MATH333: Assessment Week 16

Assessment Deadline: Week 17, Tuesday 5pm.

The following table contains data on the number of re-offending criminals in a year, separated by three geographical regions and gender. The data in each cell represents the ”number of criminals who have re-offended” followed by the ”number of criminals eligible to re-offend”.

Gender	Region 1	Region 2	Region 3
Male	16,030 / 63,225	6,794 / 27,089	6,987 / 27,412
Female	2,062 / 12,094	1,107 / 6,305	1,086 / 6,353

1. Complete the $3\times 2$ table below that tabulate the number of people who have or not have re-offended by each region. [2]

   	Region 1	Region 2	Region 3	Total
   Have re-offended	18,092			34,066
   Have not re-offended
   Total		33,394		142,478

2. Perform the Pearson’s chi-squared test for independence between re-offending and region. What do you conclude? [3]

3. Create the $2\times 2$ contingency table for re-offending against gender. Calculate the odds ratio for re-offending for a female criminal relative to a male criminal. [2]

4. Evaluate an approximate 95% confidence interval for the odds ratio of re-offending for a female criminal relative to a male criminal. What do you conclude. [3]