1. Calculate the Banzhaf Power Distribution In a sports team selection committee, the voting weights are distributed as follows: • Team Captain (P1): 5 votes • Head Coach (P2): 3 votes • Assistant Coach (P3): 2 votes • Medical Staff Representative (P4): 1 vote The total number of votes is 11, and a simple majority of 6 votes is required to approve a new player signing. This can be represented as the weighted voting system [6: 5, 3, 2, 1].
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- The librarian at a public library wants to determine what proportion of the library users are children. The librarianhas a tally sheet on which she marks whether books are checked out by an adult or a child. She records this datafor every fourth patron who checks out books.e. A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate,the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone oris available to come to the phone, that registered voter is asked whom he or she intends to vote for and whetherthe debate changed his or her opinion of the candidates.The committee on scholarship had ranked three (3) students vying for scholarship sponsored by a certain organization. Name of Students Ranking John Johnson. 1 3. 1 3 Mary Smith 3 1 Joseph Khan Number of votes 25 30 21 Use the Borda Count method to determine the total points earned of the winner of the grant.2. Six candidates, Sophia, Mark, John, Jenny, Mike and Sky were nominated for Chairman position in an organization. After the polls close, ranked ballots were tallied, and the results are summarized below. a. What percent of the votes did the winner receive? b. Determine the winner using plurality with elimination, Borda Count and pairwise comparative methods of voting. Rankings Sophia 16325 Mark 65633 John 34516 Jenny 52444 Mike 23162 Sky 41251 Number of Votes 28 12 25 30 25
- The General Social Survey (GSS) is an opinion survey that has been conducted for more than 30 years by the National Opinion Research Center at the University of Chicago. About 2000 adult Americans are given a 90-minute interview asking about opinions and behaviors for a wide variety of issues. To access the GSS website, go to sda.berkeley.edu/GSS using No Weight as the default weight selection. 1. Americans were asked: Is it the government's responsibility to impose strict laws to make industry do less damage to the environment? Results from both 1996 and 2006 can be found in the GSS. Type GRNLAWS in Row: and YEAR in Column: then Run the table. a) Use StatCrunch and the 2006 data to create a 90% confidence interval for the true proportion of all Americans answering 'definitely should be' to this question. Include a check of the necessary conditions in your answer. Copy and paste the output from StatCrunch. Interpret your interval in context. b) c) Can you conclude whether a majority of…The city of Raleigh has 7400 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 550 randomly selected registered voters was conducted. 232 said they'd vote for Brown, 288 said they'd vote for Feliz, and 30 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: Divide the number who said they would vote for Brown by the sample size. The proportion should be a fraction or decimal to 4 places, not a percent.Suppose a state has 10 representatives and a population of 14 million; party affiliations are 40% Republican and 60% Democrat. a. If districts were drawn randomly, what would be the most likely distribution of House seats? b.lf the districts could be drawn without restriction (unlimited gerrymandering), what would be the maximum and minimum number of Republican representatives who could be sent to Congress? a. What would be the most likely distribution of House seats? Republicans, Democrats Wen b. The maximum number of Republicans representatives could be The minimum number of Republicans representatives could be
- The Dean, Mr.Gregor is interested in the overall performance of the students in the academic year 2020/2021. There were 1460 students registered for this academic year. The Dean decides to select a sample of 150 students from each of the 5 faculties- Science, Medicine, Law, Social Science and Humanities in proportion to the number of students in each faculty. a) Identify the population of interest for this scenario. b) Identify the sampling technique used by the researcher. c) State one advantage and one disadvantage of the sampling technique described in the given scenario. d) If the medical faculty has 584 students registered, calculate how many medical students would be part of the sample of 150.10The members of campus club are having a cleanup drive.There are three departments who will participate theactivity: BSAB, BSPA, and BSCD. The members areasked to rank these choices in order of preference (table). f. Use Borda Count method to determine the winner.g. How many points did the winner in letter (f) receive?
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