Module 4

An auditor randomly samples 70 out of 1,000 items and discovers an overstatement of $9000. What is the projected misstatement for the entire population?

$128571

In a probability-proportional-to-size sample with a sampling interval of $5,000, an auditor discovered that a selected account receivable with a recorded amount of $10,000 had an audit amount of $8,000. If this were the only error discovered by the auditor, the projected error of this sample would be:

$2,000

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 audited amount of $4,000. If this were the only misstatement discovered by the auditor, the projected misstatement of this sample would be:

$2,000.

Which of the following factors should an auditor consider in making a judgment about whether an internal control deficiency is so significant that it is a significant deficiency?

-Diversity of the entity's business -Size of the entity's operations

For uncorrected misstatements, the auditor should document which of the following?

-all misstatements accumulated during the audit and whether they have been corrected. -the amount below which misstatements would be regarded as clearly trivial. -the auditor's conclusion about whether uncorrected misstatements are material, individually or in the aggregate, and the basis for that conclusion.

According to the PCAOB, which of the following statements are true with respect to the auditor's responsibility to communicate material weaknesses in internal control over financial reporting?

-all such weaknesses must be communicated in writing to the audit committee. -all such weaknesses must be communicated in writing to management. -all such weaknesses must be communicated prior to the issuance of the auditor's report on internal control over financial reporting.

Which is a type of factual misstatement?

-an inaccuracy in processing data. -the misapplication of accounting principles.

Uncorrected misstatements should be documented in a manner that allows the auditor to:

-consider the qualitative factors that are relevant to the auditor's consideration whether misstatements are material. -separately consider the effects of known and likely misstatements, including uncorrected misstatements identified in prior periods. -consider the aggregate effect of misstatements on the financial statements.

In evaluating the overall effect of audit findings on the auditor's report, the auditor should document which of the following?

-the levels of materiality and tolerable misstatement, including any changes thereto, used in the audit and the basis on which those levels were determined. -a summary of uncorrected misstatements, other than those that are trivial, related to known and likely misstatements. -the auditor's conclusion as to whether uncorrected misstatements, individually or in aggregate, do or do not cause the financial statements to be materially misstated, and the basis for that conclusion. -all known and likely misstatements identified by the auditor during the audit, other than those that are trivial, that have been corrected by management.

When determining whether uncorrected misstatements are material, individually or in the aggregate, an auditor of a nonissuer would consider which of the following?

-the particular circumstances of each misstatement. -the effect of uncorrected misstatements related to prior periods. -the size and nature of the misstatements.

An auditor desired to test credit approval on 10,000 sales invoices processed during the year. The auditor designed a statistical sample that would provide a 1% risk of assessing control risk too low (99% confidence) that not more than 7% of the sales invoices lacked approval. The auditor estimated from previous experience that about 2.5% of the sales invoices lacked approval. A sample of 200 invoices was examined and 7 of them were lacking approval. The auditor then determined the achieved upper precision limit to be 8%. The allowance for sampling risk was:

4.5%

What is the maximum number of days in which a nonissuer's auditor should complete the assembly of the final audit file following the report release date?

60 days

Find the auditing standard and paragraph in the AICPA's Codification of Statements on Auditing Standards (clarified standards) that define the risk of incorrect acceptance.

AU-C 530.A13

Adjusting Journal Entry #3: (See Exhibit #3, "Audit Workpaper," Tickmark B.)

Accounts receivable DR - 75,000 Unbilled receivables CR - 75,000

Which of the following statements concerning material weaknesses and significant deficiencies is correct?

All material weaknesses are significant deficiencies.

Which of the following factors would the auditor explicitly consider when determining sample size in an attribute sample for a test of controls?

An acceptable level of the risk of overreliance The tolerable deviation rate The expected population deviation rate

How would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details?

An increase in tolerable misstatement would decrease the sample size; an increase in assessed level of control risk would increase the sample size.

In an audit of financial statements, which of the following would most likely be considered a known misstatement?

An unrecorded liability related to services rendered by a vendor during the period under audit

In performing tests of controls over authorization of cash disbursements, which of the following statistical sampling methods would be most appropriate?

Attribute

Which of the following types of sampling allows an auditor to quantify sampling risk?

Attribute

Which of the following is true regarding significant deficiencies?

Auditors must communicate them to the audit committee.

What is the statistical sampling term that describes the risk that the results of the sample to test an account balance will result in incorrect acceptance of the population, when the population actually contains misstatement?

Beta risk, the risk of incorrect acceptance of conclusions

Which of the following factors is considered in determining the sample size for a test of controls?

Both expected and tolerable deviation rates

Uncollectible accounts expense could be either understated or overstated because the lack of established credit limits may make it more difficult to identify uncollectible amounts.

Credit is not granted on the basis of established limits.

Adjusting Journal Entry #1: (See Exhibit #2, "Debt Restructuring Email.")

Current portion of long-term debt DR - 2,500,000 Long-term debt CR - 2,500,000

An auditor has determined a materiality threshold of $100,000 for a client. The auditor has accumulated audit evidence that supports an allowance for bad debts in the range of $1.5 million to $1.8 million. The client recorded $800,000 as the allowance for bad debts and declines to record any additional allowance. What proposed adjustment will the auditor include in the summary of unadjusted differences?

Debit bad debt expense $700,000; credit allowance for bad debts $700,000.

Which of the following statements is correct concerning statistical sampling in tests of controls?

Deviations from specific internal control procedures at a given rate ordinarily result in misstatements at a lower rate.

Which of the following circumstances most likely would cause an auditor to suspect that material misstatements exist in a client's financial statements?

Differences between reconciliations of control accounts and subsidiary records are not investigated.

An auditor finds several errors in the financial statements that the client prefers not to correct. The auditor determines that the errors are not material in the aggregate. Which of the following actions by the auditor is most appropriate?

Document the errors in the summary of uncorrected errors, and document the conclusion that the errors do not cause the financial statements to be misstated

Which of the following is the term used in financial statement audits to indicate unintentional misstatements of amount or disclosures?

Errors

Which of the following sample planning factors would influence the sample size for a substantive test of details for a specific account?

Expected amount of misstatements Measure of tolerable misstatements

Which of the following is an example of a likely misstatement in a financial statement audit?

Extrapolation of errors in a sample of inventory price testing

Non-statistical sampling is not permitted under generally accepted auditing standards.

False

Only non-statistical sampling requires auditor judgment.

False

Statistical sampling enables the auditor to make subjective statements about the population on the basis of the sample.

False

Variables sampling is used when testing controls.

False

Which of the following is an example of a known misstatement in a financial statement audit?

Fixed asset addition in-transit was recorded in the wrong reporting period.

For which of the following audit tests would a CPA most likely use attribute sampling?

For which of the following audit tests would a CPA most likely use attribute sampling?

The table below depicts an auditor's estimated maximum deviation rate compared with the tolerable rate, and also depicts the true population deviation rate compared with the tolerable rate. As a result of tests of controls, the auditor assesses control risk too low and thereby decreases substantive testing. This is illustrated by situation:

III, where Deviation Rate Exceeds Tolerable Rate AND Maximum deviation rate is less than tolerable rate

Payroll expense DR - 72,000 Accrued payroll CR - 72,000

Impact on Current Ratio - Decrease Impact on Profit Margin - Decrease

Prepaid insurance DR - 15,000 Insurance expense CR - 15,000

Impact on Current Ratio - Increase Impact on Profit Margin - Increase

Depreciation expense DR - 125,000 Accumulated depreciation CR - 125,000

Impact on Current Ratio - No Impact Impact on Profit Margin - Decrease

Which of the following most likely would be an advantage in using classical variables sampling rather than probability-proportional-to-size (PPS) sampling?

Inclusion of zero and negative balances generally does not require special design considerations.

An auditor discovers that an account balance believed not to be materially misstated based on an audit sample was materially misstated based on the total population of the account balance. This is an example of which of the following sampling types of risks?

Incorrect acceptance

For which of the following audit tests would an auditor most likely use attribute sampling?

Inspecting employee timecards for proper approval by supervisors

To what degree, if at all, is a significant deficiency related to a material weakness?

It is less severe than a material weakness.

Which of the following is a characteristic of nonstatistical sampling?

It requires judgment to select a sample.

Higher expected frequency of misstatements

Larger If more frequent misstatements are expected, audit risk is high but can be reduced by increasing the sample size and reducing detection risk.

High assessment of inherent risk

Larger When a high assessment of inherent risk exists, the auditor reduces detection risk by increasing the sample size. IR x CR x DR = AR

Which of the following is required documentation when evaluating the summary of uncorrected misstatements at the end of an audit?

Levels of materiality applied, and how those considerations were determined

The types of misstatements that are relevant to the auditor's consideration of fraud include which of the following?

Misstatements arising from fraudulent financial reporting Misstatements arising from misappropriation of assets

What is an auditor's evaluation of a statistical sample for attributes when a test of 50 documents results in three deviations when the tolerable rate is 7%, the expected population deviation rate is 5%, and the allowance for sampling risk is 2%?

Modify the planned assessed level of control risk because the sample deviation rate plus the allowance for sampling risk exceeds the tolerable rate

Which of the following items does the auditor need in order to determine a sample size for attribute sampling? Select "Yes" or "No" in each indicated cell below. Projected rate Risk of assessing control risk too low Reliability level Random number table Estimated error rate Standard deviation Actual number of deviations found Maximum tolerable rate Control risk

No No Yes No Yes No No Yes No

Use of statistical sampling versus nonstatistical sampling

No difference Sample sizes are comparable for both statistical and nonstatistical sampling.

Which of the following statements about audit risks is correct for a nonissuer?

Non-sampling risk can arise because an auditor failed to recognize misstatements.

In attribute sampling, a 25% change in which of the following factors will have the smallest effect on the size of the sample?

Number of items in the population

Which of the following would be a consideration in planning a sample for a test of subsequent cash receipts?

Preliminary judgments about materiality levels

In a test of purchase orders, the auditor selected a random sample of 60 items out of a population of 1,200 purchase orders. The auditor discovered $4,000 in overstatement in the sample. The company's materiality is $65,000. The tolerable misstatement for purchases is $50,000. What should the auditor do next?

Project the detected error to the entire population

Which of the following is correct regarding the application of sampling to testing an account balance in a financial statement audit?

Project the error results from the sample to the population in which the sample was selected.

An auditor is performing substantive tests of pricing and extensions of perpetual inventory balances consisting of a large number of items. Past experience indicated numerous pricing and extension errors. Which of the following statistical sampling approaches is most appropriate?

Ratio estimation

Adjusting Journal Entry #2: (See Exhibit #3, "Audit Workpaper," Tickmark C.)

Revenue DR - 25,000 Deferred revenue CR - 25,000

Which of the following is a sampling risk that is associated with the efficiency of an audit?

Risk of assessing control risk too high

Larger measure of tolerable misstatement for the account

Smaller As the auditor allows acceptance of a greater misstatement, the sample size is decreased.

Smaller expected value of misstatements

Smaller As the expected size of misstatements decreases, audit risk is low. In balancing the audit risk with the cost associated with audit tests, audit risk can be increased by reducing the sample size.

Low assessment of risk associated with other relevant substantive procedures

Smaller When a low level of risk exists, the auditor increases detection risk by decreasing the sample size.

Low assessment of control risk

Smaller When the assessment of control risk is low, the auditor increases detection risk by decreasing the sample size. IR x CR x DR = AR

Which of the following is an acceptable approach to sampling as a means to obtain evidence through tests of details in a financial statement audit?

Statistical or nonstatistical is acceptable based on the auditor's professional judgment.

Which of the following courses of action would an auditor most likely follow in planning a sample of cash disbursements if the auditor is aware of several unusually large cash disbursements?

Stratify the cash disbursements population so that the unusually large disbursements are selected

You have decided to use Probability Proportional to Size (PPS) sampling, sometimes called dollar-unit sampling, in the audit of a client's accounts receivable balances. Few, if any, errors of account balance overstatement are expected. You plan to use the provided PPS sampling table. Calculate the total projected error if errors were discovered in a PPS sample.

Tainting Percentage = (Recorded Amount - Audited Amount) ÷ Recorded Amount 1st Error Tainting = 20% 2nd Error Tainting = 100% 3rd Error Tainting = 0% (recorded value is greater than the sampling interval) Projected Error = Tainting Percentage x Sampling Interval 1st Error Projected Error = $200 2nd Error Projected Error = $1000 3rd Error Projected Error = $500 Total Projected Error = $1700

Which of the following audit procedures most likely will involve sampling?

Testing of process for approval of credit to customers for sales on account

Which of the following auditing procedures most likely would provide assurance about a manufacturing entity's inventory valuation?

Testing the entity's computation of standard overhead rates

A senior auditor conducted a dual-purpose test on a client's invoice to determine whether the invoice was approved and to ascertain the amount and other terms of the invoice. Which of the following lists two tests that the auditor performed?

Tests of controls and tests of details

Which of the following qualitative factors would an auditor consider most relevant to the consideration of whether a discovered misstatement is material?

The audit team found a misstatement that, if recorded, affects the client's compliance with loan covenants.

Which of the following statements is correct concerning probability-proportional-to-size (PPS) sampling, also known as dollar-unit sampling?

The auditor controls the risk of incorrect acceptance by specifying that risk level for the sampling plan.

The degree of audit risk always present in an audit engagement is referred to as a combination of nonsampling and sampling risk. Which of the following is an example of nonsampling risk?

The auditor selecting inappropriate auditing procedures

Which of the following statements is correct about the sample size in statistical sampling when testing internal controls?

The auditor should consider the tolerable rate of deviation from the controls being tested in determining sample size.

An audit client sells 15 to 20 units of product annually. A large portion of the annual sales occur in the last month of the fiscal year. Annual sales have not materially changed over the past five years. Which of the following approaches would be most effective concerning the timing of audit procedures for revenue?

The auditor should inspect transactions occurring in the last month of the fiscal year and review the related sale contracts to determine that revenue was posted in the proper period.

Which of the following would be a consideration in planning an auditor's sample for a test of controls?

The auditor's allowable risk of assessing control risk is too low.

An auditor has set the materiality level for the financial statements as a whole at $125,000. Which of the following misstatements would the auditor most likely consider material?

The client did not disclose $47500 of related party transactions in the footnotes.

Fees earned and cash receipts could be understated because of omitted or inaccurate billing.

The employee who initially handles cash receipts also prepares billings.

The cash balance per books may be overstated because not all cash is deposited.

The employee who makes bank deposits also reconciles bank statements.

Accounts receivable may be understated because write-offs of accounts receivable could be approved for accounts that are, in fact, collectible; or accounts receivable may be overstated because write-offs of accounts receivable might not be recorded for accounts that are uncollectible.

The employees who approve credit also approve write-offs of uncollectible accounts.

Uncollectible accounts expense could be overstated because write-offs of accounts receivable could be approved for accounts that are, in fact, collectible, or uncollectible accounts expense could be understated because write-offs of accounts receivable might not be initiated for accounts that are uncollectible.

The employees who approve credit also approve write-offs of uncollectible accounts.

Uncollectible accounts expense could be understated and accounts receivable could be overstated because of the lack of an appropriate credit check.

The employees who perform services also are permitted to approve credit without an external credit check.

A client decides not to make an auditor's proposed adjustments that collectively are not material and wants the auditor to issue the report based on the unadjusted numbers. Which of the following statements is correct regarding the financial statement presentation?

The financial statements are free from material misstatement, and no disclosure is required in the notes to the financial statements.

Which of the following statements is ordinarily correct about the sample size in statistical sampling when testing controls?

The population size has little effect on the sample size.

Which of the following statements is generally correct about the sample size in statistical sampling when testing internal controls?

The population size has little or no effect on the sample size.

For audit sampling purposes, audit risk is the risk that material errors will not be detected by the auditor. Which of the following describes the element of sampling risk that must be assessed in designing an audit sample?

The risk that the conclusion would be different if the entire population were tested

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.

Which of the following factors would the auditor not explicitly consider when determining sample size in an attribute sample for a test of controls?

The tolerable misstatement

Fees earned and accounts receivable may be understated because not all services performed might be reported for billing or the same two accounts might be overstated or understated because of the use of incorrect price or service date or because of mathematical errors.

There is no independent verification of the billing process.

Which of the following objectives is achieved when an auditor decides to employ classical variable sampling?

To determine the inventory quantities on hand

Which of the following is the primary objective of probability proportional to sample size?

To identify overstatement errors

You have decided to use Probability Proportional to Size (PPS) sampling, sometimes called dollar-unit sampling, in the audit of a client's accounts receivable balances. Few, if any, errors of account balance overstatement are expected. You plan to use the provided PPS sampling table: Given the following information, calculate the sampling interval and the sample size you should use.

Tolerable error = $15,000 Risk of incorrect acceptance = 5% Number of errors allowed = 0 Recorded amount of accounts receivable = $300,000 Reliability factors for errors of overstatement = 3.00 Sampling Interval = $5000 Sample Size = 60

Fees earned, cash receipts, and uncollectible accounts expense could be understated or overstated because of undetected differences between the subsidiary and general ledger, or fees earned, cash receipts, or accounts receivable could be understated because of failure to record billings, cash receipts, and write-offs accurately.

Trial balances of the accounts receivable subsidiary ledger are not prepared independently of, or verified and reconciled to, the accounts receivable control account in the general ledger.

Discovery sampling is used when the auditor believes that the population occurrence rate is near zero.

True

Sampling risk is a component of audit risk.

True

The risk of incorrect rejection is related to the efficiency of the audit.

True

Uncollectible accounts expense could be either understated or overstated because of the lack of established write-off criteria.

Uncollectible accounts are not determined on the basis of established criteria.

Which of the following sampling methods would be used to estimate a numerical measurement of a population, such as a dollar value?

Variables sampling

The sampling unit in a test of controls pertaining to the existence of payroll transactions ordinarily is:

a payroll register entry.

In an audit of a nonissuer's financial statements, projected misstatement is:

an auditor's best estimate of misstatements in a population extrapolated from misstatements identified in an audit sample.

The expected population deviation rate of client billing errors is 3%. The auditor has established a tolerable rate of 5%. In the review of client invoices the auditor should use:

attribute sampling.

When planning a sample for a substantive test of details, an auditor should consider tolerable misstatement for the sample. This consideration should:

be related to preliminary judgments about materiality levels.

In testing controls for operating effectiveness, the risk of assessing control risk too low is called _____, which impacts _____.

beta risk; effectiveness

An auditor is determining the sample size for an inventory observation using mean-per-unit estimation, which is a variables sampling plan. To calculate the required sample size, the auditor usually determines:

both the variability in the dollar amounts of inventory items and the risk of incorrect acceptance.

As a result of tests of controls, an auditor assesses control risk too high. This incorrect assessment most likely occurred because:

control risk based on the auditor's sample is greater than the true operating effectiveness of the client's control activity.

In assessing the tolerable rate of deviations of a test of controls that was performed using statistical sampling, an auditor should consider that:

deviations from pertinent controls at a given rate ordinarily result in misstatements at a lower rate.

The likelihood of assessing control risk too high is the risk that the sample selected to test controls:

does not support the auditor's planned assessed level of control risk when the true operating effectiveness of internal control justifies such an assessment.

When issuing an unmodified opinion, the auditor who evaluates the audit findings should be satisfied that the:

estimate of the total likely misstatement is less than a material amount.

The objective of a dual-purpose test of details of transactions performed as tests of controls is to:

evaluate whether internal controls operated effectively.

An auditor is selecting prenumbered purchase orders for testing an entity's internal control activities related to their proper approval before office equipment is ordered. The auditor is matching random numbers with the purchase order numbers to determine which purchase orders to inspect. If a random number matches a voided purchase order, the auditor ordinarily would replace the voided purchase order with another if the voided purchase order:

has been properly voided in the normal course of business.

An auditor is selecting vouchers for testing an entity's internal control activities related to the proper approval of vouchers before checks are prepared. The auditor is matching random numbers with voucher numbers to determine which vouchers to inspect. If a random number matches a voided voucher, that voucher ordinarily would be replaced by another voucher in the random sample if the voided voucher:

has been properly voided.

While performing a test of details during an audit, an 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.

If an auditor of a nonissuer discovers an unexpectedly high number of deviations during procedures performed on a sample to test management's review and approval of time sheets, then the auditor would most appropriately:

increase the assessed risks of material misstatement.

In confirming a client's accounts receivable in prior years, an auditor discovered many differences between recorded account balances and confirmation replies. These differences were resolved and were not misstatements. In defining the sampling unit for the current year's audit, the auditor most likely would choose:

individual invoices.

In addition to evaluating the frequency of deviations in tests of controls, an auditor should also consider certain qualitative aspects of the deviations. The auditor most likely would give broader consideration to the implications of a deviation if it were:

initially concealed by a forged document.

Sampling risk varies _____ with sample sizes.

inversely

In a financial statement audit of a nonissuer, an auditor would consider a judgmental misstatement to be a misstatement that:

involves an estimate.

In determining the number of documents to select for a test to obtain assurance that all sales returns have been properly authorized, an auditor should consider the tolerable rate of deviation from the control activity. The auditor should also consider the:

likely rate of deviations

An advantage of statistical sampling over nonstatistical sampling in tests of controls is that statistical sampling helps an auditor to:

measure the sufficiency of the audit evidence obtained provide an objective basis for quantitatively evaluating sample risk.

As a result of tests of controls, an auditor assessed control risk too low 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.

An auditor is using statistical sampling in testing whether cash disbursements were properly authorized. The sample results indicate that the sample rate of deviation plus the allowance for sampling risk exceeds the tolerable rate. Under these circumstances, the auditor most likely would reduce the:

planned reliance on the prescribed control.

When using classical variables sampling for estimation, an auditor normally evaluates the sampling results by calculating the possible error in either direction. This statistical concept is known as:

precision.

To determine whether accounts payable are complete, an auditor performs a test to verify that all merchandise received is recorded. The population of documents for this test consists of all:

receiving reports.

An auditor who uses statistical sampling for attributes in testing internal controls should reduce the planned reliance on a prescribed control when the:

sample rate of deviation plus the allowance for sampling risk exceeds the tolerable rate.

To determine whether internal control relative to the revenue cycle of a wholesaling entity is operating effectively in minimizing the failure to prepare sales invoices, an auditor most likely would select a sample of transactions from the population represented by the:

shipping document file.

A widely used statistic that is employed to measure the extent to which the values of the items are spread about the mean in sampling applications is referred to as:

standard deviation.

In selecting an appropriate sample for a substantive test, the auditor most likely would stratify the population if:

the auditor plans to give greater representation to large recorded amounts.

The use of the ratio estimation sampling technique is most effective when:

the calculated audit amounts are approximately proportional to the client's book amounts.

An auditor may decide to increase the risk of incorrect rejection when:

the cost and effort of selecting additional sample items is low.

As a result of sampling procedures applied as tests of controls, an auditor incorrectly assesses control risk higher than appropriate. The most likely explanation for this situation is that:

the deviation rate in the auditor's sample exceeds the tolerable rate, but the deviation rate in the population is less than the tolerable rate.

In statistical sampling methods used in substantive testing, an auditor most likely would stratify a population into meaningful groups if:

the population has highly variable recorded amounts.

An auditor established a $60,000 tolerable misstatement for an asset with an account balance of $1 million. The auditor selected a sample of every twentieth item from the population that represented the asset account balance and discovered overstatements of $3,700 and understatements of $200. Under these circumstances, the auditor most likely would conclude that:

there is an unacceptably high risk that the actual misstatements in the population exceed the tolerable misstatement because the total projected misstatement is more than the tolerable misstatement.

In determining the sample size for a test of controls, an auditor should consider the likely rate of deviations, the allowable risk of assessing control risk too low, and the:

tolerable deviation rate.

An auditor desired to test credit approval on 10,000 sales invoices processed during the year. The auditor designed a statistical sample that would provide a 1% risk of assessing control risk too low (99% confidence) that not more than 7% of the sales invoices lacked approval. The auditor estimated from previous experience that about 2.5% of the sales invoices lacked approval. A sample of 200 invoices was examined and seven of them were lacking approval. The auditor then determined the achieved upper precision limit to be 8%. In the evaluation of this sample, the auditor decided to increase the level of the preliminary assessment of control risk because the:

tolerable rate (7%) was less than the achieved upper precision limit (8%).

The sample size of a test of controls varies inversely with:

tolerable rate.