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

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Statistics

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?

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3.6 Ratings (530 Votes)

using minitabstattables chi square we have ChiSquare GoodnessofFit Test for Observed Counts in Variable frequency Using category names in Data Test Contribution Cate ObservedProportion Expected to ChiSq 1 87 See Answer

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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

First Nonzero Digit	1	2	3	4	5	6	7	8	9
SampleFrequency	87	46	34	23	21	18	13	17	16