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 Benfords law, the check amounts appear to
be the result of fraud. Use a 0.05 significance level to test for goodness-of-fit with Benfords law.
1. Calculate the χ2 test statistic.
2. Calculate the χ2 critical value.
3. Is there sufficient evidence to conclude that the checks are the result of fraud?
Alert nurses at the Veterans 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
Shifts Without a Death
Gilbert Was Not Working
4. Calculate the χ2 test statistic.
5. Calculate the χ2 critical value.
6. Is there sufficient evidence to reject the defense claim that deaths on shifts are independent of
whether Gilbert was working?
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