Assignment Task 1: Hans Langenscheidt is a German historian studying various demographic characteristics German immigrants and their influence on colonial America in eighteenth century. Although accurate records are found rarely, some records showed that the cost of an adult fare (one freight) from Rotterdam to New York was approximately $2000 in today's currency. Children between the ages of 4 and 13 were charged at half the adult rate (one-half freight). Children under 4 were not charged. He was also able to find a partial list of passengers for a ship called NeuWelt. This list contains the names of the head of families, a list of family members traveling with them, their parish of origin, and the number of freights each family purchased. Unfortunately, some information is missing for some families on this list. Langenscheidt believes that the demographic parameters of the passenger list are likely to be similar to those of the other numerous voyages taken from Germany to America during the mid-eighteenth century. Assuming that he is correct, he believes that it is appropriate to create a discrete probability distribution for a number of demographic variables for this population of German immigrants. His distributions are presented in the Excel 1 file attached in the Final Project learning object.
Based on this background information and the distributions data on the Excel file, answer the following questions. In your answers provide any supporting statistical work (graphs, probability calculations, etc.) and be thorough in your explanations. Summarize all your findings in a report.
Q1. Using the information provided, describe each probability distribution in the given Excel file. Use histograms and numerical summaries such as the mean and standard deviation and their interpretations in your explanations.
Q2. Estimate the average cost of the travel for a family in U.S. dollars, using the mean number of freights purchased per family.
Q3. Is it appropriate to estimate the average cost of the voyage from the mean family size? Why or why not?
Q4. Langenscheidt came across a partial list of passengers from another ship. This list included information for six families only. Of these six, five families purchased more than four freights. Using the information contained in the appropriate probability distribution for the NeuWelt, calculate the probability that at least five of six German immigrant families purchased more than four freights. Does it seem likely that these families came from a population similar to that of the Germans on board the NeuWelt? Explain.
Q5. What additional points can you deduce from this analysis? Discuss any assumptions made throughout your analysis.
Assignment Task 2: In this part of your project, you will be asked to evaluate the performance of the judges in County X of Ohio. Here is the background:
The judges of County X try thousands of cases per year. Although in a big majority of the cases disposed the verdict stands as rendered, some cases are appealed. Of those appealed, some are reversed. Because appeals are often made as a result of mistakes by the judges, you want to determine which judges are doing a good job and which ones are making too many mistakes.
The attached Excel file has the results of 182,908 disposed cases over a three year period by the 38 judges in various courts of County X. Two of the judges (Judge 3 and Judge 4) did not serve in the same court for the entire three-year period. Using your knowledge of probability and conditional probability you will make an analysis to decide a ranking of judges. You will also analyze the likelihood of appeal and reversal for cases handled by different courts.
The Excel 2 file is attached in the Final Project learning object. It provides the data for the total cases disposed, numbers of appealed cases and the numbers of reversed cases for judges in each court.
Using Excel or SAS Studio, calculate the following probabilities for each judge. Use the attached Excel file to fill in these numbers on the tables for each court. Each court is given on a separate tab.
A. The probability of a case being appealed for each judge.
B. The probability of a case being reversed for each judge.
C. The probability of a reversal given an appeal for each judge.
D. Probability of cases being appealed and reversed in the three courts.
E. Rank the judges within each court.
Prepare a report summarizing all of your findings, including your charts, calculations and your ranking of the judges with your criteria you used and a rationale for your choice.
Assignment Task 3: Provide a case scenario of a problem (actual or hypothetical) that involves a continuous random variable X that follows a normal probability distribution. Ideally, it will come from your work or field of study, but it is not absolutely necessary. You will need to use the normal probability rules to solve that problem.
Important Note: Email a draft of your problem scenario early in the week to your instructor for him/her to review it and provide feedback early in the process.
Complete the following:
Q1. Describe the setting in your problem scenario and short background information.
Q2. Define exactly what you want to solve in this scenario and your solution plan.
Q3. Describe the type of data you collected for solving this problem.
Q4. Describe possible variable(s). (Are they continuous?)
Q5. Describe the statistical method(s) that you used to analyze the data. (Such as numerical summaries, graphs, etc.) Provide evidence that this data follows a normal distribution.
If you use software to get these analyses done, cut the related output and paste it on to your assignment document.
Q6. Provide detailed step by step explanations of the solution to the chosen problem. In your solution, include the following:
a) Probability that the continuous random variable is greater than a specific value pertaining your problem.
b) Probability that the continuous random variable is less than a specific value pertaining your problem.
c) Probability that the continuous random variable is between two values pertaining your problem.
d) Percentile(s) of some data values.
e) Graphs to visualize your solution.
Q7. Explain your thinking behind your choices of using formulas, tables, charts, etc.
Q8. Discuss the results.
Q9. Utilize proper/correct APA citations in the body of the paper and in all your references, including figures/tables in your report.
Create a 10-15 slide professional PowerPoint presentation of Part III of the Final Project. Allow a minimum of ten minutes for delivery of your presentation and 3-4 minutes for feedback from your professor and peers.
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