Problem 2. On February 20, 2017, 163 students took the first midterm exam in Econ 410. Let mid; be the midterm score of student i, which is between 0 and 100. Two problem sets were due before the midterm. Let pal; be a dummy variable, which is equal to 1 if student i turned in the first problem set (and 0 otherwise). Let ps2; be a dummy variable, which is equal to 1 if student i turned in the second problem set (and 0 otherwise). Using the model mid; Both , . psl; +8 2 . p$2; + U. yields the following (partial) Stata output: mid | Coef. Std. Err. t P>Itl [95%% Conf. Interval] ps1 / 8.29 3.763 2.20 0. 029 0. 914 15. 67 ps2 | 11. 06 3.847 2.87 0. 005 3.520 18.60 _cons | 51. 77 3.500 14.79 0.000 44.91 58. 63 (a) Interpret the estimated slope coefficients , = 11.06 in a causal manner. (b) Is6 2 economically significant? Explain. (c) Can you think of a potential omitted variable that would bias the result in part (a)? Explain. (d) AreB", or8 2 individually statistically significant at the 5% level? Explain. (e) If a student only had time to do one problem set, which problem set would you rec- ommend the student to do? Explain. (f) Let pssum; = pal; + ps2; . Regressing mid; on pssum; and ps2; yields mid | Coef. Std. Err. t P>It/ [95% Conf. Interval] pssum | 8. 29 3.763 2.20 0. 029 0.914 15. 67 ps2 | 2.77 6. 602 0. 42 0. 675 -10.17 15.71 cons | 51.77 3. 500 14.79 0.000 44.91 58. 63 Use these results to test the null hypothesis that doing either problem set 1 or doing problem set 2 has the same effect on the midterm score. Choose both the alternative and the significance level