ExpertHard1 markMultiple Choice
CPA · Question 13 · Area III: Performing Procedures
An auditor is calculating the sample size for a test of details of balances using probability-proportional-to-size (PPS) sampling. The recorded amount of the population is $1,000,000. The auditor determines a reliability factor of 3.0 (based on risk of incorrect acceptance), a tolerable misstatement of $50,000, and an expected misstatement of $10,000. The expansion factor is 1.6. What is the sampling interval?
An auditor is calculating the sample size for a test of details of balances using probability-proportional-to-size (PPS) sampling. The recorded amount of the population is $1,000,000. The auditor determines a reliability factor of 3.0 (based on risk of incorrect acceptance), a tolerable misstatement of $50,000, and an expected misstatement of $10,000. The expansion factor is 1.6. What is the sampling interval?
Answer options:
A.
$16,666
B.
$11,363
C.
$50,000
D.
$33,333
How to approach this question
Recall PPS formulas. 1. Calculate Sample Size: (Book Value * Reliability Factor) / (Tolerable Misstatement - (Expected Misstatement * Expansion Factor)). 2. Calculate Interval: Book Value / Sample Size.
Full Answer
B.$11,363✓ Correct
$11,363 (approx)
Sample Size = (Book Value * Reliability Factor) / (Tolerable Misstatement - (Expected Misstatement * Expansion Factor)).<br/>Numerator: 1,000,000 * 3.0 = 3,000,000.<br/>Denominator: 50,000 - (10,000 * 1.6) = 50,000 - 16,000 = 34,000.<br/>Sample Size = 3,000,000 / 34,000 = ~88.24.<br/>Sampling Interval = Book Value / Sample Size = 1,000,000 / 88.24 = ~11,333. (Option B is the closest approximation).
Common mistakes
Forgetting to reduce Tolerable Misstatement by the expected misstatement portion in the denominator.
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