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You are interested in understanding whether mentally ill offenders are better able to avoid re-arrest if...

You are interested in understanding whether mentally ill offenders are better able to avoid re-arrest if they are assigned a mental health case manager upon their release from jail or prison. You study a sample of formerly incarcerated people with mental health diagnoses. You are comparing people with a case manager to those who do not have one (measured as: has a case manager / does not have a case manager), on whether or not they are re-arrested within one year (measured as two categories: rearrested vs. not re-arrested). 1. Write a one-tailed, directional research hypothesis that is appropriate for the above research project. 2. Specify your dependent and independent variables, and at what level they are measured. 3. Write the corresponding null hypothesis for this research study. 4. Specify the type of statistical test you would use in this situation and why. 5. Assume that you find that 50% of people with a case manager are re-arrested, and 60% of people without a case manager are re-arrested within one year. If your statistical analysis produced a test value of 2.70 (and you have 1 df), what would this tell you (assuming you use alpha=.05 as the cut-off for your rejection region)? 6. Write up your results as if you were reporting them in an official report. Examples of appropriate write-ups are available in the videos and powerpoints for each kind of statistical test.

Solutions

Expert Solution

1.

The research hypothesis is,

H1: Percentage of people with a case manager which are re-arrested within one year are less than the percentage of people without a case manager re-arrested within one year.

2.

Dependent variable is whether or not they are re-arrested within one year (measured as two categories: rearrested vs. not re-arrested)

Independent variable is whether mentally ill offenders has a case manager or does not have a case manager.

3.

The null hypothesis is,

H0: Percentage of people with a case manager which are re-arrested within one year is equal to the percentage of people without a case manager re-arrested within one year.

4.

We are comparing the proportions (or percentages) from two independent samples (mentally ill offenders has a case manager or does not have a case manager). To compare the proportions (or percentages) from two independent samples, we use two-proportion z-test as the sampling distribution of difference in proportions of two independent samples approximately follow normal distribution.

5.

P-value = P(z > 2.70) = 0.0035

Since p-value is less than 0.05 significance level, we reject null hypothesis H0.

6.

We conclude that there is significant evidence that percentage of people with a case manager which are re-arrested within one year are less than the percentage of people without a case manager re-arrested within one year.

milcah answered 9 months ago
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