An investigator analyzed the leading digits of the amounts

Question

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 χ2 test statistic.

2. Calculate the χ2critical 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 χ2 test statistic.

5. Calculate the χ2critical value.

6. Is there sufficient evidence to reject the defense claim that deaths on shifts are independent of whether Gilbert was working?

Answer 1

Analyze the statistics problem and on the basis of requirement answer the following by applying the proper concept and formulas. Remember to show your complete work. The investigator examined the leading digits of the amounts from 200 checks issued via three suspect companies. The frequencies were discover to be 68, 40, 18, 19, 8, 20, 6, 9, 12 and such digits correspond to leading digits of 1, 2, 3, 4, 5, 6, 7, 8 and 9 correspondingly. If the surveyed frequencies are substantially dissimilar from the frequencies expected with Benford's law, the check amounts come out to be the result of fraud. Make use of a 0.05 significance level to test for the goodness-of-fit by Benford's law. 1) Compute the ?2 test statistic. 2) Compute the ?2critical value. 3) Is there adequate proof to comprise that the checks are the outcome of fraud?