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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A statistics student wants to determine if a quiet room is a better study environment for students than a noisy environment. 151 students were recruited for an experiment. 75 students were randomly assigned to a quiet study environment while the other 76 were assigned to a noisy environment. Students in each group were given a short booklet from which to study and then were given a brief multiple- choice test. 52 of the students who studied in the quiet study environment passed the test, compared to 43 students who were in the noisy environment. Let Pi = the true proportion of all students like these who study in a quiet environment and pass the test and P2 = the true proportion of all students like these who study in a noisy environment and pass the test. Which of the following are correct for conducting a significance test of P1 – P2? 1. Но: Р1 — Р2 — 0 II. Ha: P1 – P2 + 0 II. Both the Random and Large Counts conditions are met.
11) 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. Due to an irregularity in the original vote count, a recount is required. Before the recount takes place, candidate B drops out of the race. In the recount, still using voting method X, candidate D wins the election. Based on this information, which criterion can say that voting method X violates? A) IIA B) majority C) monotonicity D) Condorcet
Suppose that Fiona likes cashews better than almonds and likes almonds better than walnuts. She likes pecans equally well as hazelnuts and prefers hazelnuts to almonds.Can we characterize Fiona’s preferences of being “complete”? Can we characterize them of being “transitive”? Justify your answer
6) For a certain election with 5 candidates, Sequential Pairwise found candidate D to be the winner when the agenda was: D, B, C, A, E. If the agenda was changed to: C, B, E, D, A, who would be the winner?
Suppose that the Borda count method is used on the following preference table. If B drops out, is the irrelevant alternatives criterion satisfied? Explain. Choose the correct answer below. OA. No; C wins by the Borda count method. If B drops out, A wins. OB. Yes; A wins by the Borda count method. If B drops out, A still wins. OC. Yes; C wins by the Borda count method. If B drops out, C still wins. OD. No; A wins by the Borda count method. If B drops out, C wins. C TUBA 3BAC B GAC6 Number of votes 9 8 7 First Second Third
If you and another person are using the divide-and-choose procedure to divide something between you, would you rather be the divider or the chooser? (Assume that neither of you knows anything about the preferences of the other.)
Tayshia is participating in an experiment on intergroup attitudes. At the beginning of the experiment, the experimenter flips a coin to assign Tayshia to Group A or Group B. According to the research on the minimal groups paradigm, will Tayshia show a preference people in the same group? -Yes, because Group A and Group B are meaningful groups competing for resources. -Yes, because even arbitrary groups can elicit intergroup bias. -No, because groups must have a history of violence and oppression to produce intergroup bias. -No, because Tayshia realizes that the groups are completely random.
A weighted voting system is given by [q : 5, 2, 2], where the voters are A, B, and C. List all the possible values of q satisfying the quota restriction. For each of these values of q, determine the voters that have veto power.
Suppose you have populations of 7000, 5000, 1000 in 3 states and n representatives are to be allocated using Hamilton's method. There is an Alabama paradox from n=6 to n=7. Please find a second pair (n,n+1) where a paradox is observed.
Consider an election with three candidates with the following results: (ACB) 2, (BAC) 5, (CBA) 4, (CAB) 2. a) Is there a Majority winner? If not who is the Plurality winner. b) who wins using the Borda count method? c) Who wins if he or she first eliminates the one with the most Las place votes and then has a runoff between the other two?
Consider 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 N

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Please solve fast Use the following preference schedule to show that the Plurality method violates the Condorcet criterion.