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 (a = 0.05) to see if these values are consistent with Benford's Law. If they are not consistent, it there might be embezzelment.

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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 (a = 0.05) to see if these values are consistent
with Benford's Law.
If they are not consistent, it there might be embezzelment.
Complete this table. The sum of the observed frequencies is 97
Observed
Expected
Frequency
(Counts)
Benford's
x Frequency
(Counts)
Law P(X)
1 20
.301
2 27
.176
3 9
.125
4|| 10
.097
5 10
.079
6| 8
.067
73
.058
8 5
.051
95
.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.)
X =
What is the P-value for this sample? (Report answer accurate to 3 decimal places.)
P-value =
The P-value is...
O less than (or equal to) a
greater than a
This P-Value leads to a decision to...
O reject the null hypothesis
O fail to reject the null hypothesis
As such, the final conclusion is that...
O There is sufficient evidence to warrant rejection of the claim that these expenses are consistent
with Benford's Law..
O There is not sufficient evidence to warrant rejection of the claim that these expenses are consistent
with Benford's Law..
Transcribed Image Text: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 (a = 0.05) to see if these values are consistent with Benford's Law. If they are not consistent, it there might be embezzelment. Complete this table. The sum of the observed frequencies is 97 Observed Expected Frequency (Counts) Benford's x Frequency (Counts) Law P(X) 1 20 .301 2 27 .176 3 9 .125 4|| 10 .097 5 10 .079 6| 8 .067 73 .058 8 5 .051 95 .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.) X = What is the P-value for this sample? (Report answer accurate to 3 decimal places.) P-value = The P-value is... O less than (or equal to) a greater than a This P-Value leads to a decision to... O reject the null hypothesis O fail to reject the null hypothesis As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that these expenses are consistent with Benford's Law.. O There is not sufficient evidence to warrant rejection of the claim that these expenses are consistent with Benford's Law..
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