Benford's Law states that the first nonzero digits of numbers drawn at random from a large complex data file have the following probability distribution.† 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 at random from a large accounting file of a major corporation. The first nonzero digits were recorded for the sample. First Nonzero Digit 1 2 3 4 5 6 7 8 9 Sample Frequency 88 46 30 25 22 18 13 17 16 State the null and alternate hypotheses. H0: The distributions are different. H1: The distributions are the same.H0: The distributions are the same. H1: The distributions are the same. H0: The distributions are the same. H1: The distributions are different.H0: The distributions are different. H1: The distributions are different. (b) 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.) What are the degrees of freedom? (c) Estimate the P-value of the sample test statistic. P-value > 0.1000 .050 < P-value < 0.100 0.025 < P-value < 0.0500 .010 < P-value < 0.0250 .005 < P-value < 0.010 P-value < 0.005
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 first nonzero digits of numbers drawn at random from a large complex data file have the following
| 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 at random from a large accounting file of a major corporation. The first nonzero digits were recorded for the sample.
| First Nonzero Digit | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Sample Frequency | 88 | 46 | 30 | 25 | 22 | 18 | 13 | 17 | 16 |
State the null and alternate hypotheses.
H1: The distributions are the same.H0: The distributions are the same.
H1: The distributions are the same. H0: The distributions are the same.
H1: The distributions are different.H0: The distributions are different.
H1: The distributions are different.
(b) 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.)
What are the degrees of freedom?
(c) Estimate the P-value of the sample test statistic.
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