QUESTION 3 Benford\'s Law is a probability rule frequently used by accounting au

Question

QUESTION 3 Benford's Law is a probability rule frequently used by accounting auditors to detect systematic fraud. It states that approximately 12.3% of numbers will begin with the number 2. An auditor decides to investigate a particular firm further if a sample proportion of their invoices, with the invoiced number beginning with a 2, is in the highest 0.5% of all possible sample proportions. What sample proportion will cause further investigation of the firm if a random sample of 780 invoices is selected? Express your answer in decimal form (ie not as a percentage), corect to two decimal places.

Explanation / Answer

The top 0.5% is the 99.5th percentile. So you need to find the z-score for the 99.5th percentile.
z*99.5* = 2.576

Use the formula z=(p-hat - p)/sqrt(p(1-p)/n)

P = 0.123

2.576 = (p-hat - 0.123)/sqrt(0.123(0.877)/780)
Solve this for p-hat.
p-hat = 0.15

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