An investigator analyzed the leading digits from 792 checks

Last updated: 11/27/2023

An investigator analyzed the leading digits from 792 checks issued by seven suspect companies The frequencies were found to be 255 143 110 87 49 46 46 41 and 15 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 shown below the check amounts appear to result from fraud Use a 0 01 significance level to test for goodness of fit with Benford s law Does it appear that the checks are the result of fraud Leading Digit Actual 1 2 3 4 5 6 7 8 9 255 143 110 87 49 46 46 41 15 Frequency Benford s Law 30 1 17 6 12 5 9 7 7 9 6 7 5 8 5 1 4 6 Distribution of Leading Digits Determine the null and alternative hypotheses Ho The leading digits are from a population that conforms to Benford s law H At least one leading digit has a frequency that does not conform to Benford s law Calculate the test statistic x x Round to three decimal places as needed