# Mathematics

## Applied Statistics

CompetencyIn this project, you will demonstrate your mastery of the following competency:Apply statistical techniques to address research problemsPerform hypothesis testing to address an authentic problemOverviewIn this project, you will apply inference methods for means to test your hypotheses about the housing sales market for a region of the United States. You will use appropriate sampling and statistical methods.ScenarioYou have been hired by your regional real estate company to determine if your regions housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report:Are housing prices in your regional market higher than the national market average?Is the square footage for homes in your region different than the average square footage for homes in the national market?For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?You are given a real estate data set that has houses listed for every county in the United States. In addition, you have been given national statistics andgraphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and providea reportto the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below.DirectionsIntroductionPurpose: What was the purpose of your analysis, and what is your approach?Define a random sample and two hypotheses (means) to analyze.Sample: Define your sample. Take a random sample of 100 observations for your region.Describe what is included in your sample (i.e., states, region, years or months).Questions and type of test: For your selected sample, define two hypothesis questions and the appropriate type of test hypothesis for each. Address the following for each hypothesis:Describe the population parameter for the variable you are analyzing.Describe your hypothesis in your own words.Describe the inference test you will use.Identify the test statistic.Level of confidence: Discuss how you will use estimation and conference intervals to help you solve the problem.1-Tailed TestHypothesis: Define your hypothesis.Define the population parameter.Write null (Ho) and alternative (Ha) hypotheses.Specify your significance level.Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.Summarize your sample data using appropriate graphical displays and summary statistics.Provide at least one histogram of your sample data.In a table, provide summary statistics including sample size, mean, median, and standard deviation.Summarize your sample data, describing the center, spread, and shape in comparison to the national information.Check the conditions.Determine if the normal condition has been met.Determine if there are any other conditions that you should check and whether they have been met.Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.Calculate the hypothesis statistics.Determine the appropriate test statistic (t).Calculate the probability (p value).Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.Relate the p value and significance level.Make the correct decision (reject or fail to reject).Provide a conclusion in the context of your hypothesis.2-Tailed TestHypotheses: Define your hypothesis.Define the population parameter.Write null and alternative hypotheses.State your significance level.Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.Summarize your sample data using appropriate graphical displays and summary statistics.Provide at least one histogram of your sample data.In a table, provide summary statistics including sample size, mean, median, and standard deviation.Summarize your sample data, describing the center, spread, and shape in comparison to the national information.Check the assumptions.Determine if the normal condition has been met.Determine if there are any other conditions that should be checked on and whether they have been met.Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.Calculate the hypothesis statistics.Determine the appropriate test statistic (t).Determine the probability (p value).Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.Relate the p value and significance level.Make the correct decision (reject or fail to reject).Provide a conclusion in the context of your hypothesis.Comparison of the test results: See Question 3 from the Scenario section.Calculate a 95% confidence interval. Show or describe your method of calculation.Interpret a 95% confidence interval.Final ConclusionsSummarize your findings: Refer back to the Introduction section above and summarize your findings of the sample you selected.Discuss: Discuss whether you were surprised by the findings. Why or why not?What to SubmitTo complete this project, you must submit the following:Project Two Template: Use this template to structure your report, and submit the finished version as a Word document.

## Parallel Transported Lines

Symmetries of Parallel Transported LinesConsider two lines, r and r’, that are parallel transports of each other along a third line, l. Consider now the geometric figure that is formed by the three lines and look for the symmetries of that geometric figure.What can you say about the lines r and rl Do they intersect? If so, where? Look at the plane, spheres, and hyperbolic planes.If a transversal cuts two lines at congruent angles, are the lines, in fact parallel in the sense of not intersecting?Suggestions can be found on the book.Problem 9.1, 9.2 and 10.1 Due date is March 6thProblem 9.1 Side-Side-Side (SSS)Are two triangles congruent if the two triangles have congruent corresponding sides?SuggestionsStart investigating SSS by making two triangles coincide as much as possible, and see what happens. For example, in Figure 9.2, if we line up one pair of corresponding sides of the triangles, we have two different orientations for the other pairs of sides as depicted in Figure 9.2. Of course, it is up to you to determine if each of these orientations is actually possible, and to prove or disprove SSS. Again, symmetry can be very useful here. 6n a sphere, SSS doesnt work for all triangles. The counterexample in Figure 9.3 shows that no matter how small the sides of the triangle are, SSS does not hold because the three sides always determine two different triangles on a sphere. Thus, it is necessary to restrict the size of more than just the sides in order for SSS to hold on a sphere. Whatever argument you used for the plane should work for suitably defined small triangles on the sphere and all triangles on a hyperbolic plane. Make sure you see what it is in your argument that doesnt work for large triangles on a sphere.

## Ford Agency

Unit 7: DiscussionFords Trucks and SUVs Offer Greater Return on InvestmentBusiness FocusFord Motor Company plans to spend $7 billion to develop more trucks and sport-utility vehicles (SUVs). The companys CEO, Jim Hackett, is making the sizable investment in response to a rapid shift in customer tastes away from sedans toward vehicles with greater space and utility. He also supported the cash outlay because trucks and SUVs earn higher margins than sedans.As youll learn in Chapter 11, return on investment (ROI) is a function of margin multiplied by turnover. In Fords case, its trucks and SUVs offer an attractive margin and turnover. Margin is calculated as net operating income divided by sales, whereas turnover is a function of sales divided by average operating assets. Hackett also plans to reduce materials and engineering costs across the companys vehicle lineup by $14 billion over five years.Source: Mike Colias, Ford Shifts $7 Billion to Trucks and SUVs, The Wall Street Journal, October 4, 2017, p.B1.Source: Garrison, R., Noreen, E., & Brewer, P. (2021). Managerial accounting (17th ed.). New York, NY: McGraw-Hill Education.DirectionsInitial PostingFord Motor Companys CEO Jim Hackett tied financial metrics to corporate strategy. This strategic initiative/move worked to Fords benefit. You can read about this on Fords website and learn how Hackett did this in previous positions which he occupied. You can begin reading about this at Ford Motors Strategic Analysis. (Links to an external site.)Please perform more scrutiny as to how and what Hackett did. Try to discover what metrics or financial ratios were used in Hacketts strategic initiative at Ford or other companies in which he worked. He was a master at linking metrics with corporate strategy.Next, disclose your research findings in your initial post. Include supporting information from websites to examine and illustrate the linkage of financial metrics with corporate strategy. Then please respond to the following questions:1. How does Ford Motor Company routinely use financial metrics to drive changes in corporate strategy? Provide examples of collaborating information from corporate websites to support your response.2. Differentiate which financial ratios are commonly used for continuation of corporate strategy? Which ratios are specifically used for changes in corporate strategy? Is there any differentiation for continuation vs. changing strategies and reported ratios?

## The Gradient Method

Using matlab to do the “The Gradient Method” and “Newton’s Method”

## Planet Marketing Management

Video link : https://www.dropbox.com/s/osgf0qw222dal1w/Wild_Planet.mov?dl=0What type of research design options and strategies are leveraged at Wild Planet?Are they using Exploratory, Descriptive or Causal Research Design techniques? What specific methodologies did you notice in the video?Is there anything further you would recommend for Wild Planet marketing management to give them the information to further grow their business?

## County Building

Assuming that in 2014, Broward County had 952 miles of paved roads. Starting in 2015, the County has been building 12 miles of new paved roads each year. At this rate, how many miles of paved road will Broward County have in 2030? (Assume that no paved roads go out of service and nothing block the project.). What would be your approach to solve this problem? Elaborate. 250 words

## Alternative Hypothesis

Homeworkweek61(11.9pg.409)ThefollowingdatarepresentsthepriceofregulargasolineatselfservicestationsinfourcountiesinNewYorkCityMay17,2014ManhattenBronxQueensBrooklynnassauSuffolk2.3392.1992.2392.1592.0992.1792.2992.1392.2392.1992.1992.1592.2392.2392.1792.3592.2592.1192.1992.1592.2992.1592.2392.1592.1992.1792.2791.9992.2392.219At the .05 level of significance, is there evidence of a difference in the mean price of gasoline in the six countiesa. State the null hypothesis, state the alternative hypothesisb. using excel, analyze the gas data using the ANOVA:single factorc. explain your results comparing the F results to Fcritical and how this determines whether we can accept or reject Ho. What is your conclusion from this analysis.2. (12.5 pg. 452) A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was Do you enjoy shopping for clothing? the results are summarized in the following contingency tableGENDEREnjoy Shopping for ClothingMaleFemaleTotalyes136224360no10436140Total24260500a. Is there evidence of a significant difference between the proportion of males and females who enjoy shopping for clothing at the .01 level of significance? Watch the video provided to do this problem in Excel.c. What is your answer to a) if 206 males enjoyed shopping for clothingClass Work week 6 problem.xlsx Class Work week 6 problem.xlsxFebruary 21 2020, 3:33 PM

## Mathematical Explanation

Topic: Categories of continuity: uniform continuity, absolute continuity, Lipschitz continuityThe written portion of this project should be around 5-7 pages (before references). Each write-up should include the following three components:1- Historical context/motivation.2- Detailed mathematical explanation.3- Discussion of how the results/ideas/concepts are used more broadly.In terms of writing style, write as though you were writing part of a textbook (directed to college students who are taking upper classes). In the “detailed mathematical explanation” make sure to explain any new notation, provide plenty of justification for the steps in the proof, and explain as best as you can the overall strategy of the proof.Please include a references section at the end.you can use the book I uploaded.please do not Plagiarism

## Fundamentals Of Geometry

Respond to one or more of the following in a minimum of 175 words:This week we learn about the foundations of geometry. Geometry uses various modes of thinking. Describe inductive and deductive reasoning. Provide some examples from everyday life that compare and contrast these two ways of thinking?Where in your world do you see segments, rays, and angles? If you were going to explain these geometric figures to someone how would you describe them?Discuss the different types of angles we will be learning this week and also discuss some special angle pairs.

## An Exponential Distribution

1. A statistician has a sample X1, . . . , Xn from N(µ, ? 2). Also, the statis-tician has a sample Y1, . . . , Yk from an exponential distribution with param- eter ?. Suppose that these samples are independent. Find the variance of a random variable Z = 3X? ? 5Y? .2. Let a sample of size n from a distribution with the pdf f(x) be given. What is the pdf of X(1)?3. Let X1, . . . , Xn be independent RVs with E?(Xl) = l?. Consider an es- timator ?? =?n l=1 alXl. What condition should be imposed on a1, a2, . . . , anso that ?? is an unbiased estimator? 4. Let X1, . . . , Xn be iid Bernoulli with the probability of success ?. Sug-gest the minimal variance unbiased estimator, and then prove, using Cramer- Rao inequality, its efficiency.5. Consider a sample of size n from Unif(?, ?). Find (minimal) sufficient statistic for the pair (?, ?).6. Consider a sample of size n from Unif(0, ?). Find a method of mo- ments estimator of ?.7. Let we observe a sample X1, . . . , Xn where Xl = ? + Yl, with Yl being iid Expon(?). Find the MLE of ?. Hint: Do not forget about support of the exponential RV.8. For the problem 7, let ? be given. Find the MLE of cos(?). 9. Consider a sample of size n from Poisson(?). Find a method ofmoments estimator for the estimand ?2. 10. Let a sample of size n from N(?, ?2) be given. A statistician believes

Use Promo Code: FIRST15

**FIRST15**and enjoy expert help with any task at the most affordable price.