# Economics of Sports

Assignment Instructions

Problem Set 1

Ec 370                                                                                                                                                    Summer, 2012
Michigan State University                                                                                                            L. Martin

In their paper on peer effect in golf, Guryan, Kroft and Nodowidigdo investigate whether a player’s score is lower if his playing partners are better golfers. Ability is measured by the average score per round over the season. Other influences on score are controlled using fixed effects. (Don’t worry about this term – we will study it later.) Standard errors appear in parentheses below the coefficient estimate. The data involve scores from rounds played during several Professional Golf Association seasons. The paper is here:

http://www.nber.org/papers/w13422.pdf

You should not have to read the paper to answer this question.

Consider this regression table from their paper.

Consider the first regression (left hand column).

What is the dependent variable?                                                                    _____________
What is the hypothesis being tested?
Which variable captures the hypothesis?                    ___________
What is its coefficient?                                                                                               ____________
What does the coefficient mean?
Is it significant at the 5% level?                                                                                  ____________
What does this mean?
Would you say that there is good evidence for peer effects? Explain.

i. Is the coefficient on own ability significant at the 5% level?                               ______________

j. What type of variable is this?                                                                                           ______________

k. What does this estimate mean (in English)?
2. Bobo, who is from Ghana, likes to wrestle. He wrestles on Tuesday and Friday. (By the way, his name means, “born on Tuesday.”)   The following table gives his results this year on the two days.

Tuesday                               Thursday

Win                        20                                           15

Lose                       8                                              13

He wants to know if he wrestles better on Tuesday. What statistical test should he use?

_____________

What is the hypothesis to be tested?

c. What is the null hypothesis?

d.   He performs the test that you recommend and finds a p-value = 0.167. Interpret this number.

e. What is learned from this test? Explain.
3. Fred, like all normal people, loves to bowl. He never has an open frame. That is, each frame is either a strike (x) or a spare (/). Strikes are better. Here is his data.

xxx/xxx/////xxxx////x

What is the conditional probability of a strike in the frame following a strike?

_________

How many runs for Fred?                                                                              __________

The runs test for this data gives the following.

Expected Number of Runs: 11.5; sd: 2.2279
z-value= -2.0091

Explain the results of this test.   Does it show evidence of the hot hand?

Draw a nice picture of the distribution of runs and show the actual value, the z-statistic.

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