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. For​example, 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 obey​Benford'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 the​results, 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