You are interested in understanding whether mentally illoffenders are better able to avoid re-arrest if they are assigned amental health case manager upon their release from jail or prison.You study a sample of formerly incarcerated people with mentalhealth diagnoses. You are comparing people with a case manager tothose who do not have one (measured as: has a case manager / doesnot have a case manager), on whether or not they are re-arrestedwithin one year (measured as two categories: rearrested vs. notre-arrested). 1. Write a one-tailed, directional researchhypothesis that is appropriate for the above research project. 2.Specify your dependent and independent variables, and at what levelthey are measured. 3. Write the corresponding null hypothesis forthis research study. 4. Specify the type of statistical test youwould use in this situation and why. 5. Assume that you find that50% of people with a case manager are re-arrested, and 60% ofpeople without a case manager are re-arrested within one year. Ifyour statistical analysis produced a test value of 2.70 (and youhave 1 df), what would this tell you (assuming you use alpha=.05 asthe cut-off for your rejection region)? 6. Write up your results asif you were reporting them in an official report. Examples ofappropriate write-ups are available in the videos and powerpointsfor each kind of statistical test.