1. 0n Blackboard under the Homework2 folder, you can nd a zip le CPSDS.zip which contains a database CPSOS.csv for full-time, full-year workers age 25-34, with a high school diploma or B.A./B.S. as their highest degree. A detailed description is given in the pdf le CPS|08_Description. In this exercise, you will investigate the the relationship between a worker's education (BACHELOR) and average hourly earnings (AHE). BACHELOR takes value 1 if the individual has a bachelor degree and 0 otherwise. (a) Assume both the wage distribution of people with a bachelor degree and the wage distribution of people without a bachelor degree follow normal distribution and having mean 11.1 and Hg respectively. Write down the estimators for 1:31 and 11.9 respectively. (1)) Write down the (null and alternative) hypotheses that difference between the average wages of people with a bachelor degree and people without a bachelor degree is zero. Then write down test statistic for the hypothesis test(Assume the variances of the two groups are not equal) and the p-value for the test. (c) Construct a 1 o: condence interval for n11 an. (d) Use R to compute the sample mean and sample variance of AHE for individuals with a bachelor degree and for individuals without a bachelor degree. (e) Use R to compute the test statistic and p-value. Will you reject the null hy- pothesis at the 5% signicance level based on the pvalue? (f) Use R to compute the 95% condence interval for n11 no