Question

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 219 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer.

Digit   Probability   Frequency
1   0.301   42
2   0.176   32
3   0.125   28
4   0.097   26
5   0.079   23
6   0.067   36
7   0.058   9
8   0.051   16
9   0.046   7

​(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-fit test?

Use α=0.01.

​(b) Using the level of significance chosen in part​ (a), test whether the first digits in the allegedly fraudulent checks obey​ Benford's Law. Do the first digits obey​ Benford's Law?

What are the null and alternative​ hypotheses?

A.

H0​: The distribution of the first digits in the allegedly fraudulent checks obeys​ Benford's Law.

H1​: The distribution of the first digits in the allegedly fraudulent checks does not obey​ Benford's Law.

B.

H0​: The distribution of the first digits in the allegedly fraudulent checks does not obey​ Benford's Law.

H1​: The distribution of the first digits in the allegedly fraudulent checks obeys​ Benford's Law.

Answer 1

Answer:

a) As we want prove that someone is guilty offraud; therefore we want larger level of significance

Hence correct option is 0.01

b) We need to test whether the distribution of first digits obeys Benford's law. Hence, our hypotheses will be:

H0: The distribution of the first digits in the allegedly fraudulent checks obeysBenford’s Law.

H1: The distribution of the first digits in the allegedly fraudulent checks does not obeyBenford’s Law.

Option A is correct.