Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
1st Edition
ISBN: 9780321977274
Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher
Publisher: PEARSON
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Chapter 15.2, Problem 31E
To determine
The voter profile for 41 voters and 3 candidates g, j and e, so that j wins the first Borda election with the most Borda points, and where irrelevant alternatives criterion is violated after candidate e is deleted.
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The 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.…
2. Three friends decides whether to go to the night club on Friday night or not every week.
The data of several votings is presented in the table.
Andrey Bob Constantine | Final decision
1| yes
| 2 | no
3 no
4 yes
5 yes
yes yes
yes yes
yes
no
no
yes
no
no
no
no
yes no
yes
There is no more information about the voting system, the results of other polls are also unknown. Is their
rule: 1) anonymous, 2) neutral, 3) monotone? Explain your answer.
The 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.
Chapter 15 Solutions
Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by Alternative Methods For...Ch. 15.1 - Choosing a Poster Dog by Alternative MethodsFor...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...
Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Holding a Runoff Election One common solution to...Ch. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - The Pairwise Comparison Method Each table...Ch. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - The Borda Method Each table represents a Borda...Ch. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - The Coombs Method The Coombs method of voting is a...Ch. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Condorcet...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Irrelevant Alternatives in a Hare Method Election...Ch. 15.2 - 21. Explain why a violation of the majority...Ch. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Solve each problem.
5. New Trees for Wisconsin...Ch. 15.3 - Apportioning Computers to Schools Enrollments for...Ch. 15.3 - Assigning Faculty to Courses The English...Ch. 15.3 - 8. Apportioning Sailboats to Resorts The number of...Ch. 15.3 - Prob. 9ECh. 15.3 - 10. Show that the Webster method apportionment of...Ch. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Find the Huntington-Hill cutoff point for rounding...Ch. 15.3 - Creating a Profile of School Bus Riders Create a...Ch. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - The standard quotas rounded up to the nearest...Ch. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - 26. The Jefferson and Adams methods are both...Ch. 15 - How many different complete rankings are possible...Ch. 15 - Prob. 2TCh. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Why is the irrelevant alternatives criterion an...Ch. 15 - Prob. 7TCh. 15 - Prob. 8TCh. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - Prob. 12TCh. 15 - Prob. 13TCh. 15 - Prob. 14TCh. 15 - Prob. 15TCh. 15 - Prob. 16TCh. 15 - Prob. 17TCh. 15 - Prob. 18TCh. 15 - Prob. 19TCh. 15 - Prob. 20TCh. 15 - Prob. 21TCh. 15 - Prob. 22TCh. 15 - Prob. 23TCh. 15 - Prob. 24TCh. 15 - Prob. 25TCh. 15 - One hundred seats are to be apportioned to 4...Ch. 15 - Prob. 27TCh. 15 - Prob. 28TCh. 15 - Prob. 29TCh. 15 - Explain the Alabama paradox.Ch. 15 - Prob. 31TCh. 15 - Prob. 32T
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- A telecommunication company proposed construction of a cell site tower in a certain city. To determine whether this is to be constructed, a vote is to be taken among the residents of a city and the surrounding barangays. Many residents in the barangays feel that the proposal will pass because of the large proportion of city voters who favor the construction. A poll is taken to determine if there is a significant difference in the proportion of city voters and barangay voters favoring the proposal. If 250 of 400 city voters favor the proposal and 360 of 500 barangay residents favor it, would you agree that the proportion of city voters favoring the proposal is higher than the proportion of barangay voters? Use a 0.025 level of significance.arrow_forwardA county clerk wants to improve voter registration. He wants to send out reminders in the mail to all citizens in the county who are eligible to vote. To determine if it will actually improve voter registration, a random sample of 1250 potential voters was taken. No reminders were sent out to a group of 625 eligible voters and of those 625, 299 registered to vote. Reminders were sent out to another group of 625 voters and of those 348 registered to vote. The county clerk claims that the proportion of people who registered was significantly greater in the group that was sent the reminders. Using a 0.10 significance level, test the claim that the proportion of registered voters is higher in the group that received the reminders. What is the test statistic for this test? A county clerk wants to improve voter registration. He wants to send out reminders in the mail to all citizens in the county who are eligible to vote. To determine if it will actually improve voter registration, a…arrow_forwardAnswer the following questions for the voter profile shown to the right. Number of Voters Ranking 17 a >b>c> d >e (a) Which alternative is a majority candidate? (b) Which alternative is the Borda method winner? (c) Does the Borda method violate the majority criterion for the voter profile? 4 b>c>d>e > a 3 c>d>b> e>a 4 d>b>c> a >e 3. e >c>d> a > b (a) Which alternative is a majority candidate? e a There is no majority candidate. (b) Which alternative is the Borda method winner? e a b. O There is no Bordamethod winner. (c) Does the Borda method violate the majority criterion for the voter profile? Yes No O Time Remaining: 01:53:38 Next E O O O @ O 0 oarrow_forward
- An election is held among four candidates (A, B, C, and D). Using a voting method we will call X, the winner of the election is candidate A. However, candidate D has more than 50% of the possible votes. Based on this information, we can say that voting method X violates the O Condorcet criterion O monotonicity criterion. O independence of irrelevant alternatives criterion. O majority criterion.arrow_forwardConsider the weighted voting system [q: 13, 11, 10, 8, 4]. Assume that this system has no dictators and is not subject to gridlock. (a) What is the weight of the coalition formed by P,, P3, and P? (b) For what values of the quota q is the coalition formed by P,, Pa, and P, a winning coalition? (c) For what values of the quota q is the coalition formed by P,, P3, and Pa a losing coalition? (a) What is the weight of the coalition formed by P2, Pa, and P? The weight of the coalition (P2, P3, Pa) is. (b) For what values of the quota q is the coalition formed by P2, P3, and Pa a winning coalition? The coalition {P2, P3, Pa) is a winning coalition for all values of q from through . (c) For what values of the quota q is the coalition formed by P,, Pa, and P a losing coalition? The coalition {P2, P3, Pa) is a losing coalition for all values of q from through . MacBook Air F2 G00 F4 FS F9 @ #3 2$ % * 3 4 8 9. Q Y A S D K V alt option command comm ర Narrow_forwardWhy is it impossible, with an odd number of voters, to have two distinct candidates win the same election using Condorcet's method.arrow_forward
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