INSTRUCTIONS: Answer all questions in the spaces provided (or indicate clearly where you have continued your answer). [NOTE:  Ample space was provided in the hardcopy version of the exam.]  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. All parts of both questions are worth 10 points (and some are much easier than others). Total points = 150. This means roughly 5 minutes for each answer. Budget your time carefully. NOTE: these data are fictitious.

1. Imagine that you are in charge of head office personnel at Huge Corp. The corporate vice president keeps getting other people's mail by mistake, so she tasks you to conduct a study of mailroom productivity. Fortunately, the mailroom supervisor has, for years, been sampling productivity during his monthly employee reviews. For a random sample of 27 reviews (all from different employees) he provides you with data on productivity (prod_i = letters correctly sorted per minute), and experience (months_i = months of experience in the Huge Corp. mailroom). You match these data to other information about each employee (score_i = score on the aptitude test they were required to take when they applied for a position at Huge Corp.). The statistical analyses you perform are given in Exhibit A.

a.) Fill in the blanks:

Across these 27 employees, what is the mean number of months on the job? ______
What is the maximum score on the aptitude test? ________
What is the standard deviation in productivity? ________
Do the descriptive statistics you have just provided refer to the joint distribution of these three variables, or to their marginal distributions? ______________
What is the correlation between score and months in this sample? ________
What are the units for this correlation measure? ________

b.) Using the STAT output, test the hypothesis that the true marginal mean value of productivity in the population of all mailroom workers is 11 letters per minute.

c.) The vice-president of Huge Corp. asks you (not rhetorically): "Don't these mailroom people ever learn?" Translate this question into a simple regression specification and test an appropriate hypothesis statistically, using the information in Exhibit A.

d.) How is it that we can argue that a "t-test" statistic, if the null hypothesis is true, has a t-distribution?

e.) What productivity would you expect from a new hire, based on Regression 2? Give a point estimate and explain explicitly how a 95% confidence interval for this prediction would be constructed.

f.) Now you realize that cognitive skills and manual dexterity may also affect productivity and account for differences across employees. You include aptitude scores in the regression and obtain the results in Regression 3. What does this alternative specification suggest about "learning-by-doing" in the mailroom? Is there any statistical evidence that experience affects productivity? Conduct an appropriate hypothesis test.

g.) Observe the STAT output. Statistically, what accounts for the difference between the implications of Regressions 2 and 3 regarding the effect of experience on productivity?

h.) Can you give a logical intuitive explanation for the process that leads to the relationship between months_i and score_i that is revealed in the STAT output?

i.) If a new employee scores 75% on his aptitude test, what should mailroom management expect in terms of productivity at his 2-month review?

j.) In these specifications, what fraction of the variation in productivity across employees can be explained by a model that uses only months of experience? _______ What fraction can be explained by a model that uses both experience and aptitude test scores? ______ Can these be compared? Why or why not?

k.) On any give shift, the mailroom is staffed by three people. The mailroom supervisor observes that productivity of any particular mailroom worker seems to depend on how hard the other people in the mailroom are working. What data would you collect, what variable(s) would you construct and what model would you estimate in order to test a statistical hypothesis that would show whether there is any evidence to support the supervisor's conjecture?
 

2. You have always wanted to start your own business, and the specialty coffee-bar business appeals to you. You have a friend at the Association of Specialty Coffee Retailers who manages to get you data on the average costs of different establishments. The technology is virtually identical across firms. You have data on 21 firms, for atc_i = average total costs of production and for q_i the rate of output (in cups per hour). Exhibit B shows the analyses you perform.

a.) - What is the interpretation of the intercept in this model? Is it "meaningful"? Explain.
- By how much do average costs change if output is higher by 1 unit?
- By how much do average costs change if output is lower by 10 units?

b.) Are all firms in your sample experiencing "increasing returns to scale" (declining average costs)? Answer carefully.

c.) Suppose you plan to open a shop that will operate at 80 cups per hour. What do you expect will be your average total costs? What is the 95% confidence interval for these average costs?

d.) Suppose that in the market area where you plan to open your shop, perfect competition prevails and you can be certain that your price per unit for a cup of coffee will be exactly $0.70. Is it statistically likely that you will make some positive profit?

e.) (BONUS) Given what you know about average total costs (from Economics 1 or the equivalent), is the regression you have specified likely to be appropriate to capture the shape of a typical average total cost function? Explain why or why not. Do you have enough information to determine the profit-maximizing level of output to produce?