Module 6 Homework
Assignment
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An investigator analyzed the leading digits of the amounts from
200 checks issued by three suspect companies. The frequencies were found to be
68, 40, 18, 19, 8, 20, 6, 9, 12 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, the check amounts appear to be the result of fraud. Use a 0.05
significance level to test for goodness-of-fit with Benford's law.
1. Calculate
the ?2 test
statistic.
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Solution:
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Instructor Comments:
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2. Calculate
the ?2 critical
value.
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Solution:
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Instructor Comments:
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3. Is there sufficient evidence to conclude that the checks are the result of fraud?
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Solution:
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Instructor Comments:
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Alert nurses at the Veteran's Affairs Medical Center in
Northampton, Massachusetts, noticed an unusually high number of deaths at times
when another nurse, Kristen Gilbert, was working. Kristen Gilbert was arrested
and charged with four counts of murder and two counts of attempted murder. When
seeking a grand jury indictment, prosecutors provided a key piece of evidence
consisting of the table below. Use a 0.01 significance level to test the
defense claim that deaths on shifts are independent of whether Gilbert was
working.
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Shifts With a Death
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Shifts Without a Death
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Gilbert Was Working
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40
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217
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Gilbert Was Not Working
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34
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1350
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4. Calculate
the ?2 test
statistic.
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Solution:
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Instructor Comments:
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5. Calculate
the ?2 critical
value.
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Solution:
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Instructor Comments:
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6. Is there sufficient evidence to reject thedefense claim that
deaths on shifts are independent of whether Gilbert was working?
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Solution:
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Instructor Comments:
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