Question

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8. or. It was discovered that first digits do not our with equal frequency Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law For example, the following dibution represents the first digits in 207 alegedly fraudulent checks written to a boa company by an employee attempting to embezzle funds from his employer. Complete paris (a) through ich below. Click the icon to view the tables (a) Because these data are meant to prove that someone is guilty of fraud, what would be an appropriate level of significance when performing a goodness of tu? Use () Using the level of significance chosen in port(a), test whether the first digits in the alegedly fraudulent chicks obey therford's Low Do the first lots obey Benford's Law What are the null and alternative hypothes? Distribution of First Digits OA H, The distribution of the first digits in the allegedly fraudulent checks obeys Benford's Law. H,: The distribution of the first digits in the alegedly fraudulent checks does not obey Benford's Low. OB. Hy: The distribution of the first digits in the allegedly fraudulent checks does not obey Benford's Law Fulldataset He: The distrbution of the first digits in the allegedly fraudulent checks obeys Benford's Low. Distribution of first digits enford's Law Digit 1 2 5 What is the best statistic? Probability 0301 0.176 0.125 01002 0070 Digit 6 7 8 x-Round to three decimal places as needed) Probability 0002 07658 0.051 0.046 What is the value of the best? First digits in alegedly fraudulent checks First digit 1 2 7 3 P.valueRound to three decimal places as needed) Frequency 36 3245 20 24 17 9 3 4 5 9 7 Click to select your answers) Print Done

Answer 1

Oi Ei 36 62.307 32 45 20 Pi 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Total 36.432 25.875 20.079 16.353 13.869 12.006 (Oi - Ei)^2/Ei 11.10723 0.539159 14.13587 0.000311 3.575895 0.70684 0.752627 3.932201 0.667978 a) The appropriate level of significance is 0.05 Use alpha = 0.05 24 17 9 10.557 17 7 9.522 1 207 207 35.41811

- 35.4181 solution b) Here to the distubution of the first digits in the first digits in the alegedly fradulent checks obeys Benford's law- Hi the distribution of the first digits in the first digits in the alegedly frodulent checks does not obsegs Benford's lam. Test statutic x²= € 60; -ED Ei Here Ei= Pix 207 O; = obser values. dif = n-1=9-1=8 assume x=0.05 P-value=0.000022=0.000 here P-value ca, so Reject Ho, because the calculated P-value is less than the given level of significance → YES, the first digits do not obey Benford's law. Because we reject Ho. / /