our research team was interested in looking at the impact of providing students a tutor. These tutors work with students who are preparing for the SAT. You recruited 200 students with 100 students randomly assigned to the treatment and control group each. Students in the treatment group receive a tutor for the preparation. Six months later, you found that the average SAT scores are 1150 among students in the treatment group and 1100 for the control group. The standard deviation of the test scores is 200 in both groups. Note: For this question, please use the formulas that we learned in class and do the calculations yourself instead of using the software (with the exception of referencing the t- distribution). Show all your work. It is okay if your answers are not round numbers. For all the following questions, use t0.8 = 0.84 and t0.025 = 1.96. [34 TOTAL POINTS] a. Calculate the difference-in-means estimate of ATE, . [2 points] b. Find the estimated standard error for . [3 points] c. In this part, you would perform a two-tailed test at 5% significance level with the null hypothesis H0 : = 0. i. Find the t-statistics. [3