In: Statistics and Probability
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 of 1, 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: 1 2
3 4 5 6 7 8 9
Actual Frequency: 4 11 2
72 371 281 7 16
23
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, χ2.
χ2 = _______________
(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