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In a study, college students repeatedly played a version of the game "prisoner's dilemma," where competitors chose cooperation, defection, or costly punishment (Cooperation meant paying 1 unit for the opponent to receive 2 units, defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player. The accompanying scatterplots plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively. Complete parts a through d below. Click the icon to view the scatterplots. X Prisoner's Dilemma Scatterplots a. Q 1.2 T .. Q a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable increases. b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable decreases c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, there is no pattern to the value of the y-variable. 0.8 0.44 ✔ + H . 0- 20 40 60 80 Cooperation use d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative? The slope is negative. 2 -0.4 0 0.8 0.4- 0- -0.4- 0.8 0.4 0 . 20 40 60 80 Defection use 0- -0.4+ 0 10 15 20 Punishment use Q Q C Q a C

In a study, college students repeatedly played a version of the game "prisoner's dilemma," where competitors chose cooperation, defection, or costly punishment (Cooperation meant paying 1 unit for the opponent to receive 2 units, defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player. The accompanying scatterplots plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively. Complete parts a through d below. Click the icon to view the scatterplots. X Prisoner's Dilemma Scatterplots a. Q 1.2 T .. Q a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable increases. b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable decreases c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, there is no pattern to the value of the y-variable. 0.8 0.44 ✔ + H . 0- 20 40 60 80 Cooperation use d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative? The slope is negative. 2 -0.4 0 0.8 0.4- 0- -0.4- 0.8 0.4 0 . 20 40 60 80 Defection use 0- -0.4+ 0 10 15 20 Punishment use Q Q C Q a C

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 27PPS
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In a study, college students repeatedly played a version of the game "prisoner's dilemma," where competitors chose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for the opponent to receive 2 units, defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player. The accompanying scatterplots plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively. Complete parts a through d below. Click the icon to view the scatterplots. X Prisoner's Dilemma Scatterplots a. Q 1.27 ● ● Q 0.8- P a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable increases. b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable decreases. c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, there is no pattern to the value of the y-variable. 0.4- d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative? The slope is negative. b. C. Average payoff Average payoff Average payoff 0- -0.4- 0 0.8- 0.4- 0- -0.4- 0 0.8 0.44 0- -0.4+ ● ● " • ● T . · ● • ● 20 40 Cooperation use +8 60 80 . : ● ● 20 40 60 80 Defection use ● . 5 10 15 20 Punishment use Q G Q Q
Transcribed Image Text:In a study, college students repeatedly played a version of the game "prisoner's dilemma," where competitors chose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for the opponent to receive 2 units, defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player. The accompanying scatterplots plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively. Complete parts a through d below. Click the icon to view the scatterplots. X Prisoner's Dilemma Scatterplots a. Q 1.27 ● ● Q 0.8- P a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable increases. b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable decreases. c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, there is no pattern to the value of the y-variable. 0.4- d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative? The slope is negative. b. C. Average payoff Average payoff Average payoff 0- -0.4- 0 0.8- 0.4- 0- -0.4- 0 0.8 0.44 0- -0.4+ ● ● " • ● T . · ● • ● 20 40 Cooperation use +8 60 80 . : ● ● 20 40 60 80 Defection use ● . 5 10 15 20 Punishment use Q G Q Q
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