Medical researchers at the Cleveland Clinic and St. Vincent\'s randomly assigned
ID: 3376619 • Letter: M
Question
Medical researchers at the Cleveland Clinic and St. Vincent's randomly assigned 227 General Electric employees with alcohol problems to one of three alcohol-treatment groups: a 28-day hospitalization only Alcoholics Anonymous (AA) meetings only, or individual counseling sessions only. Two years later, the researchers identified the patients who had remained sober after completing the program. The data is summarized in the table below Hospital AA Only Individual Counseling 12 63 75 Stayed sober Did not stay sober 13 53 174 227 76 76 Using ? 01, the 5-step procedure, and the critical value approach, do a complete and appropriate hypothesis test to determine whether the type of treatment program entered is independent of an employee's status following treatment. If and only if it is appropriate to do so, offer an informal comment as to where the single largest difference isExplanation / Answer
Ans:
H0:Type of treatment program entered is independent of an employee's status following treatment.
Ha:Type of treatment program entered is not independent of an employee's status following treatment.
Test statistic:
Chi square score=11.650
df=(2-1)*(3-1)=2
p-value=CHIDIST(11.650,2)=0.0030
As,p-value<0.01,we reject the null hypothesis and we can conclude that Type of treatment program entered is not independent of an employee's status following treatment.
Observed freq.(fo) Hospital AA only Ind. couns. Total Stayed sober 28 13 12 53 Did not stay 48 63 63 174 Total 76 76 75 227 Expected freq.(fe) Hospital AA only Ind. couns. Total Stayed sober 17.74 17.74 17.51 53 Did not stay 58.26 58.26 57.49 174 Total 76 76 75 227 Chi square=(fo-fe)^2/fe Hospital AA only Ind. couns. Total Stayed sober 5.927 1.269 1.734 8.930 Did not stay 1.805 0.386 0.528 2.720 Total 7.733 1.655 2.263 11.650