According to Benford’s Law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the data table below. Data sets that follow Benford’s Law include a class of errors in clinical trials, as well as magnitudes of gradients from MRI scans, CT scans, and ultrasound images. The data presented below show the observed leading digits from MRI gradients. Do these data follow the distribution predicted by Benford’s Law?
|
Leading Digit |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Benford’s Law Distribution (%) |
30.1 |
17.6 |
12.5 |
9.7 |
7.9 |
6.7 |
5.8 |
5.1 |
4.6 |
|
Observed frequency from MRI gradient |
59 |
30 |
22 |
16 |
15 |
12 |
12 |
17 |
4 |
Please answer the following:
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H0 |
|
|
HA |
|
|
Test Statistic & Value |
|
|
p-value |
|
|
Effect size |
|
|
Statistical Decision |
|
|
Written Conclusion |
|