Benford's Law states that the first nonzero digits of numbersdrawn at random from a large complex data file have the followingprobability distribution.â€
| First Nonzero Digit | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Probability | 0.301 | 0.176 | 0.125 | 0.097 | 0.079 | 0.067 | 0.058 | 0.051 | 0.046 |
Suppose that n = 275 numerical entries were drawn atrandom from a large accounting file of a major corporation. Thefirst nonzero digits were recorded for the sample.
| First Nonzero Digit | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| SampleFrequency | 87 | 46 | 34 | 23 | 21 | 18 | 13 | 17 | 16 |
Use a 1% level of significance to test the claim that thedistribution of first nonzero digits in this accounting filefollows Benford's Law.
A. What is the level of significance?
B. State the null and alternate hypotheses.
C. Find the value of the chi-square statistic for the sample.(Round the expected frequencies to at least three decimal places.Round the test statistic to three decimal places.)
D. Are all the expected frequencies greater than 5?
E. What sampling distribution will you use?
F. What are the degrees of freedom?
G. Estimate the P-value of the sample teststatistic.
H. Based on your answers in parts (a) to (g), will you reject orfail to reject the null hypothesis of independence?
