The New York Times (2/5/90) reported three-point shooting performance for the top 10 three...

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 Yi =1 if the shot is made, and Yi = 0 if the shot is missed. Let θ denote the probability of making any particular three-point shot attempt. The natural estimator of θ is = FGM/FGA.

(i) Estimate θ 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: θ = .5 against H1: θ= .5 for Mark Price. Use a 1% significance level.