Benford's law states that the probability distribution of the first digits of many items (e.g. populations and expenses) is not uniform, but has the probabilities shown in this table. Business expenses tend to follow Benford's Law, because there are generally more small expenses than large expenses. Perform a "Goodness of Fit" Chi-Squared hypothesis test ( = 0.05) to see if these values are consistent with Benford's Law. If they are not consistent, it there might be embezzelment. fill out this table. The sum of the observed frequencies is 85

X	Observed Frequency (Counts)	Benford's Law P(X)	Expected Frequency (Counts)
1	19	.301
2	5	.176
3	16	.125
4	13	.097
5	3	.079
6	10	.067
7	8	.058
8	9	.051
9	2	.046

Report all answers accurate to three decimal places. What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.) 2=2= What is the P-value for this sample? (Report answer accurate to 3 decimal places.) P-value = The P-value is...

• less than (or equal to)
• greater than

This P-Value leads to a decision to...

• reject the null hypothesis
• fail to reject the null hypothesis

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that these expenses are consistent with Benford's Law..
• There is not sufficient evidence to warrant rejection of the claim that these expenses are consistent with Benford's Law..