# STATISTICS A3140 An investigator analyzed the leading digits

March 13, 2016

Question
Name:______________________________________

Module 6 Homework Assignment
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.
Solution:

2. Calculate the ?2 critical value.
Solution:

3. Is there sufficient evidence to conclude that the checks are the result of fraud?
Solution:

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.

Gilbert Was Working

Shifts With a Death
40

Shifts Without a Death
217

Gilbert Was Not Working

34

1350

4. Calculate the ?2 test statistic.
Solution: