Audit Sampling

Question 1

Risk

Answer 1

Auditing is all about risk

Risk is unavoidable because auditor’s do not examine 100% of the evidence

Question 2

Statistical Sampling

Answer 2

Allows an auditor to quantify risk

Measures in mathematical terms the amount of risk that an auditor is taking

Question 3

Types of Sampling

Answer 3

Attribute Sampling - tests of controls (compliance)
Test population for a certain characteristic (i.e. attribute). Used as a test of internal controls (compliance)
Ex. How many accounts receivable have never filed a credit application?

Variable samping - substantive tests
Trying to estimate the dollar value of a population. Used as a substantive test of details
Ex. How much does the value vary from stated amount in financials?

Question 4

Sampling Plan: Step 1

Answer 4

# Define the population
 Almost infinite amount of potential populations are in a typical set of financial statements

Must use auditor judgment to define in precise terms the population to be sampled

Question 5

Sampling: Concept 1

Answer 5

Concept 1: Must assume that the defined population has the properties of a Normal Curve

Central Limit Theorem: The arithmetic mean of all the samples drawn from the population would form a perfect normal curve

Question 6

Sampling: Concept 2

Answer 6

In order for the sample to be mathematically valid, it must be an unrestricted, random sample

Randomness - every item in the population must have an equal chance of being selected

One place where auditor judgement (bias) may not exist

Random Sample: use a random number generator; audit the transactions/balances indicated by the random numbers; come to a conclusion about each

Question 7

Systematic Sampling

Answer 7

Weak form of randomness:
Randomly select a first item
Select every 10th item after that
A weak form of randomness
If the population has any order, misleading results

Strongest form of randomness is the use random number generator and audit the transaction until the end.

Question 8

Sampling: Concept 3

Answer 8

Variability

Variability causes uncertainty; the more variability, the larger the sample size

Standard Deviation - the standard measure of variability

Question 9

Mean per unit projection/estimation

Answer 9

Audited Sample Size divided by sample size = Sample arithmetic mean

Multiply that by population size = estimated popluation value (point estimate)

Question 10

1 Standard Deviation / Precision at 68%

Answer 10

Will encompass 68% of the curve

Number of standard deviations (1) x standard error of the mean x population size = precision

68% confident that the value is the point estimate plus or minus the precision

Question 11

1.96 Standard Deviation

Answer 11

Will encompass 95% of the curve

Number of standard deviations (1.96) x standard error of the mean x population size = precision

95% confident that the value is the point estimate plus or minus the precision

Question 12

Tolerable Misstatement

Answer 12

What the auditor is willing to accept

Relates to auditor’s judgement of materiality

Smaller tolerable misstatement, larger sample size (inverse relationship)

Question 13

Ratio Estimation

Answer 13

Audited Sample value divided by book sample value = ratio

Ratio multiplied by book population value = point estimate

Question 14

Difference Estimation

Answer 14

Audited sample value minus book sample value = sample value difference

Divded by number of sample items = difference per item

Difference multiplied by number of population = population value difference

Add book population value = point estimate

Question 15

Stratified Sampling

Answer 15

Split population into several smaller populations

Reduce variability for smaller sample sizes

Question 16

Sampling Risk

Answer 16

Sample could be wrong

No guarantee that a random sample is representative of a population

Question 17

Alpha Risk in Variable Sampling

Answer 17

Financial statement correct (they are fairly stated)

Sample says material error (sample is wrong)

Modify opinion unnecessarily

Risk of incorrect rejection

Question 18

Beta Risk in Variable Sampling

Answer 18

Financial statements incorrect

Sample says correct (sample is wrong)

Fail to modify opinion

Risk of incorrect acceptance

Question 19

Attribute Sampling: Looking for?

Answer 19

Error rate (point estimate)

Question 20

Tolerable Error Rate

Answer 20

Error rate auditor is willing to tolerate

Question 21

Alpha Risk in Attribute Sampling

Answer 21

Internal Control is effective

Sample says material weakness (sample is wrong)

Assess control risk too high (risk of under-reliance on controls)

Result: Too much substantive testing

Question 22

Beta Risk in Attribute Sampling

Answer 22

Internal Control is ineffective

Sample says no material weakness (sample is wrong)

Assess control risk too low (risk of over-reliance on controls)

Result: Too little substantive testing

Question 23

Expected Error Rate and relationship to sample size

Answer 23

Direct relationship:

High error rate: Large Sample

Low error rate: Small sample

Question 24

Tolerable Error Rate and relationship to sample size

Answer 24

inverse relationship:

High error rate: Small Sample

Low error rate: Large sample

Question 25

Discovery Sampling

Answer 25

Type of attribute sampling

A predetermined probability of discovering one item
use with critical items
expect error rate to be very low

Question 26

PPS Sampling (dollar unit sampling)

Answer 26

Probability proporationate to size

Uses attribute sampling table to assist in sampling variables

From table obtain reliability factor

Tolerable misstaement divided by reliability factor = sampling interval

Population value / sampling interval = sample size

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Question 27

PPS Sampling Advantages

Answer 27

Sample size not affected by variability

Start picking sample before the entire population is available

Population automatically stratified… larger value items have a higher change to be selected in the sample.

Question 28

Calculating Allowance for Sampling Risk

Answer 28

Equals the difference between the upper precision limit and the sample deviation risk (errors/sample size)