The first significant digit in any number must be 1, 2, 3, 4,5, 6, 7, 8, or 9. It was discovered that first digits do not occur 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. Forexample, the following distribution represents the first digits in 187 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. a.) Using the level of significance alpha 0.10, test whether the first digits in the allegedly fraudulent checks obeyBenford's Law. What is the null hypothesis?
b.) What is the alternative hypothesis?
c.) What is the test statistic?
d.) What is the p-value?
e.) Using the P-value approach, compare the P-value with the given alpha = 0.10, level of significance. Based on theresults, do the first digits obey the Benford's Law?
f.) (b) Based on the results of part (a),could one think that the employee is guilty of embezzlement?
Digit Probability Frequency
1 0.301 36
2 0.176 25
3 0.125 28
4 0.097 26
5 0.079 23
6 0.067 17
7 0.058 9
8 0.051 16
9 0.046 7