Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 8

The New York Times (2/5/90) reported three-point shooting performance for the top 10 three-point shooters in the NBA. The following table summarizes these data:

Player	FGA-FGM
Mark Price	429-188
Trent Tucker	833-345
Dale Ellis	1,149-472
Craig Hodges	1,016-396
Danny Ainge	1,051-406
Byron Scott	676-260
Reggie Miller	416-159
Larry Bird	1,206-455
Jon Sundvold	440-166
Brian Taylor	417-157

Note: FGA = field goals attempted and FGM = field goals made.

For a given player, the outcome of a particular shot can be modeled as a Bernoulli (zero-one) variable: if Yi is the outcome of shot i, then Yi =1 if the shot is made, and Yi = 0 if the shot is missed. Let ? denote the probability of making any particular three-point shot attempt. The natural estimator of ? is = FGM/FGA.

(i) Estimate ? for Mark Price.

(ii) Find the standard deviation of the estimator in terms of and the number of shot attempts, n.

(iii) The asymptotic distribution of (-)/se()is standard normal, where se() = . Use this fact to test H0: ? = .5 against H1: ?= .5 for Mark Price. Use a 1% significance level.

Step 1 of 3

(i)

The natural estimator ? is defined as. For Mark Price, the value of FGM is 188 and the value of FGA is 429. Therefore,

The estimate ? for mark price is.