Question

Teen Court is a juvenile diversion program designed to circumvent the formal processing of first-time juvenile offenders within the juvenile justice system. An article reported on a study in which offenders were randomly assigned either to Teen Court or to the traditional Department of Juvenile Services method of processing. Of the 56 Teen Court individuals, 17 subsequently recidivated during the 18-month follow-up period, whereas 12 of the 51 Department of Juvenile Services individuals did so. Does the data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals who do so? Test the relevant hypotheses using a significance level of 0.10. (Use p₁ for the true proportion of Teen Court individuals who recidivate during the follow up period and p₂ for the true proportion of individuals from the traditional Department of Juvenile Services who recidivate during the follow up period.)

relevant hypothesis =

H0: p1 - P2 = 0

Ha: P1 - P2 =/ 0

z =

P-value =

Answer 1

The statistical software output for this problem is :

H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ≠ 0

z = 0.7936

P-value = 0.4274