Answer:
Z-statistic = 1.4017 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
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
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given first sample size (n₁ ) = 57
Of the 57 Teen Court individuals, 18 subsequently recidivated during the 18-month follow-up period
First sample proportion
Second sample proportion
Null Hypothesis : p₁⁻ = p₂⁻
Alternative Hypothesis : p₁⁻ ≠ p₂⁻
<u><em>Step(ii)</em></u>:-
Test statistic
where
Q = 1 - P = 1 - 0.2612 = 0.7387
Z = 1.4017
Level of significance ∝ =0.05
The tabulated value Z₀.₀₅ = 1.96
Z-statistic = 1.4017 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
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