An article made a strong case for central statistical monitoring as an alternative to more expensive onsite data verification. It suggested various methods for identifying data characteristics such as outliers, incorrect dates, anomalous data patterns, unusual correlation structures, and digit preference. Benford's Law gives a probability model for the first significant digit in many large data sets: p(x) = log,o(* + 1) ) for x = 1, 2, ..., 9. The article gave the following frequencies for the first significant digit in a variety of variables whose values were determined in one particular clinical trial. Digit 1 2 3 4 5 6 7 8 Freq. 349 180 162 155 86 65 57 45 58 Carry out a test of hypotheses to see whether or not these frequencies are consistent with Benford's Law using a significance level of 0.05. State the appropriate hypotheses. (Round your answers to four decimal places.) O Ho: P1 = 0.3490, p, = 0.1800, p3 = 0.1620, P4 = 0.1550, P5 = 0.0860, P6 = 0.0€ H: at least one p, + Po O Ho: P1 = 0.3016, p2 = 0.1556, p3 = 0.1400, p4 = 0.1340, p5 = 0.0743, P6 = 0.0! H: at least one p, + Po O Ho: P1 = 0.3010, p2 = 0.1761, p3 = 0.1249, P4 = 0.0969, P5 = 0.0792, p6 = 0.00 H: at least one p, + Po O Ho: P1 = P2 = P3 = P4 = Ps = P6 = P7 = P8 = P9 = 1 H: at least one p, + Calculate the test statistic. (Round your answer to two decimal places.) x? = %3D What can be said about the P-value for the test? O P-value < 0.005 O 0.005 < P-value < 0.01 O 0.01 < P-value < 0.025 O 0.025 < P-value < 0.05 O 0.05 < P-value < 0.10 O P-value > 0.10 State the conclusion in the problem context. O Reject Ho. There is enough evidence to conclude that at least one of the first significant digits deviates from Benford's law. O Fail to reject Ho. There is enough evidence to conclude that none of the first significant digits deviates from Benford's law. O Reject Ho. There is enough evidence to conclude that all of the first significant digits deviate from Benford's law. O Fail to reject Ho. There is enough evidence to conclude that at least one of the first significant digits doesn't deviate from Benford's law.
An article made a strong case for central statistical monitoring as an alternative to more expensive onsite data verification. It suggested various methods for identifying data characteristics such as outliers, incorrect dates, anomalous data patterns, unusual correlation structures, and digit preference. Benford's Law gives a probability model for the first significant digit in many large data sets: p(x) = log,o(* + 1) ) for x = 1, 2, ..., 9. The article gave the following frequencies for the first significant digit in a variety of variables whose values were determined in one particular clinical trial. Digit 1 2 3 4 5 6 7 8 Freq. 349 180 162 155 86 65 57 45 58 Carry out a test of hypotheses to see whether or not these frequencies are consistent with Benford's Law using a significance level of 0.05. State the appropriate hypotheses. (Round your answers to four decimal places.) O Ho: P1 = 0.3490, p, = 0.1800, p3 = 0.1620, P4 = 0.1550, P5 = 0.0860, P6 = 0.0€ H: at least one p, + Po O Ho: P1 = 0.3016, p2 = 0.1556, p3 = 0.1400, p4 = 0.1340, p5 = 0.0743, P6 = 0.0! H: at least one p, + Po O Ho: P1 = 0.3010, p2 = 0.1761, p3 = 0.1249, P4 = 0.0969, P5 = 0.0792, p6 = 0.00 H: at least one p, + Po O Ho: P1 = P2 = P3 = P4 = Ps = P6 = P7 = P8 = P9 = 1 H: at least one p, + Calculate the test statistic. (Round your answer to two decimal places.) x? = %3D What can be said about the P-value for the test? O P-value < 0.005 O 0.005 < P-value < 0.01 O 0.01 < P-value < 0.025 O 0.025 < P-value < 0.05 O 0.05 < P-value < 0.10 O P-value > 0.10 State the conclusion in the problem context. O Reject Ho. There is enough evidence to conclude that at least one of the first significant digits deviates from Benford's law. O Fail to reject Ho. There is enough evidence to conclude that none of the first significant digits deviates from Benford's law. O Reject Ho. There is enough evidence to conclude that all of the first significant digits deviate from Benford's law. O Fail to reject Ho. There is enough evidence to conclude that at least one of the first significant digits doesn't deviate from Benford's law.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:An article made a strong case for central statistical monitoring as an alternative to more expensive onsite data verification. It suggested various methods for identifying data characteristics such as outliers, incorrect dates, anomalous data patterns, unusual correlation structures, and digit preference. Benford's Law gives a probability model for the first significant digit in many large data sets: \( p(x) = \log_{10} \left( \frac{(x + 1)}{x} \right) \) for \( x = 1, 2, \ldots, 9 \). The article gave the following frequencies for the first significant digit in a variety of variables whose values were determined in one particular clinical trial.
**Digit Frequencies:**
| Digit | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|-------|-----|-----|-----|-----|-----|-----|----|----|----|
| Freq. | 349 | 180 | 162 | 155 | 86 | 65 | 57 | 45 | 58 |
Carry out a test of hypotheses to see whether or not these frequencies are consistent with Benford's Law using a significance level of 0.05.
**State the appropriate hypotheses. (Round your answers to four decimal places.)**
- \(H_0: p_1 = 0.3490, p_2 = 0.1800, p_3 = 0.1620, p_4 = 0.1550, p_5 = 0.0860, p_6 = 0.0677, p_7 = 0.0580, p_8 = 0.0512, p_9 = 0.0458\)
\(H_a\): at least one \(p_i \neq p_{i0}\)
- \(H_0: p_1 = 0.3016, p_2 = 0.1556, p_3 = 0.1400, p_4 = 0.1340, p_5 = 0.0743, p_6 = 0.0669, p_7 = 0.0550, p_8 = 0.0420, p_9 = 0.030
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