Tag: Mathematics

The project is adapted from the Chapter 4 Case Study dealing with North–South Airline In
January 2012, Northern Airlines merged with Southeast Airlines to create the fourth largest U.S.
carrier. The new North–South Airline inherited both an aging fleet of Boeing 727-300 aircraft
and Stephen Ruth. Stephen was a tough former Secretary of the Navy who stepped in as new
president and chairman of the board.
Stephen’s first concern in creating a financially solid company was maintenance costs. It was
commonly surmised in the airline industry that maintenance costs rise with the age of the
aircraft. He quickly noticed that historically there had been a significant difference in the
reported B727-300 maintenance costs (from ATA Form 41s) in both the airframe and the engine
areas between Northern Airlines and Southeast Airlines, with Southeast having the newer fleet.
On February 12, 2012, Peg Jones, vice president for operations and maintenance, was called into
Stephen’s office and asked to study the issue. Specifically, Stephen wanted to know whether the
average fleet age was correlated to direct airframe maintenance costs and whether there was a
relationship between average fleet age and direct engine maintenance costs. Peg was to report
back by February 26 with the answer, along with quantitative and graphical descriiptions of the
relationship.
Peg’s first step was to have her staff construct the average age of the Northern and Southeast
B727-300 fleets, by quarter, since the introduction of that aircraft to service by each airline in
late 1993 and early 1994. The average age of each fleet was calculated by first multiplying the
total number of calendar days each aircraft had been in service at the pertinent point in time by
the average daily utilization of the respective fleet to determine the total fleet hours flown. The
total fleet hours flown was then divided by the number of aircraft in service at that time, giving
the age of the “average” aircraft in the fleet.
The average utilization was found by taking the actual total fleet hours flown on September 30,
2011, from Northern and Southeast data, and dividing by the total days in service for all aircraft
at that time. The average utilization for Southeast was 8.3 hours per day, and the average
utilization for Northern was 8.7 hours per day. Because the available cost data were calculated
for each yearly period ending at the end of the first quarter, average fleet age was calculated at
the same points in time. The fleet data are shown in the following table.
Airframe cost data and engine cost data are presented below (please note, I have altered the
number presented in the text so that online solutions cannot be used) paired with fleet average
age in that table.
The project is derived from a case study located at the end of chapter 4 dealing with regression
analysis. Please note, however that some of the numbers in the project tables in the text have
been changed so students should get their complete instructions from the Project area provided in
Getting Started section of the Table of Contents. Students should use the Data Analysis add-on
pack from the standard Microsoft Excel software available in every Microsoft Office software
since 2007. The project requirements are:
1. Prepare Excel Data Analysis Regression Tables demonstrating your excellence at
determining Northern and Southeast Costs to Average Age. Besides the data tables,
copied from the project instructions, four regression models are required each on a
separate tab. STUDENTS CANNOT USE MULTIPLE REGRESSION as this is not part
of Excel software. Place each regression model with supporting data labels, line fit plots,
and other required items on a separate worksheet tab.
2. On each worksheet tab (other than the data table tab) include:
a. a copy of your data entry screen (Use Alt Print Screen to copy picture of
Regression Data Entry from Data Analysis in Excel and paste on correct
worksheet tab).
b. The regression model derived from the data tables.
c. Line Fit Plot for each Worksheet tab.
d. Labels of the data included.
e. Highlight with yellow and label the following four items on each regression
model:
i. Coefficient of determination
ii. Coefficient of correlation or covariance
iii. Slope, and
iv. Beta or intercept
3. Finally prepare a formal response, using Microsoft Word, from Peg Jones’s to Stephen
Ruth explaining your numbers and calculations. Which costs are correlated with the
average age of the aircraft? What is the slope and beta? Explain the coefficient of
determination and covariance. Explain how this information benefits each airline. Finally,
Stephen wants to know:
a. If Northern’s average age gets to 20,000 hours how much will the Airframe and
Engine cost.
b. If Southeast’s average age gets to 12,000 hours how much will the Airframe and
Engine cost.
Submit your Excel Worksheet with five tabs (data, plus 4 tabs for the regressions) to the
assignment drop box. Also include your formal response in a Microsoft Word document. Late
work will not be accepted. The Excel worksheet and Word documents must be submitted
BEFORE then end of Unit 7. This project is worth 160 points.
Note: Dates and names of airlines and individuals have been changed in this case to maintain
confidentiality. The data and issues described here are real.
Northern Airline Data (numbers have been changed from text)
Airframe Cost Engine Cost Average Age
Year per Aircraft per Aircraft (Hours)
2001 61.80 33.49 6,512
2002 54.92 38.58 8,404
2003 69.70 51.48 11,077
2004 68.90 58.72 11,717
2005 63.72 45.47 13,275
2006 84.73 50.26 15,215
2007 78.74 80.60 18,390
Southeast Airline Data (numbers have been changed from text)
Airframe Cost Engine Cost Average Age
Year Per Aircraft per Aircraft (Hours)
2001 14.29 19.86 5,107
2002 25.15 31.55 8,145
2003 32.18 40.43 7,360
2004 31.78 22.10 5,773
2005 25.34 19.69 7,150
2006 32.78 32.58 9,364
2007 35.56 37.07 8,259

Required Textbook link: http://www.opentextbookstore.com/mathinsociety/2.5/MathinSociety.pdf
– There will be specific numbered problems under the assignments descriiption. Only do those in accordance with the textbook.

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Log-in Info will be available for the assigned writer.

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MDM 4U Culminating Task: Lie to Me For this assignment my Topic : The A relationship between the Great Depression and decline in the stock market. In many of the units we have studied, there have been discussions about how someone can use statistics to convince people to believe different ideas. In this task, you’re being asked to choose a topic of study, conduct research and statistical analysis, complete a final report on your findings, and share your results with the class. But here’s the catch: using statistics, you’re being asked to mislead and misrepresent when you share your results with the class. Specific Expectations: 1.1 Pose a significant problem of interest that requires the organization and analysis of a suitable set of primary or secondary data, and conduct appropriate background research related to the topic. 1.2 Design a plan to study the problem. 1.3 Gather data related to the study of the problem and organize the data. 1.4 Interpret, analyze, and summarize data related to the study of the problem. 1.5 Draw conclusions from the analysis of data, evaluate the strength of the evidence, specify any limitations of the conclusions, and suggest follow-up problems or investigations. 2.1 Compile a clear, well-organized, and detailed report of the investigation. 2.2 Present a summary of the investigation to the class within a specified length of time (for our purposes, 5 – 10 minutes), using carefully selected statistics to help prove/disprove your investigation by misleading the class. 2.3 Answer questions about the investigation and respond to critiques. Use the following video to guide your misleading/misrepresenting statistics: This is How Easy It Is to Lie With Statistics Topic : The A relationship between the Great Depression and decline in the stock market. Process: 1) Determine your topic ● First, develop a question or series of questions – choose a topic that interests you and that you feel you will be able to collect data on. ● Once you choose your question or series of questions, you should come up with a hypothesis for what you think the answer to each question will be. ● Make sure you backup your hypothesis with reasoning relevant to the social context of your particular question 2) Proposal (5% of your overall final mark) ● Clearly state your thesis question. If it helps, use the format: “Is there a relationship between….” ● Clearly state your hypothesis (i.e. what you predict the answer to your question will be) ● Cite the sources you have already found for your project. Your sources may be online or in printed form. ○ You should include sources where you have found raw data for your project (i.e. Statistics Canada, Nationmaster, etc.) AND sources for related research (i.e. studies performed by someone else that relate to your research question/hypothesis). ○ Use a recognized format to cite sources properly (i.e. APA, MLA, etc. Easybib.com is a helpful website to cite sources properly). 3) Data Analysis and Final Reporting (15% of your overall final mark) ● Organize your data using a variety of graphs. Graphs and tables should be formatted so that they are easy to read and understand (i.e. label the axes, title the graph, remove any unnecessary legends, etc.) ● Look for trends in your data and confirm these trends using statistics. Your analysis should include one-variable statistics (studied in Chapter 2) AND two-variable statistics (studied in Chapter 3). (Include standard deviation, variance, line of best fit (linear regression), correlation coefficient or coefficient of determination, etc,) ● You should do your calculations using technology (i.e. Excel), so there is no need to show all of your calculation steps. You should, however, ensure that you are applying the correct kind of statistical analysis to your data (linear or exponential, etc.) ● Highlight which statistics you will be altering in your presentation, and give a brief explanation (one or two sentences) about how you got that statistic Note: There should be NO misleading statistics in your final report! 4) Class Presentation (5% of your overall final grade) ● Create a presentation summarizing your research and findings. ● The presentation should outline your research question, data, statistical analysis and conclusions. ● Take a step back and try to find an angle for your research to mislead the class ● You must include some changed statistics, but you don’t need all of them to be changed, unless they help serve the purpose of proving/disproving your hypothesis ● Your presentation is expected to be 5-10 minutes long.

Write and post a linear equation in two variables and graph the linear equation using Desmos.com (Links to an external site.).

Please view this video on how to create and embed a graph using Desmos.com:
https://screencast-o-matic.com/watch/c3hXVsVrjgf

identify two points (written as ordered pairs) on the line and verify that they are true solutions. To do this, you need to plug both values into the equation and make sure that you get a true statement.

Complete the Redistricter code to perform the following functions.

Implement the MCMC process that iteratively produces candidate redistricting plans and accepts or rejects these candidates based on the Metropolis criterion.
Run this process at least 1,000 times and record each run’s resulting plan.
Visualize the results of this simulation in a plot that displays the number of nodes in each district (3 districts => 2 dimensions required) and also a histogram of this information.
Produce a number of plan visualizations that illustrate the results
The data file which is given includes the adjacency matrix that is the connectivity of node, coordinates of node, the number of the nodes, and the population of the party.
The report should be written in complete sentences and structured with an appropriate introduction and conclusion. Its intended audience and tone should match the redistricting paper. Make sure to write in the words and do not plagiarize the other paper. The best way to do this is to write in several stages and not reference the original wording of the other paper after the first stage.
Build off of the work in Project 2 according to the following items. Write up your results in a well structured and organized report, using a similar tone and audience to the redistricting paper.

Basic geographical and demographic information about the map and initial plan.

Underlying theory of the MCMC algorithm that you’ve implemented.

Practical details of the MCMC algorithm (e.g. how many trials, how many samples, estimated runtime).

Equal population constraint implemented via Gibbs distribution: include information on how you tuned the beta parameter in order to achieve an appropriate constraint. You are permitted to allow relatively high variation in district population (even ±25% is OK with me) in order to allow your algorithm the flexibility to really explore the search space. Just make a choice for yourself and explain how you tuned the beta parameter to achieve this.

Resampling 1000 times to simulate uniform distribution after obtaining a Gibbs stationary distribution.

Analysis of electoral competitiveness of your sampled plans compared to the initial plan, visualized with a scatter plot.

Plan diagrams for notable plans in your analysis, together with commentary about what makes them notable.

Overall assessment of whether the initial plan exhibits partisan gerrymandering. If so, explain how this is observed and offer less biased alternatives. If not, explain how this is observed and exhibit some alternatives with a higher level of bias for comparison.

Important: the code needs to work in order to do this project properly. The codes need to succeed in performing the MCMC algorithm with an appropriate depth and breadth. Therefore, make sure to prototype the code by running it at small scales and identify any errors that may appear. If the code is working, it should never end prematurely with a Traceback.

Have you ever watched Let’s Make a Deal? One of the games is based on a famous problem in probability. The game goes like this:

You have three doors. Under one door is a car and under two doors is a gag prize (known as a Zoink!)
You can choose one of the three doors (A, B, C).
Once you choose one of the three doors, the host (who knows where the prize is) closes one of the doors that does not contain the prize (so if you choose A, the host might close B if he/she knows the prize isn’t there).
You are prompted to keep the first door or switch to the remaining door?
Which option do you pick? How does this relate to conditional probability?

Four homework assignments exam. The exam consists of 21 questions, 120 minutes, two tries per question, two attempts on the test (the second attempt comes with a 10% penalty), therefore treat it as a one attempt exam.) It is very important that you pass the exam with an A in order for me to release the payment.

Required Textbook link: http://www.opentextbookstore.com/mathinsociety/2.5/MathinSociety.pdf
– There will be specific numbered problems under the assignments descriiption. Only do those in accordance with the textbook.

Log-in Link: https://phx-ban-ssb8.smccd.edu (if the link doesn’t work, search “websmart smccd” on google, or with any search engine)

1. Please log in to websmart
2. Find

Overview The Final Project is due by the close of Module 14, and comprises 15 percent of your course grade. Your instructor may or may not accept late work for a reduced grade. The Final Project is a stand-alone paper that you create, submit to Turnitin.com, and then post in the assignment topic by the due date. By “stand-alone” we mean that it is a complete product and requires no extra explanation. In other words, your assignment should not be a slideshow presentation that that you might use in support of a live presentation. Regardless of the subject, your Final Project should be in the format of an academic paper describing some research you undertook or a project that you completed on your own. Your file needs to be in .doc or .pdf format. Turnitin.com Instructors are not allowed to grade your assignment until you have submitted it to Turnitin.com. By now you should have a Turnitin.com account and have used it in this course in submitting your essays. However, there will be a topic dedicated to using Turrnitin.com for the Final Project in Module 14. Subject Choose a subject and project that furthers your understanding or skills in your major, or addresses your career goals. Some students will choose to complete a digital media-based project. In this case the digital product should be submitted, but still accompanied by an academic paper describing what you did and meeting all of the requirements described in the grading rubric. Alternatively, screen shots of digital work may be integrated into the text of your paper. Many practical projects can be documented with text and original images, whether photographs or computer-generated images. While images and graphics do not increase the page count of the paper, original images and graphics are one of the criteria on the grading rubric.. Of course, the central focus of the work should be quantitative and demonstrate the concepts and skills covered in this course. Quantitative literacy is often complex reasoning with simple math and graphics, involving the use of numbers in descriptions, analyses, organizing and analyzing data or works that have some quantitative component. Tips Start with an Introduction section. Explain what you did and why. Write your assignment to a general audience, who may or may not know much about the subject you chose. Particularly if you do some kind of practical project, include a section that explains the basic elements involved before launching into the project itself. Critical thinking, creativity, the generation of original material (text, photos, graphics, computergenerated or physical media of any kind), and the accuracy and clarity of quantitative communication are the most highly valued elements for this project. Regardless of your major, these skills are a contributing factor in navigating and succeeding in our highly digital and information-based world. Ideally, you will develops knowledge and skills in your major. This assignment could be the basic math and quantitative aspects to some project you are developing for your portfolio. See if you can get some guidance from instructors teaching courses in your major. Original charts, graphs, and images are valued in grading this assignment, but art skills are not a grading criterion. This is a Liberal Arts course, not a studio course. Your original images or graphs will be evaluated on their effectiveness in conveying quantitative information. Cite your images, even when they are your own. You can do this simply by creating a caption below the image with your name and the year.

*** Please, notify the customer about the subject you choose to write in the paper since they might need to share with you some images/screenshots according to these instructions:

“Choose a subject and project that furthers your understanding or skills in your major, or addresses your career goals. Some students will choose to complete a digital media-based project. In this case the digital product should be submitted, but still accompanied by an academic paper describing what you did and meeting all of the requirements described in the grading rubric. Alternatively, screen shots of digital work may be integrated into the text of your paper…… Quantitative literacy is often complex reasoning with simple math and graphics, involving the use of numbers in descriptions, analyses, organizing and analyzing data or works that have some quantitative component.”

Four homework assignments exam. The exam consists of 20 questions, 120 minutes, two tries per question, two attempts on the test (the second attempt comes with a 10% penalty), therefore treat it as a one attempt exam.) It is very important that you pass the exam with an A in order for me to release the payment.