Benford\'s Law states that the first nonzero digits of numbers drawn at random f
ID: 3228971 • Letter: B
Question
Benford's Law states that the first nonzero digits of numbers drawn at random from a large complex data file have the following probability distribution.†
Suppose that n = 275 numerical entries were drawn at random from a large accounting file of a major corporation. The first nonzero digits were recorded for the sample.
H0: The distributions are the same.
H1: The distributions are different.
All the expected frequencies are greater than 5.
Chi-square sampling distrubution.
Svince the P-value > , we fail to reject the null hypothesis.
t the 1% level of significance, the evidence is insufficient to conclude that the distribution of first nonzero digits in the accounting file do not follow Benford's Law.
Use a 1% level of significance to test the claim that the distribution of first nonzero digits in this accounting file follows Benford's Law.
(a) What is the level of significance? ____________
(b) 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.) ____________
(c) What are the degrees of freedom? ____________
(d) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) ____________
Explanation / Answer
a) level of significance =0.01
b|)
test statistic =3.559
c) degree of freedom =9-1=8
d) p value =0.895
observed Expected Chi square type Probability O E=total*p =(O-E)^2/E 1 0.301 83.000 82.78 0.00 2 0.176 49.000 48.40 0.01 3 0.125 32.000 34.38 0.16 4 0.097 22.000 26.68 0.82 5 0.079 25.000 21.73 0.49 6 0.067 18.000 18.43 0.01 7 0.058 13.000 15.95 0.55 8 0.051 17.000 14.03 0.63 9 0.046 16.000 12.65 0.89 1 275 275 3.5588Related Questions
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