Quick Answers to Problems
1. The national unemployment rate in a recent month was 4.9 percent. You think the rate may be different in your city, so you plan a sample survey that will ask the same questions as the Current Population Survey. Consider p as the local employment rate. Identify the null and the alternative hypotheses that you will test to see if the local rate differs significantly from 4.9 percent.· H0: p = 0.049, Ha: p < 0.049· H0: p = 0.049, Ha: p = 0.049· H0: p = 0.049, Ha: p > 0.0492. The financial aid office of a university asks a sample of students about their employment and earnings. The report says, “For academic year earnings, a significant difference (P = 0.028) was found between the sexes, with men earning more on the average.”True or false: The report shows that the difference in earnings in the sample was large enough that it would rarely occur in more than 3 percent of samples drawn from a population in which men’s and women’s average earnings are equal.
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Graph Theory Part 2
11. Does each of these graphs have an Euler circuit? If so, find it.12. Does each of these graphs have an Euler circuit? If so, find it.13. Eulerize this graph using as few edge duplications as possible. Then, find an Euler circuit.17. Does each of these graphs have at least one Hamiltonian circuit? If so, find one.19. A company needs to deliver product to each of their 5 stores around the Dallas, TX area. Driving distances between the stores are shown below. Find a route for the driver to follow, returning to the distribution center in Fort Worth:a. Using Nearest Neighbor starting in Fort Worthb. Using Repeated Nearest Neighborc. Using Sorted Edges21. When installing fiber optics, some companies will install a sonet ring; a full loop of cable connecting multiple locations. This is used so that if any part of the cable is damaged it does not interrupt service, since there is a second connection to the hub. A company has 5 buildings. Costs (in thousands of dollars) to lay cables between pairs of buildings are shown below. Find the circuit that will minimize cost:a. Using Nearest Neighbor starting at building Ab. Using Repeated Nearest Neighborc. Using Sorted Edges23. Find a minimum cost spanning tree for the graph you created in problem #3
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Discussion Post and journal entries
Discussion Post:Forecasting Models: Strengths and CaveatsForecasting models have their strengths, but also their caveats. Present an example in which a forecasting model could be used, what method you would choose and why? What are the particular strengths of the model and what would it be used for? What should we be skeptical or cautious about in interpretting the results?Please post an original response to the questions above and then respond to at least two other students’ posts with a substantial reply. Keep in mind that a substantial reply moves our discussion to deeper levels, by exploring the content, inviting others into the discussion.Journal Entry:This is your final journal assignment. So, please do the following:Reflect on what you have learned from this course. What tools will you use for sure in the next six months? Which ones are less likely of use?Let’s say you are preparing for a job interview, where the job entailed use of management science. You’ve been asked to talk about the use and value of mathematical models for business. What will you say? (You don’t need to give the full presentation, but please provide the key points you would present.)Assess your performance in this course. Have you improved as a user of quantitative information? What evidence supports your improvement?
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Symbolic Logic Rules of Implication
For each line (other than the premises) in the following proofs, state the line or lines which it follows and the valid argument form (MP, MT, DS, or HS) used to obtain it.The boxes on the left are for the applicable lines and the boxes on the right are for the applicable rules.(1)1. A ⊃ B Premise2. A ∨ C Premise3. ~B Premise4. ~A5. C(2)1. A ∨ (H ∙ K) Premise2. A ⊃ (B ∨ C) Premise3. ~ (B ∨ C) Premise4. ~A5. (H ∙ K)(3)1. ~R Premise2. ~S ⊃ T Premise3. (A ⊃ B) ⊃ ~S Premise4. ~R ⊃ (A ⊃ B) Premise5. ~R ⊃ ~S6. ~R ⊃ T7. T(4)For each line (other than the premises) in the following proofs, state the line or lines which it follows and the valid argument form (MP, MT, DS, HS, Simp, Conj, Com, Add, CD) used to obtain it.The boxes on the left are for the applicable lines and the boxes on the right are for the applicable rules.1. A ⊃ B Premise2. A ∙ ~D Premise3. B ⊃ C Premise4. A5. A ⊃ C6. C7. ~D ∙ A8. ~D9. C ∙ ~D(5)1. C Premise2. A ⊃ B Premise3. C ⊃ D Premise4. D ⊃ E Premise5. C ⊃ E6. C ∨ A7. (C ⊃ E) ∙ (A ⊃ B)8. E ∨ B(6)Use the first eight rules of inference to derive the conclusion of the following symbolized argument (you can use another sheet of paper). If you can’t access the logical operation signs, just write “dot,” “wedge”, “horseshoe” or “triple bar” wherever applicable.1. ( W ∙ X ) ⊃ ( Q ∨ R )2. ( S ∨ F ) ⊃ ( Q ∨ W )3. ( S ∨ G ) ⊃ ( ~ Q ⊃ X )4. Q ∨ S5. ~ Q ∙ H / R
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