4. Consider the following example of men and womens salaries for a particular career, after one year of working at the career: Men: 55.38, 62.44. 74.46, 81.78, 82.71, 87.39, 93.33. 94.67, 96.44, 105.40 Women: 62.92, 69.02, 69.70, 70.71, 72.47, 82.24, 88.82. 91.64, 92.25, 118.54 The goal is to assess if there is a significant differences in men and womens salaries after one year. (a) State the null and alternative.(b) Calculate the Kolmogorov-Smirnov test-statistic. (c) Find the corresponding p-value, if the distribution of all possible permutations follows: k 0.1 0.2 0.3 0.4 0.5 P(KS, 2 k) 1 0.9945 0.7869 0.4175 0.1678 k 0.5 0.6 0.7 0.8 0.9 P(KS, 2 k) 0.1678 0.0524 0.0123 0.0021 0.0002 (d) State your conclusion in terms of the problem. (e) Give an intuitive explanation for the magnitude of the p-value (why is it so large/small)