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 Exercise?, ?test for goodness-offit with Benford’s law. L e a d i n g D i g i t B e n f o r d ’ s L a w : D i s t r i b u t i o n o f L e a d i n g D i g i t s Author’s Computer Files? The author recorded the leading digits of the sizes of the files stored on his computer, and the leading digits have frequencies of 45, 32, 18, 12, 9, 3, 13, 9, and 9 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law.

Solution 24BSC Step 1 Given, the author recorded the leading digits of the sizes of the files stored on his computer, and the leading digits have frequencies of 45, 32, 18, 12, 9, 3, 13, 9, and 9 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law. We are testing Chi-square test (using EXCEL) as shown below Goodness of Fit Test expecte (Oi Ei) observed (O - E) Ei d 45 45.150 -0.150 0.000 32 26.400 5.600 1.188 18 18.750 -0.750 0.030 12 14.550 -2.550 0.447 9 11.850 -2.850 0.685 3 10.050 -7.050 4.946 13 8.700 4.300 2.125 9 7.650 1.350 0.238 9 6.900 2.100 0.639 150 150.000 0.000 10.299 chi-squa 10.30 re df 8 p-value 0.2447 Now, we have = 10.30...