An investigator analyzed the leading digits from 787 checks issued by seven suspect companies. The frequencies were found to be 4, 11, 2, 72, 371, 281, 7, 16, and 23, and those digits correspond to the leading digits of1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.025 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud?

Leading Digit:123456789

Actual Frequency:41127237128171623

Benford's Law:30.1%17.6%12.5%9.7%7.9% 6.7%5.8% 5.1%4.6%

Determine the null and alternative hypotheses.

Ho: (1)_________________H1: (2)_________________

Calculate the test statistic, 2.

2 = _______________

(Round to three decimal places as needed.)

Calculate the P-value.

P-value = _______________

(Round to four decimal places as needed.)

State the conclusion.

(3)_________________Ho. There (4)______________sufficient evidence to warrant rejection of the claim that the leading digits are from a population with a distribution that conforms to Benford's law. It (5)________________that the checks are the result of fraud.

Choose from the following options:

(1) a.At least two leading digits have frequencies that do not conform to Benford's law.

b.The leading digits are from a population that conforms to Benford's law.

c.At most three leading digits have frequencies that do not conform to Benford's law.

d.At least one leading digit has a frequency that does not conform to Benford's law.

(2) a. The leading digits are from a population that conforms to Benford's law.

b. At most three leading digits have frequencies that do not conform to Benford's law.

c. At least one leading digit has a frequency that does not conform to Benford's law.

d. At least two leading digits have frequencies that do not conform to Benford's law.

(3) Do not reject

Reject

(4) is

is not

(5) does appear

does not appear