Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 10

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: 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 Y i =1 if the shot is made, and Y i = 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 H 0 : =.5 against H 1 : =.5 for Mark Price. Use a 1% significance level.