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Chi-Square Goodness-of-Fit and Independence Tests: Analyzing Fraud Detection and Deaths at Northampton Medical Center

A statistical analysis using chi-square tests to detect fraud and analyze mortality rates.

Benjamin Clark
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Name:______________________________________Module6Homework AssignmentAn investigator analyzed the leading digits of the amounts from 200 checks issued by three suspectcompanies. The frequencies were found to be 68, 40, 18, 19, 8, 20, 6, 9, 12 and those digits correspondto the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies aresubstantially different from the frequencies expected with Benford's law, the check amounts appear tobe the result of fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's law.1.Calculate theχ2test statistic.Solution:Chi square = sum (OF-EF)^2 /EF = 143.53Instructor Comments:2.Calculate theχ2criticalvalue.Solution:χ2criticalvalue at 9-1 = 8 degrees of freedom at0.05 is 15.51Instructor Comments:3. Is there sufficient evidence to conclude thatthe checks are the result of fraud?Solution:Yes. The chi-square statistic value is much greaterthan chi-square critical value.Instructor Comments:Alert nurses at the Veteran's Affairs Medical Center in Northampton, Massachusetts, noticed anunusually high number of deaths at times when another nurse, Kristen Gilbert, was working. KristenGilbert 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 thetable below. Use a 0.01 significance level to test the defense claim that deaths on shifts are independentof whether Gilbert was working.Shifts With a DeathShifts Without a DeathGilbert Was Working40217

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