Consider the following preferences: Consider the following preferences: X = [0, 1] × [0, 1] and (x₁, x₂) ≥ (y₁, Y2) if either x₁ > Y₁ orX1x₁ = y₁ and x2 ≥ y2. These preferences are called lexicographic, because they work similarto the alphabetical order.(a) Show that this preference relation is complete and transitive but it does not have anumerical representation.(b) Is this preference monotone? continuous? convex?

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Answered: onsider the following preferences: X =…

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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The Women’s Institutional Studies group at a Midwestern university wanted to compare the percentages of female faculty members in the various units on campus in Spring 2004. Of particular interest were the percentages of female faculty in the College of Education and in the College of Business . In a sample of 80 College of Education faculties, there were 36 females, and in a sample of 70 College of Business faculties, there were 15 females. Based upon this sample information, which of the following is the 98% confidence interval for the difference in the actual percentages of female faculty between College of Education and College of Business ? a. (0.075, 0.405). b. (0.123, 0.357). c. (-0.012, 0.252). d. (0.058, 0.422). e. (0.101, 0.379).
A charity is trying to raise money by hosting a comedy club with a famous comedian. In order to maximize donations they want to bring in the best comedian, if there is one. By surveying 100 of their target donors, they find the following preferences: Comedian Zach Galifianakis Maria Bamford Patton Oswalt Brian Posehn Number of Preferences 11 44 23 22 They are trying to determine who (if anyone) should be invited. Which statistical test(s) are appropriate for this problem? (Select all that apply) Single-mean Z-test Single-mean t-test Single-proportion Z-test Chi-square test for goodness of fit Two-mean Z-test Two-mean t-test None of the above
Given the following preference table, the Condorcet winner is? Kindly refer to the image attached.
A group of seniors decide to spend their spring break away from home, attending at least one major event. The following table summarizes their preferences. Stay in state Travel out of state 86.89% 64.63% 54.73% Attend a concert 46% 214 391 What percent want to attend a concert, given that they want to travel out of state? Attend a festival 186 59
The bookstore at IRSC would like to estimate the proportion of students who prefer electronic textbooks (eBooks) over printed textbooks (hard copies). A random sample of 30 students was surveyed. Their preferences are listed below. hard copy hard copy hard copy hard copy eBook hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy hard copy eBook eBookeBook hard copy hard copy hard copy hard copy hard copyhard copy hard copy Determine the point estimate, and the sample standard deviation, hat p; s hat p Round the sample proportion to four decimal places and round the standard deviation to six decimal places, if necessary hat p = Box; s_{p} = Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the proportion of all students at the college who work prefer eBooks over printed textbooksReport the confidence interval using interval notationReport the solutions in…
The following table shows the cumulative frequency distribution of the preferred length of kitchen slabs obtained from the preference study on housewives. Length (in meters) more than 1.0 1.5 2.0 2.5 3.0 3.5Housewives 50 48 42 40 10 5 A manufacturer has to take a decision on what length of slabs to manufacture. What length would you recommend?
QUESTION 9 A group of 12 students have to decide among three types of pizza: sausage (S), mushroom (M), and beef (B). Their preference rankings are shown below. Is there a Condorcet winner among the pizza types? Number of students 3 3 2 2 2 First choice B M S B S Second choice M B M S B Third choice S S B M M A.S B. M OC. B OD. No winner can be chosen.
A charity is trying to raise money by hosting a comedy club with a famous comedian. In order to maximize donations they want to bring in the best comedian, if there is one. By surveying 100 of their target donors, they find the following preferences: Comedian Zach Galifianakis Maria Bamford Patton Oswalt Brian Posehn Number of Preferences 11 44 23 22 They are trying to determine who (if anyone) should be invited. Calculate the test statistic for one of the tests. What is the correct decision to make? (Do not reject H0, Reject H0, Nothing can be concluded, or None of the above?) What is the correct action to take? Invite Zach Galifianakis, Invite Maria Bamford, Invite Patton Oswalt, Invite Brian Posehn, Invite none of these, or None of the other options are correct)
A company is conducting election related research for four candidates. Previous research showed that candidates were equally favored. the company is interested in determining if preferences has changed. A sample of 200 customers showed the following: candidate 1 Candidate 2 Candidate 3 Candidate 4 40 55 45 60 The expected frequencies for the categories are : Select one: a. e= 40, e2= 55, e3 = 45, e4= 60 O b. e1= 25, e2= 25, e3 = 25, e4= 25 OC. e,= 60, e2= 66, e3 = 68 , e4= 50 O d. ej= 50, e2= 50, e3 = 50 , e4= 50 JUN
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.)
Which is the correct answer?

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