Question
The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits
The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in
218 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts (a) through (c) below.
Distribution of first digits (Benford's Law) | ||||||
---|---|---|---|---|---|---|
Digit | 1 | 2 | 3 | 4 | 5 | |
Probability | 0.301 | 0.176 | 0.125 | 0.097 | 0.079 | |
Digit | 6 | 7 | 8 | 9 | ||
Probability | 0.067 | 0.058 | 0.051 | 0.046 |
First digits in allegedly fraudulent checks | |||||||||
---|---|---|---|---|---|---|---|---|---|
First digit | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Frequency | 36 | 25 | 45 | 20 | 24 | 36 | 9 | 16 | 7 |
a) What is the test statistic? ____
b) P-value=____
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