Teen Court is a juvenile diversion program designed to circumvent the formal pro

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 59 Teen Court individuals, 16 subsequently recidivated during the 18-month follow-up period, whereas 12 of the 53 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 o Teen Court ndividuals who recidivate during the follow up period and p2 for the true proportion of individuals from the traditional Department of Juvenile Services who racidivate during the follow up period.) State the relevant hypotheses. Ho: P1- P2 Hai 1-2 > 0 Hai P1-p20 Ha P1-p2-0 Ha P1- P2-0 Ho: p1-P2-0 Ha P1 -P2 0 Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) p-value State the conclusion in the problem context. o Reject Ho. The deta does not suggest 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. O Reject Ho- The dota suggests 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. O Fail to reject Hg- The data suggests the true propartion 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. Fail to reject Ho- The data does not suggest that the true proportion of Teen Court individuals who recidlvate during the specified follow-up period d iffers from the proportion of Department of Juvenile Services individuals who do so

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

Hence,

z = 0.55

P - value = 0.5848

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 16 59 12 53 0.044771346 0.081949387 0.54632924 0.5848

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