CT Scan When analyzing the leading digits of the magnitudes of gradients from a CT image, the frequencies were found to be 83, 58, 27, 21, 21, 21, 6, 4, 9, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. Use a 0.01 significance level to test for goodness-of-fit with Benford’s law. Do the leading digits appear to fit the distribution of Benford’s law, as expected, or does it appear that the image has been corrupted because the leading digits do not fit the distribution of Benford’s law? Does the conclusion change if the significance level is 0.05?

Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercises 15 and 16, test for goodness-of-fit with the distribution described by Benford’s law.
Leading Digit 1 2 3 4 5 6 7 8 9 Benford’s Law: Distribution of Leading Digits 30.1%
17.6%
12.5%
9.7%
7.9%
6.7%
5.8%
5.1%
4.6%