Question

In: Statistics and Probability

An investigator analyzed the leading digits from 787 checks issued by seven suspect companies. The frequencies...

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

Solutions

Expert Solution


Related Solutions

An investigator analyzed the leading digits from 787 checks issued by seven suspect companies. The frequencies...
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...
An investigator analyzed the leading digits from 787 checks issued by seven suspect companies. The frequencies...
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...
An investigator analyzed the leading digits from 787 checks issued by seven suspect companies. The frequencies...
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...
An investigator analyzed the leading digits from 796796 checks issued by seven suspect companies. The frequencies...
An investigator analyzed the leading digits from 796796 checks issued by seven suspect companies. The frequencies were found to be 55​, 1818​, 00​, 8989​, 224224​, 412412​, 88​, 1717​, and 2323​, 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 0.0250.025 significance level to...
n investigator analyzed the leading digits from 799 checks issued by seven suspect companies. The frequencies...
n investigator analyzed the leading digits from 799 checks issued by seven suspect companies. The frequencies were found to be 235​, 148​, 96​, 90​, 68​, 47​, 43​, 38​, and 34​, 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 0.01 significance level to...
Provide an example of any two leading companies from the same industry which are competing directly...
Provide an example of any two leading companies from the same industry which are competing directly for marketshare. Give a short profile (300-500 words) for each (provide references for your answers). If you are the manager of one of these companies, what pricing policy do you adopt to be in the first position? Why? (100-200 words) When the whole sector of the market is occupied by the little number of big corporations who share the leadership, what do we call...
Provide an example of any two leading companies from the same industry which are competing directly...
Provide an example of any two leading companies from the same industry which are competing directly for marketshare. Give a short profile (300-500 words) for each (provide references for your answers). If you are the manager of one of these companies, what pricing policy do you adopt to be in the first position? Why? (100-200 words) When the whole sector of the market is occupied by the little number of big corporations who share the leadership, what do we call...
1. Provide an example of any two leading companies from the same industry which are competing...
1. Provide an example of any two leading companies from the same industry which are competing directly for marketshare. Give a short profile (300-500 words) for each (provide references for your answers). 2. If you are the manager of one of these companies, what pricing policy do you adopt to be in the first position? Why? (100-200 words) 3. When the whole sector of the market is occupied by the little number of big corporations who share the leadership, what...
Provide an example of any two leading companies from the same industry which are competing directly...
Provide an example of any two leading companies from the same industry which are competing directly for marketshare. Give a short profile (300-500 words) for each (provide references for your answers). If you are the manager of one of these companies, what pricing policy do you adopt to be in the first position? Why? (100-200 words) When the whole sector of the market is occupied by the little number of big corporations who share the leadership, what do we call...
1. Provide an example of any two leading companies from the same industry which are competing...
1. Provide an example of any two leading companies from the same industry which are competing directly for marketshare. Give a short profile (300-500 words) for each (provide references for your answers). 2. If you are the manager of one of these companies, what pricing policy do you adopt to be in the first position? Why? (100-200 words) 3. When the whole sector of the market is occupied by the little number of big corporations who share the leadership, what...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT