One word and one Excel or R

The project consists of three parts. The submission of this project will consist of two attachments:A Word document that is prepared according to the APA standards of formatting. In the Word document, explain the experiments and their respective conclusions, and additional information as indicated in each problem.

  1. Either an Excel workbook or an R script file (.R file) that contains all the work and the calculations indicated in parts 1-3 of the project. Please save your Excel workbook or R script file in the following formats, and submit all attachments together with one single submission.
  2. Project Description:
  3. Corporations have to select among many projects that are under consideration by the management. Their primary instrument for evaluating and selecting among the available projects is the benefit-cost analysis. In this analysis, both the annual benefits and the annual costs deriving from a project are estimated in several different categories. Then the total benefit is divided by the total cost to produce a benefit-cost ratio. This ratio is then used by corporations to compare numerous projects under consideration. A benefit-cost ratio greater than 1.0 indicates that the benefits are greater than the costs, and the higher a project’s benefit-cost ratio, the more likely it is to be selected over projects with lower ratios.
  4. Currently, the JET Corporation is evaluating two dam project constructions, one in southwest Georgia (Dam #1) and the other in North Carolina (Dam #2). The company has identified six areas of benefits: improved navigation, hydroelectric power, fish and wildlife, recreation, flood control, and the commercial development of the area. Furthermore, there are three estimates available for each type benefit – a minimum possible value, a most likely value (i.e., a mode or peak), and a maximum possible value. For the costs, two categories associated with a construction project of this type have been identified: the total capital cost, annualized over 30 years (at a rate specified by the creditors and the government), and the annual operations and maintenance costs. These benefits and costs estimations for both dam projects (in millions of dollars) are as follows:tabl1 1Table 1: Benefits and costs for the Dam #1 construction project in millions of dollarstable 2Table 2: Benefits and costs for the Dam #2 construction project in millions of dollarsPart 1:
    1. Perform a simulation of 10,000 benefit-cost ratios for Dam #1 project and 10,000 such simulations for Dam #2 project. Note that the two simulations should be independent of each other. Let these two ratios be denoted by LaTeX: alpha_1
      α

      1 and LaTeX: alpha_2

      α

      2 for dams 1 and 2 projects respectively.

    2. Construct both a tabular and a graphical frequency distribution for LaTeX: alpha_1
      α

      1 and LaTeX: alpha_2

      α

      2, and include both the tabular and the graphical distributions in your report (a tabular and a graphical distribution for LaTeX: alpha_1

      α

      1 and a tabular and a graphical distribution for LaTeX: alpha_2

      α

      2 – a total of 4 distributions). Also, comment on the shape of each distribution in your report.

    3. For each of the two dam projects, perform the necessary calculations in order to complete the following table. Excel users should create the table in Excel with all cells being occupied by the appropriate formulas, and R users should display the table as a “data frame”. Remember to create two such tables – one table for Dam #1 and another table for Dam #2. Include both tables in your report.

    Module2Project_table 3Part 2: Use your observation in Question (ii) of Part 1 to select a theoretical probability distribution that, in your judgement, is a good fit for the distribution of LaTeX: alpha_1

    α

    1 . Next, use the Chi-squared Goodness-of-fit test to verify whether your selected distribution was a good fit for the distribution of LaTeX: alpha_1

    α

    1. Describe the rational for your choice of the probability distribution and a description of the outcomes of your Chi-squared test in your report. In particular, indicate the values of the Chi-squared test statistic and the P-value of your test in your report.Part 3:

    1. Use the results of your simulations and perform the necessary calculations in order to complete the table below. Excel users should create the table in Excel with all cells being occupied by the appropriate formulas, and R users should display the table as a “data frame”. Include the completed table in your report.

    Module2Project_table4

    • In your report, use your observations of the results obtained in parts 1-3 to recommend one of two projects to the management. Explain all your rationales for the project that you have recommended. In particular, include with the final conclusion of your report your estimate of the probability that LaTeX: alpha_1
      α

      1 will be greater than LaTeX: alpha_2

      α

      2.

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