ECO 321 Fall 2021 Homework 2 Due September 17 by 5 pm Cut and paste at the end of your submission the R code you have used to show your work. 1. On Blackboard under the Homework2 folder, you can find a zip file CPS08.zip which contains a database CPS08.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 file CPS08 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 u1 and u0 respectively. Write down the estimators for u1 and u0 respectively. (b) 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− α confidence interval for u1 − u0. (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% significance level based on the p-value? (f) Use R to compute the 95% confidence interval for u1 − u0. 1