Instruction: Write your solutions on loose-leaf paper or a note-taking app, then scan or print to a PDF file and upload it here. Your solutions must show all related work. A random sub-sample of size n = 80 individuals is selected from the 2018 American Community Survey 1-year estimate for Puerto Rico. The personal income during the last 12 months are summarized below for males and females. Sample standard Group Sample size Sample mean deviation Male 34 16015 18077 Female 46 15053 29544 a) (4 pts) State the null and alternative hypotheses of a one-sided significance test to test that in Puerto Rico, the population mean of incomes for males is greater than that for females. b) (4 pts) Calculate the test statistic. c) (6 pts) Show how to make a conclusion for the test, using the significance level a = 0.05. Interpret your conclusion in the context of this problem. d) (6 pts) Find a 95% confidence interval for the difference between the population means of incomes for males and females in Puerto Rico. e) (4 pts) Interpret the confidence interval in part d in context