Economics 143 - Sample Midterm


Questions below refer to associated computer output.

INSTRUCTIONS: [On actual exam] Answer all questions in the space provided (or indicate clearly where you have continued your answer). Calculators are NOT permitted. Reduce all computations to the simplest form so that anyone with a calculator could attain the answer easily. Show your work and reasoning to the fullest extent possible so that part marks can be assigned as warranted. You have 75 minutes to complete this exam. Each question is worth 5 points. Total points = 75. Budget your time carefully. Exhibit pages should not be turned in with your exam.
SCENARIO:
Suppose you have been pondering the habits of college students when it comes to spending money on their social lives (broadly defined). You are most interested in knowing how typical weekly social expenditures (SPEND) vary with the number of hours that the student works per week (WORK) and/or with the typical number of dollars per week (OTHER) that the student's family sends to "help out." To begin your study, you start with a group of 13 students from middle-class families.
  1. According to the descriptive statistics in EXHIBIT A, what is the marginal mean weekly expenditure for students in this group? _____________ What is the standard deviation in hours worked per week? _____________ What is the range in the amount of other family financial support? ____________ What is the correlation between hours worked and family financial support?_____________ Precisely what formula would you use to calculate the covariance between social spending and family financial support?
  2. You regress SPEND on WORK for this group of 13 students. You wish to use this regression to determine whether work hours have any systematic effect on the amount spent on one's social life. Give a precise statement of the hypothesis test you would propose to address this question: H0:____________ By the results in Regression A1, is your hypothesis rejected or not rejected? Explain how you came to this conclusion.
  3. "Nonworking students have no social lives (at least no social lives that involve spending any money)." Formulate this assertion into an hypothesis about one of the estimated quantities in Regression A1:
  4. Test this assertion using the results in Regression A1. (Explain how you reached your conclusion.)
  5. Is there anything about your hypothesis test in question 3 that would lead you to qualify the conclusion? (HINT: think about the interpretation of the parameter you are asking about; keep in mind the descriptive statistics for this sample.)
  6. Now, in addition to WORK, you include family financial support (OTHER) in your model in Regression A2. What does this model imply regarding the average effect of an additional hour of work on the amount of spending on a student's social life, and how do this model's implications differ from those of Regression A1? Explain WHY the estimated coefficient on WORK was different in Regression A1.
  7. What is the interpretation of the intercept in Regression A2. Test the hypothesis that this intercept is zero. Explain your results.
  8. One classmate's mother has been overheard to complain that "students nowadays just squander on entertainment all the money you send them to help out with their educations." Translate this assertion into a statistical hypothesis and write down the formula that would be used in a t-test of this hypothesis (plug sample values into the general formula).
  9. Another classmate's mother would disagree. She thinks "students squander on their social lives only half of the money you send them to help with their educations." Translate this assertion into a statistical hypothesis and write down the formula that would be used in a t-test of this hypothesis (again, plug sample values into the general formula).
  10. To precisely what "population" would you ascribe the results from the regression models in EXHIBIT A?
SCENARIO
Now you become concerned that your small middle-class sample of students is not representative of all students. To get a more representative sample of students, you survey an additional nineteen students from other types of backgrounds and family circumstances. Pooling all of these data yields a sample of 32 students. Analysis of these data appears in EXHIBIT B.
  1. Ordinarily, a larger sample would tend to increase the precision with which you can estimate a particular regression slope parameter. Why?
  2. What happens in Regression B1, as opposed to its counterpart Regression A1? (HINT: refer to the descriptive statistics for the smaller and larger samples in your answer.)
  3. According to Regression B2, is an additional hour of work each week associated, on average, with greater spending on one's social life? Explain.
  4. According to Regression B2, do students tend to "waste half of every dollar they get from home" on their social lives? Explain.
  5. In Regression B2, what proportion of the variation in SPEND is explained by WORK and OTHER? How does this compare to the proportion of the variation in SPEND that could be explained by WORK alone in Regression B1?
  6. What is the effect on SPEND of a one-standard-deviation change in WORK? of a one-standard-deviation change in OTHER? (Be sure to give units.)
  7. The results in Regression B2 in EXHIBIT B are now free from "omitted variables bias" when it comes to assessing the average effect of work hours on the amount spent on one's social life. True, False, Uncertain? Explain.
  8. OPTIONAL: Potential 5 points extra credit)
    a.) There isn't much "theory" motivating the regression specifications explored so far. What are your "priors" concerning the signs of the coefficients in a regression of SPEND on WORK and OTHER? Explain.
    b.) Among other things, some implicit maintained hypotheses in the above analysis include that:
    - i.) the derivatives of SPEND with respect to WORK and OTHER are constant (i.e. each has the same value no matter where in (WORK,OTHER)-space you calculate it);
    - ii.) the effect of an extra dollar of OTHER does not depend upon WORK;
    - iii.) WORK decisions are made independently of preferences for spending money on one's social life;...
    Comment on these maintained hypotheses. Are they likely to be met in this sample?
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