An investigator analyzed the leading digits from 792 checks issued by seven suspect companies. The frequencies were found to be 235, 136, 99, 87, 51, 49, 43, 45, and 47, and those digits correspond to the leading digits of1, 2,3, 4,5, 6,7, 8, and9, respectively. If the observed frequencies are substantially different from the frequencies expected withBenford's law shownbelow, the check amounts appear to result from fraud. Use a 0.01 significance level to test forgoodness-of-fit withBenford's law. Does it appear that the checks are the result offraud?

Leading Digit

1

2

3

4

5

6

7

8

9

Actual Frequency

235

136

99

87

51

49

43

45

47

Benford's Law: Distribution of Leading Digits

30.1%

17.6%

12.5%

9.7%

7.9%

6.7%

5.8%

5.1%

4.6%

Determine the null and alternative hypotheses.

H0:

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

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

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

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

H1:

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

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

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

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

Calculate the teststatistic, 2.

2=

nothing

(Round to three decimal places asneeded.)

Calculate theP-value.

P-value=

nothing

(Round to four decimal places asneeded.)

State the conclusion.

Do not reject

Reject

H0. There

is

is not

sufficient evidence to warrant rejection of the claim that the leading digits are from a population with a distribution that conforms toBenford's law. It

does appear

does not appear

that the checks are the result of fraud.