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Fraudulent checks obey benford law

Assignment Help Basic Statistics
Reference no: EM13835968

1.  The first significant digit in any number must be I, 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 215 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts (a) and (b) below.

(a) Using the level of significance a = 0.10, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. What is the null hypothesis?

  • H0: The distribution of the first digits in the allegedly fraudulent checks does not obey Benford's Law.
  • 110: The distribution of the first digits in the allegedly fraudulent checks obeys Benford's Law.
  • None of these.

What is the alternative hypothesis?

  • HI: The distribution of the first digits in the allegedly fraudulent checks does not obey Benford's Law.
  • Ht: The distribution of the first digits in the allegedly fraudulent checks obeys Benford's Law.
  • None of these.

What is the test statistic?

What is the P-value of the test?

Using the P-value approach, compare the P-value with the given ? = 0.10 level of significance. Based on the result, do the first digits obey the Benford's Law?

  • Do not reject the Ho because the calculated P-value is less than the given ? level of significance.
  • Do not the reject the Ho because the calculated P-value is greater than the given ? level of significance.
  • Reject the Ho because the calculated P-value is less than the given ? level of significance.
  • Reject the Ho because the calculated P-value is greater than the given ? level of significance.

b. Based on the result of part (a), could one think that the employee is guilty of embezzlement?

  • No, the first digits obey the Benford's Law.
  • Yes, the first digits obey the Benford's Law.
  • Yes, the first digits do not obey the Benford's Law.
  • No, the first digits do not obey the Benford's Law.

Distribution of First Digits

Distribution of First Digits (Benford's Law)

Digit

1

2

3

4

5

Probability

0.301

0.176

0.125

0.097

0.079

Digit

6

7

8

9

 

Probability

0.067

0.058

0.051

0.046

 

First digits in allegedly fraudulent checks

First  digit

1

2

3

4

5

6

7

8

9

Frequency

36

32

28

20

24

36

15

17

7

2. A traffic safety company publishes reports about motorcycle fatalities and helmet use. In the first accompanying data table, the distribution shows the proportion of fatalities by location of injury for motorcycle accidents. The second data table shows the location of injury and fatalities for 2062 riders not wearing a helmet. Complete parts (a) and (b) below.

(a) Does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all riders? Use a = 0.01 level of significance. What are the null and alternative hypotheses?

  • Ho: The distribution of fatal injuries for riders not wearing a helmet follows the same distribution for all other riders.
  • HI: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders.
  • Ho: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders.
  • HI: The distribution of fatal injuries for riders not wearing a helmet does follow the same distribution for all other riders.
  • None of these.

Compute the expected counts for each fatal injury.

Location of injury

Observed Count

Expected Count

Multiple Locations

1047

 

Head

852

 

Neck

34

 

Thorax

83

 

Abdomen/Lumbar/Spine

46

 

 

What is the P-value of the test?

Based on the results, does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all other riders at a significance level of a = 0.01?

Reject Ho. There is sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet does not follow the distribution for all riders.

Do not reject Ho. There is not sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet does not follow the distribution for all riders.

Do not reject Ho. There is sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet follows the distribution for all riders.

Reject Ho. There is not sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet follows the distribution for all riders.

(b) Compare the observed and expected counts for each category. What does this information tell you?

  • Motorcycle fatalities from head injuries occur less frequently for riders not wearing a helmet.
  • Motorcycle fatalities from head injuries occur more frequently for riders not wearing a helmet.
  • Motorcycle fatalities from thorax injuries occur more frequently for riders not wearing a helmet.

Distribution of fatalities by location of injury

Location of injuries and fatalities for 2062 riders not wearing a helmet

Location of injuries

Multiple Locations

Head

Neck

Thorax

Abdomen Lumar/Spine

Number

1047

852

34

83

46

Proportion of fatalities by location of injuries for motorcycle accidents

Location of injuries

Multiple Locations

Head

Neck

Thorax

Abdomen Lumar/Spine

Proportion

0.570

0.310

0.030

0.060

0.030

Attachment:- 8-2 problem 8.pdf

Attachment:- 8-2 problem 9.pdf

Reference no: EM13835968

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