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:

For a given player, the outcome of a particular shot can be modeled as a Bernoulli (zero-one) variable: if Y_i 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 θ denote the probability of making any particular three-point shot attempt. The natural estimator of θ is Y̅ = FGM/FGA.

(i) Estimate u for Mark Price.

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

(iii) The asymptotic distribution of (Y̅ - θ)/se(Y̅) is standard normal, where se(Y̅) = √Y̅(1 – Y̅)/n.

Use this fact to test H₀: θ = .5 against H₁: θ < .5 for Mark Price. Use a 1% significance level.

Transcribed Image Text:

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