Assignment:
Benford's Law. According to Benford's law, a variety of different data sets includenumbers with leading ( first) digits that follow the distribution shown in the table below. In Exercises, test for goodness-of-fit with Benford's law.
Check Amounts In the trial of State of Arizona vs. Wayne James Nelson, the defendant was accused of issuing checks to a vendor that did not really exist. The amounts of the checks are listed below in order by row. When testing for goodness-of-fit with the proportions expected with Benford's law, it is necessary to combine categories because not all expected values are at least 5. Use one category with leading digits of 1, a second category with leading digits of 2, 3, 4, 5, and a third category with leading digits of 6, 7, 8, 9. Using a 0.01 significance level, is there sufficient evidence to conclude that the leading digits on the checks do not conform to Benford's law? Test for goodness-of-fit with Benford's law.
|
Leading Digit
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
Benford"s law
distribution of
leading digit
|
30.1%
|
17.6%
|
12.5%
|
9.7%
|
7.9%
|
6.7%
|
5.8%
|
5.1%
|
4.6%
|
|
$ 1,927.48
|
$27,902.31
|
$86,241.90
|
$72,117.46
|
$81,321.75
|
$97,473.96
|
|
$93,249.11
|
$89,658.16
|
$87,776.89
|
$92,105.83
|
$79,949.16
|
$87,602.93
|
|
$96,879.27
|
$91,806.47
|
$84,991.67
|
$90,831.83
|
$93,766.67
|
$88,336.72
|
|
$94,639.49
|
$83,709.26
|
$96,412.21
|
$88,432.86
|
$71,552.16
|
|