Observed frequencies of the leading digit of credit card purchases made are list
ID: 3318615 • Letter: O
Question
Observed frequencies of the leading digit of credit card purchases made are listed below, along with Benford's Law expected number. Using a 0.05 Significance Level test the claim that the leading digits of the purchases conform to Benford's Law, and answer the questions: Leading1 2 3 4 Digit Observed 68 40 18 19 8 20 6 9 12 Benford's Law 60.2 35.2 25 19.4 15.8 13.4 11.6 10.2 9.2 What is the Null hypothesis? What is the Alternate hypothesis? The Test Statistic is? The Critical Value is? Resulting in The P-Value is? the Null hypothesis because Resulting in the Null hypothesis because The conclusion of the analysis is?Explanation / Answer
null hypothesis: Ho: leading digits of the purchase conform to Benford;s law
alternate hypothesis:Ha: leading digits of the purchase does not conform to Benford;s law
applying chi square goodness of fit:
from abve test statistic =14.4316
the critical value is =15.5073
resulting in failed to reject null hypothesis because test statistic is less than critical value
p vlaue =0.0712
resulting in failed to reject null hypothesis because p value is greater than 0.05 level
the conclusion: leading digits of the purchase conform to Benford;s law
observed Expected Chi square category Probability O E=total*p =(O-E)^2/E 1 0.301 68.000 60.20 1.01 2 0.176 40.000 35.20 0.65 3 0.125 18.000 25.00 1.96 4 0.097 19.000 19.40 0.01 5 0.079 8.000 15.80 3.85 6 0.067 20.000 13.40 3.25 7 0.058 6.000 11.60 2.70 8 0.051 9.000 10.20 0.14 9 0.046 12.000 9.20 0.85 1 200 200 14.432Related Questions
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