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Benford's Law states that the first nonzero digits of numbers drawn at random from a large...

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.† 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 at random from a large accounting file of a major corporation. The first nonzero digits were recorded for the sample. First Nonzero Digit 1 2 3 4 5 6 7 8 9 Sample Frequency 87 46 31 23 24 18 13 17 16 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? State the null and alternate hypotheses. H0: The distributions are the same. H1: The distributions are the same. H0: The distributions are the same. H1: The distributions are different. H0: The distributions are different. H1: The distributions are different. H0: The distributions are different. H1: The distributions are the same. (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.)

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Answer #1

using minitab>stat>tables

we have

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Frequency

Test Contribution
Category Observed Proportion Expected to Chi-Sq
1 87 0.301 82.775 0.215652
2 46 0.176 48.400 0.119008
3 31 0.125 34.375 0.331364
4 23 0.097 26.675 0.506303
5 24 0.079 21.725 0.238234
6 18 0.067 18.425 0.009803
7 13 0.058 15.950 0.545611
8 17 0.051 14.025 0.631061
9 16 0.046 12.650 0.887154


N DF Chi-Sq P-Value
275 8 3.48419 0.900

(a) the level of significance is 0.01

the null and alternate hypotheses is

H0: The distributions are the same.

H1: The distributions are different.

(b)\the value of the chi-square statistic for the sample is 3.484

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