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The New York Times (2/5/90) reported three-point shooting performance for the top 10 three-point shoot- ers 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 Y, is the outcome of shot i, then Y, = 1 if the shot is made, and Y; = 0 if the shot is missed. Let 0 denote the probability of making any particular three-point shot attempt. The natural estimator of 0 is Y = FGM|FGA. (i) Estimate 0 for Mark Price. (ii) Find the standard deviation of the estimator Y in terms of 0 and the number of shot attempts, n. (iii) The asymptotic distribution of (Y – 0)/se(Y) is standard normal, where se(T) = VT(1 – Y)/n. Use this fact to test H,: 0 = .5 against H,: 0 < .5 for Mark Price. Use a 1% significance level.

The New York Times (2/5/90) reported three-point shooting performance for the top 10 three-point shoot- ers 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 Y, is the outcome of shot i, then Y, = 1 if the shot is made, and Y; = 0 if the shot is missed. Let 0 denote the probability of making any particular three-point shot attempt. The natural estimator of 0 is Y = FGM|FGA. (i) Estimate 0 for Mark Price. (ii) Find the standard deviation of the estimator Y in terms of 0 and the number of shot attempts, n. (iii) The asymptotic distribution of (Y – 0)/se(Y) is standard normal, where se(T) = VT(1 – Y)/n. Use this fact to test H,: 0 = .5 against H,: 0 < .5 for Mark Price. Use a 1% significance level.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 23PPS
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The New York Times (2/5/90) reported three-point shooting performance for the top 10 three-point shoot- ers 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 Y, is the outcome of shot i, then Y, = 1 if the shot is made, and Y; = 0 if the shot is missed. Let 0 denote the probability of making any particular three-point shot attempt. The natural estimator of 0 is Y = FGM|FGA. (i) Estimate 0 for Mark Price. (ii) Find the standard deviation of the estimator Y in terms of 0 and the number of shot attempts, n. (iii) The asymptotic distribution of (Y – 0)/se(Y) is standard normal, where se(T) = VT(1 – Y)/n. Use this fact to test H,: 0 = .5 against H,: 0 < .5 for Mark Price. Use a 1% significance level.
Transcribed Image Text:The New York Times (2/5/90) reported three-point shooting performance for the top 10 three-point shoot- ers 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 Y, is the outcome of shot i, then Y, = 1 if the shot is made, and Y; = 0 if the shot is missed. Let 0 denote the probability of making any particular three-point shot attempt. The natural estimator of 0 is Y = FGM|FGA. (i) Estimate 0 for Mark Price. (ii) Find the standard deviation of the estimator Y in terms of 0 and the number of shot attempts, n. (iii) The asymptotic distribution of (Y – 0)/se(Y) is standard normal, where se(T) = VT(1 – Y)/n. Use this fact to test H,: 0 = .5 against H,: 0 < .5 for Mark Price. Use a 1% significance level.
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