In 1938 Dr. Frank Benford, a physicist at General Electric, noticed that, given a list of numbers, more numbers started with the digit 1 than any other digit. He analyzed 20,222 sets of numbers including areas of rivers, baseball statistics, numbers in magazine articles, and street addresses. He concluded that the probability of the numeral d appearing as the first digit was log (1 + 1/d) and this property is known as Benford’s law. The probabilities are shown.

A textbook was analyzed to see whether the pattern of leading digits of the numbers in the book differed from that predicted by Benford. Pages were randomly selected and the leading digits of the numbers on those pages are shown in the following table. 

a. What are the expected frequencies for each leading digit if they are distributed in the long run according to Benford’s law? 

b. Write out the hypotheses. 

c. Calculate the test statistic and appropriate p-value. 

d. State your conclusion in the context of the research question.

Transcribed Image Text:

d 12 3 4 5 6 7 8 Probability the leading digit starts with d 9 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046