978-0134065823 Chapter 15 Solution Manual Part 1

15-1

Chapter 15

Audit Sampling for Tests of Controls and

Substantive Tests of Transactions

 Concept Checks

P. 489

1. A representative sample is one in which the characteristics of interest for the

sample are approximately the same as for the population (that is, the sample

or she has a representative sample because the entire population is

ordinarily not tested, but certain things, such as the use of random

2. Statistical sampling is the use of mathematical measurement techniques to

calculate formal statistical results. The auditor therefore quantifies

sampling risk when statistical sampling is used. In nonstatistical sampling, the

P. 511

1. Analysis of exceptions is the investigation of individual exceptions to

effectiveness of internal control. The analysis attempts to tell the “why” and

types of exceptions have occurred.

2. The steps of the audit sampling process that differ across statistical and

nonstatistical sampling are as follows.

 Specify acceptable risk of overreliance: the concepts are the same

evaluated.

15-2

Concept check, P. 511 (continued)

result.

 Select the sample: The only difference in sample selection is the

requirement to use a probabilistic method when using statistical

sampling.

 Generalize from the sample to the population: For statistical sampling,

 Review Questions

15–1 Sampling risk is the risk that the auditor reaches the wrong conclusion

may perform procedures incorrectly or fail to correctly interpret the audit

of audit sampling are:

1. Plan the sample

2. Select the sample and perform the tests

3. Evaluate the results

15–3 In probabilistic sample selection, the auditor randomly selects items from

a population such that each item has a known probability of being included in

approach.

15-3

15–4 A block sample is the selection of several items in sequence. Once

the first item in the block is selected, the remainder of the block is chosen

procedure would be repeated 4 other times.

15–5 In replacement sampling, an element in the population can be included

in the sample more than once if the random number corresponding to that

element is selected more than once. In nonreplacement sampling, an element

15–6 A simple random sample is one in which every possible combination of

elements in the population has an equal chance of selection. Two methods of

15–7 In systematic sampling, the auditor calculates an interval and then

17. The next is 87, then 157, 227, and so on.

The advantage of systematic sampling is its ease of use. In most

populations a systematic sample can be drawn quickly, the approach automatically

puts the numbers in sequential order, and documentation is easy.

A major problem with the use of systematic sampling is the possibility

of bias. Because of the way systematic samples are selected, once the first

item in the sample is selected, other items are chosen automatically. This

15-4

15–8 Random (probabilistic) selection is a part of statistical sampling, but it is

not, by itself, statistical measurement. To have statistical measurement, it is

15–9 The purpose of using nonstatistical sampling for tests of controls and

substantive tests of transactions is to estimate the proportion of items in a

15–10 An attribute is the definition of the characteristic being tested and the

exception conditions whenever audit sampling is used. The attributes of interest

15–11 An attribute is the characteristic being tested for in a population. An

exception occurs when the attribute being tested for is absent. The exception

TERM

DEFINITION

a. Acceptable risk of

overreliance (ARO)

The risk the auditor is willing to take of accepting a control

as effective or a rate of monetary misstatements as

tolerable, when the true population exception rate is

greater than the tolerable exception rate.

b. Computed upper

exception rate (CUER)

The highest estimated exception rate in the population

at a given ARO.

c. Estimated population

exception rate (EPER)

The exception rate the auditor expects to find in the

population before testing begins. It is necessary to

plan the appropriate sample size.

d. Sample exception rate

(SER)

The actual rate of exception discovered in the sample.

It is calculated by dividing the actual number of

exceptions in the sample by the sample size.

e. Tolerable exception

rate (TER)

The exception rate the auditor will permit in the population

and still be willing to use the assessed control risk

and/or the amount of monetary misstatements in the

transactions established during planning.

15-5

15–13 The sampling unit is the population item from which the auditor selects

sample items. The major consideration in defining the sampling unit is making

it consistent with the objectives of the audit tests. Thus, the definition of the

population and the planned audit procedures usually dictate the appropriate

sampling unit.

The sampling unit for verifying the occurrence of recorded sales would

be the entries in the sales journal since this is the record the auditor wishes to

15–14 The tolerable exception rate (TER) represents the exception rate that

the auditor will permit in the population and still be willing to use the assessed

15–15 Tolerable exception rate (TER) is the result of an auditor’s judgment.

The suitable TER is a question of materiality and is therefore affected by both

the definition and the importance of the attribute in the audit plan. It represents

acceptable.

The sample size for a TER of 7% would be smaller than that for a TER

of 4%, all other factors being equal.

15–16 The appropriate ARO is a decision the auditor must make using

auditor’s ARO.

The auditor will choose a smaller sample size for an ARO of 10% than

would be used if the risk were 5%, all other factors being equal.

15–17 The relationship between sample size and the four factors determining

sample size are as follows:

normally unchanged, or may increase slightly.

c. As the TER increases, the sample size decreases.

d. As the EPER increases, the required sample size increases.

15-6

15–18 When the CUER exceeds the TER, the auditor may do one or more of

the following:

1. Revise the TER or the ARO. This alternative should be followed

risk associated with the higher specifications.

2. Expand the sample size. This alternative should be followed when

expected in the expanded sample.

3. Revise assessed control risk upward. This is likely to increase

are possible.

4. Write a letter to management. This action should be done in

conjunction with each of the three alternatives above. Management

should always be informed when its internal controls are not

operating effectively. If a deficiency in internal control is considered

to be a significant deficiency in the design or operation of internal

15–19 Attributes sampling is a statistical, probabilistic sampling method that

results in an estimate of the proportion of items in a population containing a

15–20 In this situation, the sample exception rate (SER) is 4%, the sample

size is 100 and the ARO is 10%. From the 10% ARO table (Table 15–9) then,

15–21 The decisions the auditor must make in using attributes sampling are:

 What are the objectives of the audit test?

 Does audit sampling apply?

15-7

15–21 (continued)

 What should the TER be?

 What should the ARO be?

 What is the EPER?

 What generalizations can be made from the sample to the population?

 What are the causes of the individual exceptions?

 Is the population acceptable?

In making the above decisions, the following should be considered:

 The individual situation.

 Multiple Choice Questions From CPA Examinations

15–22 a. (3) b. (1) c. (1)

 Multiple Choice Questions From Becker CPA Review

15–25 a. (3) b. (3) c. (1)

 Discussion Questions and Problems

guidance in the reorganized standards.

a. AS 2315, Audit Sampling, lists benefits and costs of statistical

sampling in section .46. Statistical sampling allows the auditor to

design an efficient sample, measure the sufficiency of evidence,

to use a statistical or nonstatistical approach.

15-8

15–26 (continued)

uncertainties unrelated to sampling (nonsampling risk).

c. According to AS 2315.32, sampling is not always appropriate for

tests of controls. For example, procedures performed during the

planning process to obtain an understanding of internal controls

observation) or the accounting system.

d. These risks are defined in AS 2315.12. The risk of assessing

control risk too low represents the risk that the level of control risk

assessed by the auditor based on the sample is lower than the

control warrants. This risk relates to the efficiency of the audit in

that it could result in the auditor increasing the level of substantive

testing unnecessarily.

a.

SAMPLING

UNIT

NUMBERING SYSTEM

FOR THE POPULATION

EXCEL SELECTION

FORMULA

1. Sales invoice

All invoices numbered

0001 to 8274

=RANDBETWEEN(1,8274)

2. Bill of lading

All bills of lading numbered

18221 through 29427

=RANDBETWEEN(18221,

29427)

3. Customer

A pair of random numbers,

where the first random

number is the page

number (1–20), and the

second random number

is the line number on the

page (1–50)

=RANDBETWEEN(1,20)

and

=RANDBETWEEN(1,50)

15–27 (continued)

copied down to select additional random numbers. When a pair of

random numbers is required, the formula for the first random

number can be entered in the first column, and the formula for the

second random number can be entered in the second column.

b. First five numbers using systematic selection:

SAMPLING UNIT

INTERVAL

RANDOM

STARTING

POINT

FIRST 5

SAMPLE

ITEMS

1. Sales invoice

110 (8274/75)

39

149

259

369

479

2. Bill of lading

149 [(29427–18221)

= 11206/75]

18259

18408

18557

18706

18855

3. Customer

13 (979 lines/75)

Page 1, line #11

Page Line

1 11

1 24

1 37

1 50

2 13

the defined population.

15-10

15–28 (see text Web site for Excel solution for part c.- Filename P1528.xls)

be the warehouse removal slip.

b. Attributes sampling method: Assuming the auditor is willing to accept

Nonstatistical sampling method: There is no one right answer

to this question because the sample size is determined using

professional judgment. Due to the relatively small TER (4%), the

c. Systematic sample selection:

 22946 = Population size of warehouse removal slips

(34687–11741).

removal slip after (12188, 12498, etc.)

Computer generation of random numbers using Excel (P1528.xls):

=RANDBETWEEN(11741,34687)

numbers.

d. Other audit procedures that could be performed are:

1. Test extensions on attached sales invoices for clerical

accuracy. (Accuracy)