**Benford’s Law. According to Benford’s law, a variety of different data sets includenumbers with leading ( first) digits that follow the distribution shown in the table below. In Exercises, test for goodness-of-fit with Benford’s law.**

Author’s Check Amounts Exercise 21 lists the observed frequencies of leading digits from amounts on checks from seven suspect companies. Here are the observed frequencies of the leading digits from the amounts on checks written by the author: 68, 40, 18, 19, 8, 20, 6, 9, 12. (Those observed frequencies correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.) Using a 0.05 significance level, test the claim that these leading digits are from a population of leading digits that conform to Benford’s law. Do the author’s check amounts appear to be legitimate? Test for goodness-of-fit with Benford’s law.

Leading Digit |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |

Benford”s law distribution of leading digit |
30.1% |
17.6% |
12.5% |
9.7% |
7.9% |
6.7% |
5.8% |
5.1% |
4.6% |

**Exercise 21**

Detecting Fraud When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 15, 0, 76, 479, 183, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford’s law, the check amounts appear to result from fraud. Use a 0.01 significance level to test for goodnessof- fit with Benford’s law. Does it appear that the checks are the result of fraud? Test for goodness-of-fit with Benford’s law.

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