hat is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.) χ2=χ2= 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) αα greater than αα 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..
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 (αα = 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 78
| X | Observed Frequency (Counts) |
Benford's Law P(X) |
Expected Frequency (Counts) |
|---|---|---|---|
| 1 | 15 | .301 | |
| 2 | 16 | .176 | |
| 3 | 15 | .125 | |
| 4 | 8 | .097 | |
| 5 | 2 | .079 | |
| 6 | 3 | .067 | |
| 7 | 5 | .058 | |
| 8 | 7 | .051 | |
| 9 | 7 | .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.)
χ2=χ2=
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) αα
- greater than αα
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..
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