and Beta risk. It is also necessary to square each error and sum the total. Which of this information
Compare the formula to calculate the computed precision interval for ratio estimation (Figure 6-3) to the one for difference estimation (Figure 5-4). In what way are they different ? where: N CPI N.Z.SD = CPI = computed precision interval N = population size Z = confidence coefficient (two-sided)
The formula to determine sample size for both ratio and difference estimation is:Define each term in the formula. Explain the two causes for possible differences in the required sample size in a given audit situation for ratio estimation as compared to difference estimation. n= (N.Z(126). SD*) API*
Assuming all other factors are held constant, identify the effect (increase or decrease) on the required sample size for ratio estimation when each of the following four factors is independently increased: confidence level, population size, acceptable error in the population, and estimated
Assuming all other factors are held constant, identify the effect (wider, narrower, or no effect) on the computed precision interval for ratio estimation when each of the following four factors is independently decreased: Beta risk, size of the individual errors in the sample, acceptable error in
Explain the difference between the confidence level and Beta risk as it is used in ratio estimation. When should each be used?
The confidence interval for an audit test where ratio estimation was used is \($26,000\) ± \($40,000\). The allowable error for the audit test was set at \($60,000\). Show graphically by the use of the proper decision rule that the population is not acceptable. Calculate the amount of the
An auditor uses ratio estimation to determine the value of the errors in accounts receivable. He concludes that the error value is from \($(14,000)\) to \($26,000\) at a 90% reliability. State the results of the audit test in words. Identify the value in the example for the following terms:
Describe how ratio or difference estimation could be used for the confirmation of accounts receivable. Why is it necessary to use positive confirmations when a statistical estimate is to be made ? Describe the most likely problems affecting the statistical results that will be encountered in
An auditor has decided in a particular situation that the population characteristics needed to make either ratio or difference estimation a sufficiently reliable estimator for his purposes are present. Provide specific criteria that should be used in deciding whether to use ratio or difference
What is meant by the efficiency of an estimator? Under what circumstances is ratio estimation likely to be a more efficient estimator than mean-per-unit estimation ?
Sample selection and calculation costs are factors to consider in deciding upon a statistical method. Which of these two costs is apt to be affected in deciding between ratio and difference estimation, and which cost is not apt to be affected? Explain your answer. Under what circumstances is the
What is meant by the reliability of an estimator? Describe the circumstances in which ratio estimation is likely to be a reliable estimator. When is it likely to be an unreliable estimator?
Describe the circumstances in which unstratified ratio estimation is a desirable statistical method for auditors compared to mean-per-unit estimation or stratified sampling.
A CPA’s client is considering adoption of statistical sampling techniques. Accordingly, he has asked the CPA to discuss these techniques at a meeting of client employees. In connection with this presentation, the CPA prepared the following table, which shows the comparative characteristics of two
You are using statistical sampling to confirm accounts receivable of Pittance Manufacturing Company. The population of accounts receivable is as follows:You review the accounts receivable trial balance and observe that there are several extremely large balances.The sample is designed to include the
For each of the following populations concerning the valuation of raw- materials inventory, the auditor has established an allowable error for hypothesis testing using difference estimation. The auditor has also calculated actual statistical results after the audit tests have been
For each of the following populations concerning the valuation of raw-materials inventory, the auditor has established an allowable error for hypothesis testing using ratio estimation. The auditor has also calculated actual statistical results after the audit tests have been conducted.Required :a.
Rebecca Downs, CPA, is doing the audit of Berlup Gun and Rack Shop, a national wholesaler of rifles and related equipment and supplies. She is surprised at the results found in the testing to this point in sales and sales returns. There are large numbers of errors in the sales tests, which were
Reynolds Products Inc. buys large amounts of raw materials and parts from approximately 600 different vendors. Individual raw-materials purchases range from less than SI00 to more than SI0,000.All acquisitions of goods and services transactions, except payroll, are recorded on a computer listing.
Roger Goodman, CPA, is doing a test of the cost of inventory of Spiller Spring Manufacturing Company. The decision is made to use both ratio and difference estimation to determine whether the raw-materials inventory is materially misstated. Roger decides that a population error of \($25,000\) or
You are doing the audit of Baker Tool’s valuation of inventory. The inventory is made up of 8,000 different kinds of items. The value of different kinds of inventory does not vary enough to justify stratification. You conclude that an error of \($75,000\) would be material, and you expect a point
In testing the cash discounts on vendors’ invoices, the auditor did not expect to find any errors in the sample, and therefore he used attributes sampling techniques. Based upon the statistical requirements for the test, a sample size of 120 items was randomly selected and carefully tested. Much
You are in charge of the audit of the United Widget Workers of America, a labor union that your firm has been auditing for several years. In performing the audit for the year ended June 30, 198X, you note that the union signed a new contract with all employers as of January 1, 198X. The new
The following questions concern the determination of the proper sample size in attributes sampling:a. For each of the columns numbered 1 through 7, determine the initial sample size needed to satisfy the auditor’s requirements from the appropriate table in Figures 3-2 and 3-3. Wherever the sample
The following questions relate to determining the computed upper precision limit in attributes sampling.a. For each of the columns numbered 1 through 8, determine the computed upper precision limit from the appropriate table in Figures 3-2 and 3-3. Wherever the sample size is more than 10 percent
When is difference estimation a more useful statistical method than attributes? When is attributes more useful ?
During a professional development program at a CPA firm, an audit manager was instructing several younger staff members on how to calculate confidence intervals in the accounts receivable area by using difference estimation. As part of the discussion, he explained the importance of the population
An audit partner is developing an office training program to familiarize his professional staff with difference estimation applicable to the audit of dollar- value balances. He wishes to demonstrate the relationship of sample sizes to population size and variability and the auditor’s
In testing the cash discounts on vendors’ invoices, the auditor did not expect to find any errors in the sample and therefore used attributes sampling techniques. Based upon the statistical requirements for the test, a sample size of 120 items was randomly selected and carefully tested. Much to
An audit client has decided to determine the ending valuation of inventories by physically counting and costing only a sample of their total inventory. There are no perpetual records. Explain why difference estimation would not be an appropriate statistical method in these circumstances.
Distinguish between a hypothesis test and an interval estimate. When is each used ?
What is meant by the point estimate of the total errors for difference estimation? Calculate the point estimate when there are the following client errors in a sample of 120 items from a population of 3,000 (understatements are in parentheses): 48.12, 56.11, 97.16, (41.14), 13.06, 191.67, (84.91),
What is meant by the population standard deviation? Calculate the estimate of the population standard deviation based on the sample errors in question 5-7.Question 5-7:What is meant by the point estimate of the total errors for difference estimation? Calculate the point estimate when there are the
What is meant by the precision interval? What are the four factors that affect the size of the computed interval ? Calculate the precision interval, at a confidence level of 90%, for the errors in question 5-7.Question 5-7:What is meant by the point estimate of the total errors for difference
Distinguish between the terms confidence interval and confidence limits. Describe how each is calculated. Calculate both for the error information in question 5-7.Question 5-7:What is meant by the point estimate of the total errors for difference estimation? Calculate the point estimate when there
Distinguish between the following terms: confidence level, confidence limits, confidence interval, and computed precision interval. For the statistical statement, “The population value of the errors is \($50,000\) ± \($16,000\) with a reliability of 90 percent,” calculate or identify the value
In reviewing the results of a difference estimation calculation, an in-charge auditor, Roger Murphy, concluded that the confidence limits were larger than he could accept. In examining the details of the calculation, he determined that the point estimate of the population was nearly zero, but the
What is meant by materiality for hypothesis testing using difference estimation ? Explain how the auditor decides what is material and the effect of the decision on the required sample size.
Define what is meant by Alpha and Beta risk for hypothesis testing, and distinguish between the two risks. Explain the advantages and disadvantages of a small Beta risk. Do the same for Alpha risk.
Distinguish between confidence level and Beta risk. Also distinguish between confidence level and Alpha risk.
State the decision rule using hypothesis testing for difference estimation. Assume the confidence interval at a 95% confidence level is \($25,000\) ± \($15,000\) and a materiality limit of \($45,000\). What is the decision in that circumstance?
What options does the auditor have when the decision rule rejects the population as not acceptable? State the circumstances for which each option is preferable.
Two auditors follow different approaches in determining sample size for unstratified difference estimation. The first auditor always selects a sample size of 75 items. He then calculates the confidence limits and compares them to materiality. If the population is rejected, he carefully goes through
Assume that the preliminary estimate of the sample size for hypothesis testing is determined by using only Beta risk. What problem is the auditor apt to encounter when the sample results are evaluated? Under what circumstances is that problem likely to be serious ?
The following formula is to determine the preliminary estimate of the sample size for difference estimation considering only Beta risk:Define each of the terms affecting sample size and state the effect on the preliminary estimate of changing each factor independently. n = N.Z(1-28).SD*V 3). SD*)
Explain how the inclusion of Alpha risk affects the calculation of the preliminary estimate of the sample size. Explain the circumstances in which it is desirable to include or exclude Alpha risk in determining sample size.
How do determining a sample size for hypothesis testing and for interval estimation differ? Explain the reason for the difference.
Assume you are using interval estimation for the purpose of making an adjusting entry. What would you do if materiality were \($20,000\) and the calculated confidence interval were \($8,000\) ± \($16,000\) at a 95% confidence level? Would your answer be different if the confidence interval were
Explain what is meant by efficiency as the term is used in difference estimation. Under what circumstances is difference estimation apt to be more efficient than unstratified mean-per-unit ?
Explain what is meant by the reliability of difference estimation. Under what circumstances is difference estimation likely to be reliable, and when is it likely to be unreliable ?
Assume that the auditor is in a situation in which the unstratified difference estimate is an unreliable estimator. How will she know the estimator is un¬ reliable in that situation? What can the auditor do if she knows the estimator is unreliable?
Under what circumstances is unstratified difference estimation a desirable statistical method for auditors ?
The following apply to difference estimation variables sampling. Choose the best response.a. The auditor’s failure to recognize an error in an amount or an error in an internal control data-processing procedure is described as a:(i) Statistical error(ii) Sampling error(iii) Standard error of the
a. Using difference estimation, calculate the preliminary sample size for a to e from the information provided. Apply the finite correction factor when it is appropriate.b. In general, what is the effect on the preliminary sample size (increase, decrease, no effect, or cannot determine without
a. Calculate the preliminary sample size using difference estimation for a to e from the information provided. Apply the finite correction factor when it is appropriate.b. In general, what is the effect on the preliminary sample size (increase, decrease, no effect, or cannot determine without
The following are five different sets of sample information from a population of 5,000 accounts receivable with a book value of \($4,600,000\). (In each situation, the net book value of the items in the sample exceeds the audit value.)Required :a. Using difference estimation, calculate the point
In confirming accounts receivable with a recorded value of \($6,250,000\) for the Blessman Wholesale Drug Company, Gerald Bloomstad, CPA, has decided that if the total error in the account exceeds \($60,000\), he will consider the error material. He believes the point estimate of the error will
a. Calculate confidence limits for a to e using difference estimation from the information provided:b. In general, what is the effect on the upper confidence limit (increase, decrease, no effect, or cannot determine without additional information) of each of the following independent changes,
a. Using difference estimation, calculate confidence limits for a to e from the information provided.b. In general, what is the effect on the upper confidence limits (increase, decrease, no effect, or cannot determine without additional information) of each of the following independent changes,
For each of the following populations, the auditor has established an acceptable precision interval as a part of using difference estimation and has calculated actual statistical results after conducting the audit tests:Required:a. Determine which of the calculated results satisfy the acceptable
An auditor is using difference estimation for the confirmation of accounts receivable in the audit of Lafferty Hardware Supply. A random sample of 100 positive confirmations has been sent to customers. Second requests have been mailed to all no-responses. Alternate procedures have been done for all
Marjorie Jorgensen, CPA, is verifying the accuracy of outstanding accounts payable for Marygold Hardware, a large, single-location, retail hardware store. There are 650 vendors listed on the outstanding accounts payable list. She has eliminated from the population 40 verfdors that have large ending
Roybuilt Machines has computerized its fixed-asset records during the past year. The company feels that the conversion was completed with only minor errors in recording useful lives and depreciation methods, but, based on past experience, you are not so sure. When Roybuilt Machines converted its
You are using difference estimation in the costing of inventory as part of the audit of the Rubber Products and Supply Company. The following data are available or have been developed by you:Required :a. What is the sample size necessary to achieve your audit objectives ?b. What would be the
For a number of years, the accounts receivable confirmation process at John’s Printing Company has been more time-consuming than is considered desirable. Typically, about 20% of the 500 active accounts were sent positive confirmations. About 70% of these were returned either initially or after a
Your client, Dowlray Motor Co., is a small, one-plant operation that manufactures only motors for large boats, but in numerous shapes and models. The company, following the lead of the larger firms in the industry, several years ago converted from FIFO to LIFO for its raw-materials,
Phil Mayberg is reviewing the work of an assistant who performed tests of transactions in sales using attributes sampling for the audit of Rogers Supply Company. The assistant found procedural errors in several different areas, but much to Phil’s surprise, he also found a much larger number of
You are doing the audit of Maylo Supply Company. You plan to check quantities, prices, and extensions on a selected random sample of inventory tags, and to evaluate your results by using difference estimation. You will have to foot the client’s inventory listing, because this method depends on
What is meant by the term variables sampling? Explain the objective of variables sampling.
Compare and differentiate what is being measured in variables sampling and attributes sampling. Under what circumstances would variables sampling be a more appropriate statistical method than attributes ? When would attributes be more appropriate?
Define what is meant by a population distribution. What is the relevance of population distributions for variables sampling ?
Distinguish among the following three terms: frequency distribution, frequency histogram, and continuous population distribution curve.
Define and distinguish among the following three terms: population mean, mode, and median. Calculate or determine the value of each term for the following population: 26, 71,56, 3, 47, 865, 14, 3, 86, 111. Explain why the three values are dissimilar in this situation.
Explain what is meant by population standard deviation. Why is the size of the standard deviation in a given population important for variables sampling ?
Evaluate the following statement: “Every population with individual values making up a total value has a population mean, population standard deviation, and population distribution. The population standard deviation is the most important of these three for using variables sampling.”
Define what is meant by a normal population distribution. Why is a normal population distribution important in statistical sampling in auditing ?
Distinguish among the following four types of population distributions: skewed to the right, bimodal, normal, and skewed to the left. Graph each type.
An auditor is verifying inventory costs by examining supporting documentation. Explain how the auditor would approach the audit differently depending on whether his interest was in the audited value of the inventory items or in the value of errors in the population.
Why are the shape and standard deviation of populations important to auditors planning to use variables sampling? Identify two factors that make it difficult for auditors to determine the shape and standard deviation of the population.
Distinguish among the following three variables sampling methods in terms of what the auditor is measuring: difference estimation, ratio estimation, and mean-per-unit. estimation.
What is meant by stratified sampling in variables sampling? What is the purpose of using stratified as opposed to unstratified sampling ?
What is meant by a sampling distribution ? Distinguish between a sampling distribution and a population distribution.
Explain how it would be possible to determine a sampling distribution from a population in each of the following two ways: (1) repeated samples from a given population, or (2) mathematically. What information would have to be known to determine the sampling distribution mathematically?
Calculate the confidence limits of the population mean at a confidence level of 95% if one sample of 100 items resulted in a point estimate of the mean of \($937\) and a standard error of the mean of \($126\). What assumptions are necessary before the calculated confidence limits can be considered
Evaluate each of the following conclusions for correctness if an auditor selected a random sample of 100 items from a population of 2,000 and, based upon accurate statistical calculations, determined that the confidence interval was \($4,200\) \($1,500\) at the 90% confidence level:a. The
The determination of a sampling distribution requires a population with a known mean, standard deviation, sample size, and knowledge of the population distribution. In practice, the auditor is usually certain of only the sample size. Why is it important to understand sampling distributions when
What is meant by the efficiency of an estimator as it is used in variables sampling ? Why is efficiency an important factor in deciding on a variables method ?
What is meant by the reliability of an estimator as it is used in variables sampling and nominal reliability? Why is actual reliability an important factor in deciding on a variables method ?
Identify the four factors indicated by the Neter and Loebbecke research as having the greatest effect on the reliability of estimators.
The following items apply to statistical sampling. Choose the best response.a. There are many kinds of statistical estimates that an auditor may find useful, but basically, every accounting estimate is either of a quantity or of an error rate. The statistical terms that roughly correspond to
Each of the following applies to concepts used in variables sampling. Choose the best response.a. An important statistic to consider when using a statistical sampling audit plan is the population variability. The population variability is measured by the(i) Sample mean(ii) Standard deviation(iii)
The following frequency distribution is for the accounts receivable of Herman Rental Products:Required :a. Prepare a frequency histogram for Herman Rental Products’ accounts receivable.b. Prepare a continuous population distribution curve for Herman Rental Products’ accounts receivable.c.
The following frequency distribution is the physical inventory of Wholesale Natural Foods, Inc., at the balance sheet date.Required :a. Prepare a frequency histogram for Wholesale Natural Foods’ inventory.b. Prepare a continuous population distribution curve for Wholesale Natural Foods’
Below are seven population distributions and one sampling distribution:Required:a. Identify all distributions that are symmetrical.b. Identify all distributions that might be normal.c. Identify all distributions that are skewed. Label each one as “skewed to the right” or “skewed to the
The following are sampling distributions for difference estimation from two different populations. Both distributions have the same shape, and the horizontal and vertical axes have the same values and scales.Required:a. Which of the distributions has the larger mean ?b. Which of the distributions
The following are four distributions that have different shapes, but the same values and scales on the horizontal axis:Required :a. Assuming the distributions represent populations of data, explain how the sampling distribution for each population could have been determined.b. Assuming the
a. Calculate the confidence interval and confidence limits of the population mean for each of the following independent sample results from populations with unknown population characteristics:b. Assume you are using mean-per-unit estimation with population 3. Describe an example in auditing in

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