5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

Question 1

5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

Hill has decided to use probability-proportional-to-size (PPS) sampling, sometimes called dollar-unit sampling, in the audit of a client’s accounts receivable balances. Hill plans to use the following PPS sampling table:

Reliability Factors for Overstatements:

No of overstatements: 0
Risk of Incorrect Acceptance:
1%=4.61, 5%=3.00, 10%=2.31, 15%=1.9, 20%= 1.61

No of overstatements: 1
Risk of Incorrect Acceptance:
1% = 6.64, 5% = 4.75, 10% = 3.89, 15% = 3.38, 20%=3.00

No of overstatements: 2
Risk of Incorrect Acceptance:
1%=8.41, 5%=6.30, 10%=5.33, 15%=4.72, 20%=4.28

Additional information:

Tolerable misstatements (net of effect of expected misstatements) =	$24,000
Risk of incorrect acceptance = 20%
Number of misstatements =	1
Recorded amt of A/R=	$240,000
Number of accounts = 360

Which sample size should Hill use?

A) 60
B) 30
C) 108
D) 120

Answer 1

B) 30

A risk of incorrect acceptance of 20% with 1 expected misstatement results in a factor of 3.0, which is divided into the tolerable misstatement of $24,000, resulting in an interval of $8,000.

Sampling Interval (SI) = Tolerable misstatement / reliability factor
=>> $24,000 / 3.0 = $8000

Sample Size = Pop. Amt / Sample Interval
Sample Size =» $240000 / $8000 = 30

This is divided into the total value of the population to give a sample size equal to $240,000/$8,000 or 30.

Question 2

5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

Sampling Interval (SI) = _____ / _______

Sample Size = ______ / ________

Answer 2

Sampling Interval (SI) =
Tolerable misstatement / reliability factor
Example=» $24,000 / 3.0 = $8000

Sample Size =
Population Amt / Sample Interval
Example =» $240,000 / $8000 = 30

Question 3

5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

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

A) To increase the proportion of smaller-value items in the sample.

B) To identify items where controls were notproperly applied.

C) To identify zero and negative balances.

D) To identify overstatement errors

Answer 3

D) To identify overstatement errors

The purpose of variable estimation sampling, which PPS is an example of, is to measure amounts, which can be
compared to client data to identify overstatements.

PPS increases the proportion of larger, not smaller items in the sample.

PPS used in substantive testing, not tests of controls, and would not be used to determine if a control was being applied.

Since items are chosen based on the relationship of their balances to an interval, zero and negative balances are not a focus.

Question 4

5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

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

A) The sampling process can begin before the complete population is available.

B) It is particularly effective
for detecting understatements.

C) The sample size can generally be lower even if many errors are expected.

D) The selection of negative balances requires nospecial design considerations.

Answer 4

A) The sampling process can begin before the complete population is available.

Among the advantages of PPS sampling are…

• that a standard deviation is not needed; a sample is automatically stratified;
• a smaller sample will often result when few errors are expected;
• and sampling can begin before the entire population complete.

Disadvantages are that zero and negative balances require special handling; large sample sizes result when many
errors are expected; and it is not useful for detecting an understatement.

Question 5

5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

In a probability-proportional-to-size (PPS) sample with a sampling interval of $10,000, an auditor discovered that a selected account receivable with a recorded amount of $12,000 had an audited amount of $11,000. If this were the only misstatement discovered by the auditor, the projected misstatement of this sample would be

A) $1,000
B) $960
C) $10,000
D) $833

Answer 5

A) $1,000

Under PPS sampling, an interval is determined by dividing the total value of the population by the sample size.

When an item is selected from an interval that has a value lower than the interval amount, any error is measured as a percentage of the item’s value and that percentage is applied to the interval, resulting in a larger error measurement.

When the item has a value that is equal to or greater than the interval amount, any error identified is assumed to be the projected misstatement without
adjustment.

With an interval of $10,000 and a sample item with a greater recorded amount of $12,000, a $1,000 error would be considered the projected misstatement.

Question 6

5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

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 $3,000 had an audit amount of $2,700. If this were the
only error discovered by the auditor, the projected error of this sample would be

A) $500
B) $300
C) $800
D) $2,300

Answer 6

A) $500

With an audited amount of $2,700 compared to a recorded amount of $3,000, the auditor has detected a $300 error,
representing 10% of the recorded amount.

Since an interval is $5,000, the projected error would be 10% of $5,000 or $500.

Question 7

5.05 - PROBABILITY PROPORTIONAL TO SIZE SAMPLING

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

A) $1,000
B) $2,000
C) $5,000
D) $4,000

Answer 7

B) $2,000

Under PPS, the projected error for a sample is a function of the errors detected and the relationship of the size of the item containing the error to the sampling interval.

In this case, the item contained an overstatement of $2,000. If the item were smaller in amount than the sampling interval, the ratio of the error to the recorded amount would be multiplied by the sampling interval to determine the projected error.

When the item containing the sample is equal to or larger than the sampling interval, the projected error is the amount of the detected error.