Mathematics

2 hrs timed math exam. Week 1-10 4 Big questions with sub-questions I have attached a few weeks PPt. after hire, will give you the student access There are 10 weeks of the topics. Here’re 3 weeks sample video, and the topic covered. Vector https://youtu.be/Cngv6eCOcuQ https://www.youtube.com/watch?v=ogxMf3g8k9w Matrix https://www.youtube.com/watch?v=CPgwSOkytc4 https://www.youtube.com/watch?v=9_miVx_sRnI Linear approximation https://www.youtube.com/watch?v=hHp8hgmUjDM

       This exam is worth 12 percent toward your final grade in the course. ·        The exam is available on the first day of week 8. ·        You may take as long as you like on this exam, but you must complete and submit to your LEO classroom assignment folder by 11:59 pm on the Tuesday of the last day of class. ·        The online text will be a valuable resource as you work on these problems. ·         Please submit your work in the LEO assignment folder in one of these ways:   o   typed and saved as a single file   OR neatly handwritten, scanned, and saved as a single file. Be sure that the pages are right-side-up and in order.                 *** Please note that ONE single file is required. ***     ·         You MUST show all of your work to receive any credit. If you have questions about showing work, please ask. If you fail to show work and only provide the final answer, you will not receive points even if that answer is correct. PLEASE clearly indicate what your answers are either.   ·         The Final Exam is open book and open notes.  You may refer to your textbook, notes, and online classroom materials, but you may not consult with anyone in person or online.  You may not use any online service to solve any of the problems.     The following statement must be signed and dated:   I have completed this Final Exam myself, working independently and not consulting with anyone except the instructor nor with any online source except ALEKS.  I have neither given nor received help on this problem set.     Name:                                                             Date     Maria and John have been married for 2 years and just learned that they are pregnant.   1.      They have been renting a small apartment but decide to purchase a house. The selling price is $400,000. They will make a 20% down payment.   They are considering 2 financing options:   Option 1:         3.0% interest 30-year mortgage:     Option 2:         2.75% interest 15-year mortgage:   Answer the following questions showing all your work to reach each answer.   A. Which option will result in a lower monthly payment if they take the full term of the mortgage?  What will that monthly payment be?   B. Which option will result in the most total interest if they take the full term of the mortgage? What will that total interest be?     2.  They decide to shop for furnishings for the new house.  They choose items that amount to $3600.00.  The store has 2 fixed installment loan options for purchasing:   Option 1: 20% down payment and financing at 6% simple interest per year for 3 years.   Option 2: no down payment and financing at 6.35% simple interest for 4 years.   Answer each of the following questions separately, showing all your work to reach each answer.   A.    Which option will result in smaller total finance charge? What will that total finance charge be?   B.     Which option will result in the smaller monthly payment? What will that monthly payment be?   C.     They decide to defer any purchases and invest a $3600 bonus that Maria will be getting from work in a savings account.  The interest rate is 1.6% compounded every month.  How much interest will they earn in 3 years?    D.    They decide to defer any purchases and loan the $3600 bonus to a needy relative at 2.5% simple interest per year.  How long will the term of the loan need to be if they want to earn $400 in interest (assuming the loan is not paid off early).       3.      Maria and John have decided that once they live in a house, they want to have a pet. They go to an animal shelter and find several pets that they would love to take home. There are 30 cats, 4 German Shepherds, 10 Labrador Retrievers, and 22 mixed-breed dogs. Since they can’t decide, they place all the adoption cards in a container and draw one.    Answer each of the following questions separately, showing all your work to reach each answer. A.        What is the probability that they select a cat?  B.        What is the probability that they select either a German Shepherd or a Labrador Retriever?  C.        What is the probability that if they select a dog, that it is not a mixed breed? D.        If they decide to purposely choose 2 of the 36 available dogs rather than randomly choosing any 2, how many combinations of 2 dogs are possible?   4.      Use the following information from June 17, 2020 to answer the questions below.   County  Total Cases  New London 1,217 Fairfield 16,475 Windham 579 Hartford 11,405 Litchfield 1,467 Middlesex 1,259 New Haven 12,185 Tolland 895     A.  Based on the data from 6/17/20, which county has the total number of cases closest to the mean of these 8 data values?   B.     Based on the data from 6/17/20, what is the median for these 8 data values?   C.     Which measure from the 6/17/20 data – mean or median – would be the most appropriate number to describe the total number of cases by county.  Explain why using what you know about the properties of the mean or median.   D.    Suppose you decide to draw a pie chart to represent the data from 6/17/20. [Note: you do not actually have to draw a pie chart for this exam] There will be 8 segments – each one representing a county. Each segment of your pie chart will represent the percentage of total cases on 6/17/20 accounted for by that county (i.e., County X represents X% of the total cases for all 8 counties combined). Name the percentage for each of the 8 counties.   E.     Based on the data from 6/17/20, which county is at the 75th percentile for total number of cases by county.   F.      Based on the data from 6/17/20, what is the percentile rank for New London?

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (“Consumer fraud and,” 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the random variable, population parameter, and hypotheses.

ScenarioYou have been hired by your regional real estate company to determine if your region’s 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 and graphs that show the national averages for housing prices and square footage. Your job is to analyze the data, com plete the statistical analyses, and provide a report to the regional sales director. You will do so by co mpleting 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.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 co mplete 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 co mplete 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?

Click on the link below to open a PDF document of four graphs. View the images and write a paragraph length (5 or more sentences) analysis for each of the four graphs. Each graph’s analysis should, minimally, include the following:What makes the graph misleading? Find at least two flaws in the design of the graph and the presentation of the data within it. Look closely and try to find unique flaws in each of the graphs. Many flaws are repeated throughout the four graphs, but there are several that are unique to each. Describe in detail how the flaws mislead those who view the graphs and discuss the tactics from the Misuse of Statistics lesson that are being used.What questions do you have, or what additional information do you need about the information in the graphs to draw valid conclusions from them.What is the agenda of individual creating or presenting the information; why did they present the information in a misleading manner?Pertaining to each specific graph, how could belief of deceiving statistics such as this be bad for consumers, citizens, the United States, etc.? What groups are most damaged by this; what could happen if people believe this misleading information?misleading graphs.pdf

CompetencyIn this project, you will demonstrate your mastery of the following competency:· Apply statistical techniques to address research problems.· Perform hypothesis testing to address an authentic problem.OverviewIn 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 region’s 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:1. Are housing prices in your regional market higher than the national market average?2. Is the square footage for homes in your region different than the average square footage for homes in the national market?3. 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 and graphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and provide a report to the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below.DirectionsIntroduction1. Purpose: What was the purpose of your analysis, and what is your approach?a. Define a random sample and two hypotheses (means) to analyze.2. Sample: Define your sample. Take a random sample of 100 observations for your region.a. Describe what is included in your sample (i.e., states, region, years or months).3. 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:a. Describe the population parameter for the variable you are analyzing.b. Describe your hypothesis in your own words.c. Describe the inference test you will use.i. Identify the test statistic.4. Level of confidence: Discuss how you will use estimation and conference intervals to help you solve the problem.1-Tailed Test1. Hypothesis: Define your hypothesis.a. Define the population parameter.b. Write null (Ho) and alternative (Ha) hypotheses.c. Specify your significance level.2. Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.a. Summarize your sample data using appropriate graphical displays and summary statistics.i. Provide at least one histogram of your sample data.ii. In a table, provide summary statistics including sample size, mean, median, and standard deviation.iii. Summarize your sample data, describing the center, spread, and shape in comparison to the national information.b. Check the conditions.i. Determine if the normal condition has been met.ii. Determine if there are any other conditions that you should check and whether they have been met.3. Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.a. Calculate the hypothesis statistics.i. Determine the appropriate test statistic (t).ii. Calculate the probability (p value).4. Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.a. Relate the p value and significance level.b. Make the correct decision (reject or fail to reject).c. Provide a conclusion in the context of your hypothesis.2-Tailed Testa. Hypotheses: Define your hypothesis.1. Define the population parameter.2. Write null and alternative hypotheses.3. State your significance level.b. Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.b. Summarize your sample data using appropriate graphical displays and summary statistics.1. Provide at least one histogram of your sample data.1. In a table, provide summary statistics including sample size, mean, median, and standard deviation.1. Summarize your sample data, describing the center, spread, and shape in comparison to the national information.b. Check the assumptions.2. Determine if the normal condition has been met.2. Determine if there are any other conditions that should be checked on and whether they have been met.1. Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.c. Calculate the hypothesis statistics.1. Determine the appropriate test statistic (t).1. Determine the probability (p value).1. Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.d. Relate the p value and significance level.d. Make the correct decision (reject or fail to reject).d. Provide a conclusion in the context of your hypothesis.1. Comparison of the test results: See Question 3 from the Scenario section.e. Calculate a 95% confidence interval. Show or describe your method of calculation.e. Interpret a 95% confidence interval.Final Conclusions1. Summarize your findings: Refer back to the Introduction section above and summarize your findings of the sample you selected.2. Discuss: Discuss whether you were surprised by the findings. Why or why not?

JP Morgan conducted a descriptive research design using a survey. Based on their problem definition, what other research design options would you recommend to help JP Morgan reach their objectives? What informs your answer?

1.) Consider the two-round bargaining game. The minimum the seller will sell his home for 188,000 and the maximum the buyer is willing to pay is $200,000. Both players know these two amounts and are bargaining over the difference (M=$12,00). Assume the disagreement values are zero for both players. Player 1 moves first by making a proposal and Player 2 can accept and reject. If player 2 rejects Player’s 1 proposal, then Player 2 gets to make a proposal, which Player 1 can reject and accept. The game is then over. Suppose the both players discount the future income at the rate d=0.2 per period. That is, $0.20 now is equivalent to $1,00 received next round. Find the equilibrium for this 2-round game. What is the sale price of the home? Which player gets the larger share of M?2.) In Depositor versus Saving & Loan Association (S&L), suppose that the S&L can invest $100,000 in a junk bond (the official name for this sort of security is high-yield bond) with the following rates of return: with high effort (H represents high research effort), the probability is 0,98 that the rate of return is 15% and 0.02 that the money vanishes; with low effort (L represents low research effort), the probability is 0.92 that the rate of return is 15% and 0.08 that the money vanishes. The rate of return on government bonds is 4%. After paying off the depositor, the S&L is left with $2000 minus research cost. Draw the extensive form and solve. Where should the depositor put the money?3.) Find time path (general solution) of P and U, given_P= (1/4) – 2U + n dP/dt = 1/2(P-n) dU/dt = – (m-p)4.) Consider a model of a competitive market in which price is adjust to excess demand or supply and firms enter or exit the industry if profits or losses are being made. Price adjusts to excess demand according to ?=(qD-qS), >0 where = a+bp is the demand function, =mN is the supply function, p is price, N is the number of firms in the industry, is speed-of adjustment coefficient. Making these substitutions gives ?=(a+bp-mN). The number of firms adjusts according to ?=z (p – ?), z>0 where ? is the fixed average cost of production. Firms enter (?>0) if price exceeds average cost (positive profits) and exit if price is less than the average cost (negative profit). Solve this system of differential equations for price and number of firms.5.) Suppose you have won $200,000 in the state lottery and you have decided to retire on your winnings. Suppose you deposit your winnings in a bank that pays 8% annual interest (compounded annually) and make yearly withdrawals of $30,000. (Hint: if periodic withdrawals, each of amount d, are deposited in a bank account whose initial amount is that pays interest at a rate r per period, then the difference equation that describes the total amount in the account after n periods is = (1+r) – d)a. What are the difference equation and initial condition that describes the future value of your account?b. Will you ever run out of money? If so, when?6.) Consider the following model, = s , = k ( – ), = where s is the marginal propensity to save and k is the acceleration coefficient. The third equation states the equilibrium condition for the determination of national income (ex ante saving = ex ante investment). Derive the general solution for . Comment on your result. (Let = for t=0)

Answer all questions. Show all work. Contact your instructor with any question before the due date. The annual government taxes for the residents of a country is calculated using the piece-wise function below. f(x) is the annual taxes owed to the government, and x is the person’s annual income. Piece-wise Function 1a.  Find f(65,000) (5 pts) 1b.  Give a detailed explanation of what your result says  (5 pts) 2a.  Find f(40,000)  (5 pts) 2b.  Give a detailed explanation of your results (5 pts) 3a  Find f(20,000)  (5 pts) 3b.  Give a detailed explanation of the result (5 pts) 4a  Find f(8,500)  (5 pts) 4b.  Give a detailed explanation of this result  (5 pts) 5.  Explain why this function had to be piece-wise. Explain how the function works.  (10 pts) For more information on Piece-wise Function read this: https://en.wikipedia.org/wiki/Power_transform

Instructions Hypothesis Testing Imagine that you are studying automobile buyers who choose to replace their current car near the end of its expected lifetime. Specifically, you are interested in how many different dealers late purchasers visit. Let µ be the mean number of dealers visited by all late replacement buyers. A random sample of 100 late replacement buyers yields a mean and standard deviation of the number of dealers visited of x¯ = 4.32 and s = 0.67. The test statistic and the corresponding p-values are listed below:  Test Statistic p-value 4.78  < 0.0001 Tasks: Set up null and alternative hypotheses needed if we wish to attempt to provide evidence that µ differs from 4 dealers. Identify the test you will apply to test the hypothesis. Justify your choice. Choose an appropriate level of significance. Define type I and II errors in the context of your hypotheses. State your decision regarding the hypothesis. State the conclusion. Submission Details: Submit a Microsoft Word document that contains your responses to assignment questions, using APA style. Name your document SU_BUS7200_W1_ LastName_FirstInitial.doc For more information on Hypothesis Testing read this:https://en.wikipedia.org/wiki/Hypothesis_Testing