Frank Benford, a physicist working in the 1930s, discovered an interesting fact about some sets of numbers. While you might expect the first digits of numbers such as street addresses or checkbook entries to be randomly distributed, Benford showed that in many cases the distribution of leading digits is not random, but rather tends to have more ones, with decreasing frequencies as the digits get larger. Table 7.15 shows the proportions of leading digits for data that satisfy Benford€™s law.

Table 7.15

Professor Rick Cleary of Bentley University has given several public lectures about Benford€™s law. As part of his presentation, he rips out pages of a telephone book and asks audience members to select entries at random and record the first digit of the street address. Counts for the leading digits of 1188 such addresses are shown in Table 7.16 and stored in a variable called Address in the dataset Benford. Test if these counts are inconsistent with the probabilities given by Benford€™s law.

Table 7.16

Transcribed Image Text:

Leading digit Proportion 5 0.079 3 0.125 6. 0.067 4 0.097 0.176 0.051 0.301 0.058 0.046 Leading digit Observed count 4 126 5 101 345 197 170 72 69 57 51