Chapter 11.1, Problem 22BSC

Ben ford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercises 21-24, test for goodness-of-fit with the distribution described by Benford’s law.

22. 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 the most recent checks written by the author at the time this exercise was created: 83, 58, 27, 21, 21, 21, 6, 4, 9. (Those observed frequencies correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.) Using a 0.01 significance level, test the claim that these leading digits are from a population of leading digits that conform to Benford’s law. Does the conclusion change if the significance level is 0.05?