Question

Alert nurses at the Veteran's Affairs Medical Center in Northampton, Massachusetts. noticed an unusually high number of deaths when another nurse, Kristen Gilbert, was working. Those same nurses later noticed missing supplies of the drug epinephrine, which is a synthetic adrenaline that stimulates the heart. Kristen 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 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. What does the result suggest about the guilt or innocence of Gilbert? [8 pts] Gilbert Was Working Gilbert Was Not Working Shifts with a Death 40 34 Shifts Without a Death 217 1350

Answer 1

Ho: The death on shits and Gilbert was working is independent Hi the death on shifs and Gilbert was working is not independent. observed frequencies Coil shifts with death) shifts without death) Total Gilbert was working 40 217 257 Gilbert was not working L 34 1350 1384 1. Total T 74 1 1567 [1641

Expected frequeries (Ei n Total Gilbert was working shits with cleath 748257 = 11.59 1641 shifts without death 15678 257 = 245.41 1641 . 257 Gilbert was not working 1384 24x1384 = 62.41 1567x 1384 = 1321.59 164 1 1641 74 L 1567 I Total I 1641 I Expected frequencies (Ei) shifts with death I shifts without death Gilbert was coorking 245.41 Gilbert was not working 62.41 1321.59 Total T 74 1 15677 Total 257 1384 1641

E 62.41 =(40-11.59) 27+(217-245.41) 4+ (34 - 62.41) ². 245.41 -1321-59 1321.59 +/807-1693 1321.59 807, 1693 + 807.1693 145.41] [62.41 1.1693 1-59 = 63.6450 + 32891 +12.9332 + 0.610 = 86.4809 d. f = (0-1)(C-1) = (2-1) (2-1) = 1 oritical vake - X d. f, a =xi,cool critial value = 6.63 l Decision - Here . Here Reject to if sritical value (test statistic = Xed critical value = 6.63 < Tcal = 86.4809 we reject to and conclusion se may Gilbert was conclude coorking that the deaths on shifs is not independent.