1. A researcher is interested in whether gender affects the probability of being arrested. They gather a random sample of 3996 women and find that 801 of them have been arrested. This compares to 1808 men arrested from a random sample of 4155 men.

a) From a statistical perspective are women more likely to be arrested than men? Explain your method of answering this question. [10 marks] b) Describe the two types of errors that we might have made. Provide some intuition for the probability of these errors and explain what happens to them as the true population proportion increases. [5 marks] c) Explain why/why not this proves whether there is gender discrimination in arrests. [5 marks]