Question 1

Assume the following relating to a PPS sample:
• Projected Misstatement = $20,000.
• Basic Precision = $16,000.
• Incremental Allowance = $4,500.
• Tolerable Misstatement = $34,000.
The most likely amount of misstatement in the population is equal to:
A)$20,000.
B)$20,500
C)$40,000.
D)$40,500.
E)$74,500.

Accepted Answer

The most likely amount of misstatement in the population is the Projected Misstatement, which is $20,000.

Question 2

Assume the following relating to a PPS sample:
• Projected Misstatement = $20,000.
• Basic Precision = $16,000.
• Incremental Allowance = $4,500.
• Tolerable Misstatement = $34,000.
The upper limit on misstatement equals.
A)$20,000.
B)$20,500
C)$40,500.
D)$74,500.

Accepted Answer

The upper limit on misstatement is calculated using the formula: 
Projected misstatement + (Basic precision x Reliability factor) + Incremental allowance.
 
The reliability factor is determined based on the desired level of assurance and the sample size. Assuming a desired level of assurance of 90%, the reliability factor for a PPS sample with 10% of the population selected would be 3.08.

Using the formula, the upper limit on misstatement is:
$20,000 + ($16,000 x 3.08) + $4,500 = $61,780

Therefore, the best choice is C as it represents the correct upper limit on misstatement.

Question 3

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 $5000 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:
A)$1,000.
B)$2,000.
C)$5,000.
D)$10,000.

Accepted Answer

The sampling interval is $10,000, and a selected account receivable with a recorded amount of $5,000 had an audited amount of $4,000. Therefore, the misstatement in this account is $1,000 ($5,000 - $4,000). Since the sample is probability-proportional-to-size, the projected misstatement of the sample would be proportional to the misstatement detected in this account.

Therefore, the projected misstatement of the sample would be:

($1,000/$5,000) x $10,000 = $2,000

So, the best choice is B).

Question 4

Probability-proportional-to-size sampling is especially efficient for populations with high misstatement rates.

Accepted Answer

Probability-proportional-to-size sampling is more efficient for populations with low misstatement rates, as it selects larger items with a higher probability, reducing the chance of missing significant misstatements.

Question 5

Which statement is most proper for evaluating the results of this PPS sample?
A)Accept the population because the projected misstatement is less than the tolerable misstatement.
B)Accept the population because the sum of the projected misstatement and the basic precision exceeds the incremental allowance.
C)Reject the population because the sum of the projected misstatement, basic precision and incremental allowance exceeds the tolerable misstatement.
D)Reject the population because the tolerable misstatement exceeds the basic precision plus the incremental allowance.

Accepted Answer

The population should be rejected if the sum of the projected misstatement, basic precision, and incremental allowance exceeds the tolerable misstatement, indicating that the misstatement risk is too high.

Question 6

When using probability-proportional-to-size sampling,the allowance for sampling risk is the combination of basic precision and the:
A)Projected misstatement.
B)Incremental allowance.
C)Upper limit on misstatements.
D)Tainting.

Accepted Answer

When using probability-proportional-to-size sampling, the allowance for sampling risk consists of two components: basic precision and incremental allowance. Basic precision is the total amount of allowable misstatement from the sample, while the incremental allowance is the additional amount of misstatement that can be tolerated beyond the basic precision, based on the auditor's assessment of the risk of material misstatement. Therefore, the incremental allowance is necessary to take into account the additional risk that may exist beyond the basic precision. Projected misstatement, upper limit on misstatements, and tainting are not directly related to the allowance for sampling risk in probability-proportional-to-size sampling.

Question 7

Which of the following statements is correct concerning probability-proportional-to-size sampling?
A)The sampling distribution should approximate the normal distribution.
B)The auditors control the risk of incorrect rejection by specifying that risk level for the sampling plan.
C)The sampling interval is calculated by dividing the population book value by the sample size.
D)The auditors control the risk of incorrect acceptance by incorporating an expected misstatement into the sample size formula.

Accepted Answer

In probability-proportional-to-size sampling, the sampling interval is calculated by dividing the population book value by the sample size. This ensures that each item in the population has an equal chance of being selected, as the larger the item's value, the higher the probability of its selection. The other options are incorrect because: 
A) The shape of the sampling distribution depends on the type of data being analyzed and the sample size, and may not necessarily approximate a normal distribution. 
B) The auditors control the risk of incorrect acceptance or rejection by specifying the acceptable level of risk, but not by controlling it through the sampling plan. 
D) The expected misstatement is used to calculate the sample size but not to control the risk of incorrect acceptance.

Question 8

When no misstatements are identified in a PPS sample,the upper limit on misstatement equals.
A)An amount dependent upon the sample's standard deviation.
B)Basic precision.
C)½ of the allowance for sampling risk.
D)Zero.

Accepted Answer

When no misstatements are identified in a PPS (Probability Proportional to Size) sample, the upper limit on misstatement is calculated as the basic precision, which accounts for the possibility of undetected misstatements.

Question 9

The upper limit on misstatement in a probability-proportional-to-size sample plan consists of the total of the projected misstatement and the tolerable misstatement.

Accepted Answer

The upper limit on misstatement in a probability-proportional-to-size sample plan consists of the total of the projected misstatement and an allowance for sampling risk, not the tolerable misstatement.

Question 10

A normally distributed sample is assumed when using probability-proportional-to-size sampling.

Accepted Answer

Probability-proportional-to-size sampling does not assume a normally distributed sample; it selects samples based on size or magnitude, not distribution shape.

Question 11

Increasing the expected misstatement for a probability-proportional-to-size sample increases the required sample size.

Accepted Answer

This statement is true. Increasing the expected misstatement for a probability-proportional-to-size sample means that a larger sample size is required to achieve the desired level of precision. This is because the larger the expected misstatement, the greater the variability in the data, and therefore the larger the sample size needed to obtain a representative sample.

Question 12

Assume the following relating to a PPS sample:
• Projected Misstatement = $20,000.
• Basic Precision = $16,000.
• Incremental Allowance = $4,500.
• Tolerable Misstatement = $34,000.
The allowance for sampling risk is equal to:
A)$20,000.
B)20,500.
C)$40,500.
D)$74,500.

Accepted Answer

The allowance for sampling risk is calculated as Basic Precision + Incremental Allowance, which in this case is $16,000 + $4,500 = $20,500. The projected misstatement is already taken into account with the tolerable misstatement of $34,000. Therefore, options A and C are not correct. Option D does not make sense as it is not related to any of the given information.

Question 13

An increase in the scope of analytical procedures may result in a lower allowable risk of incorrect acceptance for a substantive test of details.

Accepted Answer

Increasing the scope of analytical procedures will increase the level of assurance obtained from these procedures, reducing the acceptable level of risk of incorrect acceptance. This may lead to a lower allowable risk of incorrect acceptance for a substantive test of details.

Question 14

When using probability-proportional-to-size sampling,the actual total misstatement in a population is most likely to be closest to the:
A)Projected misstatement.
B)Basic precision.
C)Allowance for sampling risk.
D)Upper limit on misstatement.

Accepted Answer

Projected misstatement is the best estimate of the actual total misstatement in the population based on the sample results.

Question 15

For which of the following populations would probability-proportional-to-size sampling be most likely to be the most efficient technique in confirming accounts receivable?
A)2,000 accounts with a standard deviation of $650, with few misstatements expected.
B)2,000 accounts with a standard deviation of $25, with few misstatements expected.
C)6,000 accounts with a standard deviation of $650, with many misstatements expected.
D)6,000 accounts with a standard deviation of $25 with many misstatements expected.

Accepted Answer

Probability-proportional-to-size sampling is most efficient when there is a large variation in account sizes (high standard deviation) and few misstatements are expected, as it focuses on larger accounts where misstatements are more likely to be material.

Question 16

In a probability-proportional-to-size sample with a sampling interval of $10,000,an auditor discovered that as selected account receivable with a recorded amount of $12,000 had an audited amount of $9,000.If this were the only misstatement discovered by the auditor,the projected misstatement of this sample would be:
A)$2,000.
B)$2,500.
C)$3,000.
D)$10,000.

Accepted Answer

To calculate the projected misstatement, the auditor needs to use the formula:

Projected misstatement = (misstated item / recorded amount) x sampling interval

In this case, the misstated item is $3,000 ($12,000 - $9,000). Therefore, the projected misstatement is:

Projected misstatement = ($3,000 / $12,000) x $10,000 = $2,500

So, the best choice is B: $2,500.

Question 17

In a probability-proportional-to-size sample with a sampling interval of $10,000,an auditor discovered that a selected account with a book value of $6,000 had an audited value of $4,000.The projected misstatement is:
A)$2,000.
B)$3,333.
C)$6,000.
D)$10,000.

Accepted Answer

In a probability-proportional-to-size sample, the projected misstatement is determined by multiplying the audited value of the sample item by the reciprocal of the sampling interval.

Therefore, projected misstatement = (audited value of the sample item) x (1/sampling interval)
= $4,000 x (1/10,000)
= $0.4

To estimate the projected misstatement for the entire population, the projected misstatement of each item in the sample is multiplied by its sampling interval and then summed up.

Projected misstatement for the entire population = ($0.4) x (10,000) = $4,000

Therefore, the best choice is B) $3,333, which is the closest value to $4,000 in the options provided.

Question 18

In a probability-proportional-to-size sample,increasing the tolerable misstatement has what effect on sample size,when all other factors are held constant?
A)Increases.
B)Decreases.
C)No effect.
D)Indeterminate.

Accepted Answer

Increasing the tolerable misstatement decreases the sample size because a higher tolerable misstatement means that the auditor is willing to accept a larger error, thus requiring a smaller sample to achieve the same level of assurance.

Question 19

In a PPS sample,the most likely misstatement in the population is equal to the:
A)Projected Misstatement.
B)Upper limit on misstatement.
C)Basic Precision.
D)Total misstatements identified in the sample.

Accepted Answer

In a PPS sample, the projected misstatement is the estimate of the total misstatement in the population. Therefore, the most likely misstatement in the population is equal to the projected misstatement.

Question 20

The use of probability-proportional-to-size sampling would be least likely to be efficient if:
A)Commercial receivable accounts are being audited.
B)Statistical inferences are to be made.
C)Many accounts are known to be in error.
D)The population has a high total dollar value.

Accepted Answer

Probability-proportional-to-size sampling works best when the population is homogeneous and without errors. If many accounts are known to be in error, then it may be more efficient to use another sampling method.

Quiz 22: Probability-Proportion-To-Size Sampling

Assume the following relating to a PPS sample: • Projected Misstatement = $20,000. • Basic Precision = $16,000. • Incremental Allowance = $4,500. • Tolerable Misstatement = $34,000. The most likely amount of misstatement in the population is equal to:

Assume the following relating to a PPS sample: • Projected Misstatement = $20,000. • Basic Precision = $16,000. • Incremental Allowance = $4,500. • Tolerable Misstatement = $34,000. The upper limit on misstatement equals.

Probability-proportional-to-size sampling is especially efficient for populations with high misstatement rates.

Which statement is most proper for evaluating the results of this PPS sample?

When using probability-proportional-to-size sampling,the allowance for sampling risk is the combination of basic precision and the:

Which of the following statements is correct concerning probability-proportional-to-size sampling?

When no misstatements are identified in a PPS sample,the upper limit on misstatement equals.

The upper limit on misstatement in a probability-proportional-to-size sample plan consists of the total of the projected misstatement and the tolerable misstatement.

A normally distributed sample is assumed when using probability-proportional-to-size sampling.

Increasing the expected misstatement for a probability-proportional-to-size sample increases the required sample size.

Assume the following relating to a PPS sample: • Projected Misstatement = $20,000. • Basic Precision = $16,000. • Incremental Allowance = $4,500. • Tolerable Misstatement = $34,000. The allowance for sampling risk is equal to:

An increase in the scope of analytical procedures may result in a lower allowable risk of incorrect acceptance for a substantive test of details.

When using probability-proportional-to-size sampling,the actual total misstatement in a population is most likely to be closest to the:

For which of the following populations would probability-proportional-to-size sampling be most likely to be the most efficient technique in confirming accounts receivable?

In a probability-proportional-to-size sample with a sampling interval of $10,000,an auditor discovered that a selected account with a book value of $6,000 had an audited value of $4,000.The projected misstatement is:

In a probability-proportional-to-size sample,increasing the tolerable misstatement has what effect on sample size,when all other factors are held constant?

In a PPS sample,the most likely misstatement in the population is equal to the:

The use of probability-proportional-to-size sampling would be least likely to be efficient if: