Freelance reporter Irwin Fletcher is examining the historical voting records of members of the U.S. Congress. For 175 representatives, Irwin has collected the voting record (yes or no) on 16 pieces of legislation. To examine the relationship between representatives' votes on different issues, Irwin has conducted an association rules analysis with a minimum support of 40% and a minimum confidence of 90%.The data included the following bills:Budget: approve federal budget resolutionContras: aid for Nicaraguan contra rebelsEl_Salvador: aid to El SalvadorMissile: funding for M-X missile programPhysician: freeze physician feesReligious: equal access to all religious groups at schoolsSatellite: ban on anti-satellite weapons testing The following table shows the top five rules with respect to lift ratio. The table displays representatives' decisions in a "bill-vote" format. For example, "Contras-y" indicates that the representative voted yes on a bill to support the Nicaraguan Contra rebels and "Physician-n" indicates a no vote on a bill to freeze physician fees. AntecedentConsequentSupport for A and CConfidenceLift RatioContras-y, Physician-n, Satellite-yEl_Salvador-n0.400.951.98Contras-y, Missile-yEl_Salvador-n0.400.911.90Contras-y, Physician-nEl_Salvador-n0.440.911.90Missile-n, Religious-yEl_Salvador-y0.400.931.79Budget-y, Contras-y, Physician-nEl_Salvador-n0.410.901.89 (a)Interpret the lift ratio of the first rule in the table. The lift ratio of the first rule in the table means that it is % likely that a representative votes no on the El Salvador bill given that he or she votes yes on the Contras bill, no on the Physician bill, and yes on the Satellite bill than a randomly selected representative. (b)What is the probability that a representative votes no on El Salvador aid given that they vote yes to aid to Nicaraguan Contra rebels and yes to the M-X missile program? Round your answer to two decimal places. (c)What is the probability that a representative votes no on El Salvador aid given that they vote no to the M-X missile program and yes to equal access to religious groups in schools? Round your answer to two decimal places. (d)What is the probability that a randomly selected representative votes yes on El Salvador aid? Round your answer to three decimal places.

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Answered: Freelance reporter Irwin Fletcher is…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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Freelance reporter Irwin Fletcher is examining the historical voting records of members of the U.S. Congress. For 175 representatives, Irwin has collected the voting record (yes or no) on 16 pieces of legislation. To examine the relationship between representatives' votes on different issues, Irwin has conducted an association rules analysis with a minimum support of 40% and a minimum confidence of 90%.

The data included the following bills:

Budget: approve federal budget resolution
Contras: aid for Nicaraguan contra rebels
El_Salvador: aid to El Salvador
Missile: funding for M-X missile program
Physician: freeze physician fees
Religious: equal access to all religious groups at schools
Satellite: ban on anti-satellite weapons testing

The following table shows the top five rules with respect to lift ratio. The table displays representatives' decisions in a "bill-vote" format. For example, "Contras-y" indicates that the representative voted yes on a bill to support the Nicaraguan Contra rebels and "Physician-n" indicates a no vote on a bill to freeze physician fees.

Antecedent	Consequent	Support for A and C	Confidence	Lift Ratio
Contras-y, Physician-n, Satellite-y	El_Salvador-n	0.40	0.95	1.98
Contras-y, Missile-y	El_Salvador-n	0.40	0.91	1.90
Contras-y, Physician-n	El_Salvador-n	0.44	0.91	1.90
Missile-n, Religious-y	El_Salvador-y	0.40	0.93	1.79
Budget-y, Contras-y, Physician-n	El_Salvador-n	0.41	0.90	1.89

(a)	Interpret the lift ratio of the first rule in the table.
	The lift ratio of the first rule in the table means that it is % likely that a representative votes no on the El Salvador bill given that he or she votes yes on the Contras bill, no on the Physician bill, and yes on the Satellite bill than a randomly selected representative.

(b)	What is the probability that a representative votes no on El Salvador aid given that they vote yes to aid to Nicaraguan Contra rebels and yes to the M-X missile program? Round your answer to two decimal places.


(c)	What is the probability that a representative votes no on El Salvador aid given that they vote no to the M-X missile program and yes to equal access to religious groups in schools? Round your answer to two decimal places.


(d)	What is the probability that a randomly selected representative votes yes on El Salvador aid? Round your answer to three decimal places.

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