# Statistics : An investigator analyzed the leading digits of the amounts from 200 checks issue

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 Bedfords law, the
check amounts appear to be the result of fraud. Use a 0.05
significance level to test for goodness-of-fit with Bedfords
law.
1. Calculate the
2test statistic.
2. Calculate the
2critical value.
3. Is there sufficient evidence to conclude that the
checks are the result of fraud?
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.
Shifts With a Death
Shifts Without a Death
Gilbert Was Working
40
217
Gilbert Was Not Working
34
1350
4. Calculate the
2test statistic.
5. Calculate the
2critical 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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