Reference no: EM133207581
Assignment:
1. I am interested in the course performance of people who attend office hours.
(a) Write out a mathematical expression for the average midterm grade that students who ever attend office hours would get if they never attended office hours.
(b) Suppose that people who ever attended office hours have an average midterm score of 70 and people who never attended office hours have an average midterm score of 50. Write this information in a single equation.
2. Your friend Pat weighed a few thousand people last week and also asked them about their personal habits over the prior year. Looking at the data, Pat found that people who dieted at some point in the prior year weighed more than people who did not.
(a) What are the three possible reasons for this correlation? How plausible is each possible reason?
(b) Think of dieting in the last year as a treatment and current weight as an outcome. Which do you think has a larger magnitude, the ATT or the selection bias? (Magnitude refers to the absolute value, such that 6 has a larger magnitude than 3 but the same magnitude as -6.).
3. The Binghamton school district is thinking of closing an afterschool program which serves 50% of Binghamton students. The average test score of students who attend the program is 85. If those students hadn't attended the program, their average test score would have been 70. The average test score of students who don't attend the program is 90. If they had attended the program, their average test score would have been 95.
(a) Think of attending the afterschool program as a treatment and test score as an outcome. What is the difference in means? What is the ATT? What is the selection bias?
(b) What is the ATE?
(c) Which treatment effect is more useful for the school district to know, ATT or ATE?
4. I am hosting a special retreat after the first midterm, in which students will be lavished with champagne, caviar, and detailed feedback on their exam performance. However, because these things are expensive, I cannot invite all the students in the class. I would like to know if participation in this exclusive retreat helps the course performance of the students who attend, so that I know whether to spend money on such retreats in the future.
I will use the following process for determining who will come on the retreat:
First, I will select half of the class by drawing names from a hat. Then, out of the set of students whose names were drawn, I will invite those students who have an overall GPA at Binghamton of at least 3.0. The retreat is lavish, so we can assume that all of the students who are invited will attend.
(a) What econometric method would you use to evaluate the effect of this retreat on final exam scores? What key assumption are you making, and why do you think it is reasonable? (You should write out the assumption in addition to naming it.)
(b) My department chair is looking at the results of the estimation you described in (a) to assess whether students with an overall GPA below 3.0 should also be invited. Which do you think would be a bigger concern, internal validity or external validity? Explain your answer in about two sentences.
5. Suppose that people who smoke zero cigarettes per day have a life expectancy of 80 years, and people who smoke have a life expectancy which is lower by 3 years for each cigarette per day that they smoke. (So, for example, people who smoke 3 cigarettes per day have a life expectancy of 79.1 years.) Express these facts in a single equation.
6. Suppose that the average IQ of college seniors is 111, the average IQ of juniors is 109, the average IQ of sophomores is 106, and the average IQ of freshmen is 102. Express these facts in a single equation using dummy variables. (Assume every college student is counted as a freshman, sophomore, junior, or senior.)
7. Which of the problems on this homework was the hardest for you?
8. Alice, Bob, and Confucius are bored during recess, so they decide to play a new game. Each of them puts a dollar in the pot, and each tosses a quarter. Alice wins if the coins land all heads or all tails. Bob wins if two heads and one tail land, and Confucius wins if one head and two tails land. The quarters are fair, and the winner receives a net payment of $2 ($3 - $1 = $2), and the losers lose their $1.
(a) What is the probability that Alice will win and the probability that she will lose?
(b) What is Alice's expected payoff?
(c) What is the probability that Confucius will win and the probability that he will lose?
(d) What is Confucius' expected payoff?
(e) Is this a zero-sum game? Please explain your answer.
9. In each of the following games, how many pure strategies (complete plans of action) are available to each player? List all of the pure strategies for each player.
