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Find the Banzhaf power distribution of a weighted voting system with four players in which the winning coalitions (with critical players underlined) are
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Chapter 2 Solutions
MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
- Find the Banzhaf power distribution of the weighted voting system[27: 17, 14, 10, 2]Give each player's power as a fraction or decimal valueP1P1 = P2P2 = P3P3 = P4P4 =arrow_forwardFor the weighted voting system, {160: 100, 90, 60, 50, 10}, what is the BPI of player A? (3 decimal places)arrow_forwardThe U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is registered to vote. Suppose that 713 employed persons and 613 unemployed persons are independently and randomly selected and that 338 of the employed persons and 244 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2 ), who have registered to vote? Use a significance level of α=0.1 for the test. Step 1 of 6 : State the null and alternative hypotheses for the test. Step 2 of 6 : Find the values of the two sample proportions, pˆ1p^1 and pˆ2p^2. Round your answers to three decimal places. Step 3 of 6 : Compute the weighted estimate of p, p‾p‾. Round your answer to three decimal places. Step 4 of 6 : Compute the value of the test statistic. Round your answer to two decimal places.…arrow_forward
- Find the Banzhaf power distribution of a weighted voting system with five players in which the winning coalitions (with critical players underlined) are as follows. {P1,P2,P3}, {P1,P2,P4}, {P1,P2,P3,P4}, {P1,P2,P3,P5}, {P1,P2,P4,P5}, {P1,P3,P4,P5}, {P1,P2,P3,P4,P5} ..... Find the Banzhaf power distribution for this system. B2 B3 =, B4 B1 (Type integers or fractions.)arrow_forwardA lecturer wishes to study the examination results of students from the Faculty of Computer Science which consists of 30 classes. He intends to choose only eight classes and all the students from these eight classes will be selected (a) State the population for this study. (b) State the variable and its type for this study. (c) State the sampling technique used for this staarrow_forwardThe U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is registered to vote. Suppose that578 employed persons and 492 unemployed persons are independently and randomly selected, and that261 of the employed persons and 194 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2 ), who have registered to vote? Use a significance level of α=0.1 for the test. Step 5 of 6 : Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to two decimal places.arrow_forward
- A company wished to study the differences among four sales-training programs on the sales abilities of their sales personnel. Thirty-two people were randomly divided into four groups of equal size and the groups were then subjected to different sales-training programs. Because there were some dropouts due to illness during the training program the number of trainees completing the programs varied from group to group. At the end of the training programs, each salesperson was randomly assigned a sales area from a group of sales areas that were judged to have equivalent sales potentials. The numbers of sales made by each of the four groups of sales people during the first week after completing the training program are listed in the table.arrow_forwardFind the Banzhaf power distribution of a weighted voting system with five players in which the winning coalitions (with critical players underlined) are as follows. {P.P2.P3), (P1,P2 P4), (P,.P2.P3.Pa), {P1,P2.P3.Ps), (P1.P2.PA.Ps), (P1,P3.PA.Ps). (P,.P2.P3.P4.Ps) Find the Banzhaf power distribution for this system. (Type integers or fractions.) MacBook Air D00 FB esc F2 F3 F4 & * 4 7 8 9. P 96 # 3arrow_forwardAmong the workers in a factory only 50% receive bonus. Among those receiving the bonus 30% are skilled. What is the pre bability of a randomly selected worker who is skilled and receiving bonus.arrow_forward
- Consider the weighted voting system [15: 14, 6, 4, 1]In the sequential coalition <P1,P2,P3,P4P1,P2,P3,P4 > which player is pivotal?Pivotal player =arrow_forwardA housewife is testing the cutting speeds of 4 brands of knives she has at home. She chose 5 cutting materials of varying degree at home. Each material was cut once by each one of the 4 knives. (Hence after all 4 cuts the material was cut into 5 pieces). Is this a randomized block design or two factor design? If random block design, what is used as the block? If two factor design, what are the two factors in the study? State the null and alternative hypotheses. Here is the output table for ANOVA test with missing values. Fill in the missing values (where the cells are underlined) Source df SS MS F Knife 310 Material 46 Error 12 24 What is the F statistic for the test? Will you reject or fail to reject (at alpha=0.05)? What is the sum square of total?arrow_forwardA study was conducted to determine smartphone users' preferences for three popular brands: Samsung, Apple and Xiomi. A total of 570 respondents were taken randomly (170 Samsung users, 205 Apple users, 195 Xiaomi users) and asked whether they were likely to buy the same brand smartphone in the near future or switch to another brand. The survey results are shown in the following table: Repurchase samsung: 110 apple: 120 xiaomi: 135 Switch samsung: 60 apple: 85 xiaomi: 60 a. Make a hypothesis that aims to answer the problem above! b. Use a = 5% to test the hypothesis using the critical value approacharrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
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