PROBLEM 3: JUDICIAL EMPATHY (60 pts. total) Do judges exhibit empathetic feelings that might be based on personal relationships? Specically, might a judge's personal relationships affect judicial decision making? A study team decided to investigate this question in the specic context of one type of personal relationship: having daughters. The team collected data on 224 judges on the United States Courts of Appeals and their rulings on 990 genderrelated cases. These cases involved discrimination against women or women's rights, such as cases about reproductive rights or employment discrimination on the basis of pregnancy. A judge was considered to have made a feminist decision in a case if they voted in favor of the plaintiff representing women's interests. The study team also collected data on the number of biological children for each judge, and the sex of each child. Oher attributes were also collected, such as religion and year of birth. Note that the party of the president who appointed a judge can be used as a proxy for the judge's political party. Data from the study are in the le judges . Rdata. The following table provides a list of the vari ables in the dataset and their descriptions. Variable Description name name ci rcuit federal circuit court the judge serves in, of the 13 circuits chi 1d ren total number of biological children daughters total number of biological daughters sons total number of biological sons sex sex of the judge, either Female or Male year. born year of birth religion religious afliation republican recorded as 'I if appointed by a Republican president, and 0 if by a Democrat vote. prop proportion of feministleaning votes in gender-related cases Use these data to answer the following questions. a) (12 pts.) Explore the variables sex and republican. i. Describe the distribution of sex, referencing appropriate numerical summaries. Do the same for the distribution of republican. ii. How much more likely is a female judge to have been appointed by a Democrat presi dent than a Republican president? b) (8 pts.) Explore the variable vote . prop. i. Describe the distribution of proportion of feministleaning votes in genderrelated cases, referencing appropriate numerical and graphical summaries. ii. Are judges observed to have vote proportions close to 1 necessarily more likely to make feminist decisions in future genderrelated cases than those observed to have vote pro portions closer to 0.50? Explain your answer. c) (10 pts.) Create a single informative plot that illustrates the difference in voting behavior in genderrelated cases between Republican male judges, Republican female judges, Democrat male judges, and Democrat female judges. Summarize your ndings. Be sure to address whether the data suggest political party, sex, or both are related to progressive voting be- havior