Case Study: Structured Settlements

Students are presented with a report that offers a present value analysis of a Structured Settlement and asked to decide whether they agree with its conclusions. The case tests quantitative, financial and spreadsheet skills, exposes students to the world of law and legal statutes, and requires value judgments about fairness. The case is appropriate for senior-level undergraduate business majors and MBAs, in courses that involve decision-making. &nbsp

A Historical Note On The Proof Of The Area Of A Circle

Proofs that the area of a circle is ?r2 can be found in mathematical literature dating as far back as the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges and then fitting the wedges together in a way to approximate a rectangle. Later more sophisticated proofs relied on arguments involving infinite sequences and calculus. Generally speaking, both of these approaches are difficult to explain to unsophisticated non-mathematics majors. This paper presents a less known but interesting and intuitive proof that was introduced in the twelfth century. It discusses challenges that were made to the proof and offers simple rebuttals to those challenges

Developing Transparent Health Care Reimbursement Auditing Procedures

The continued computerization of health care records has enabled easier sampling and analysis of large sets of medical records, making it easier than ever for Medicare, Medicaid and other private insurers to use statistical audits to determine and demand return of alleged overpayments to health care providers. However, there are sometimes statistical difficulties with the audits, and there is frequently not sufficient transparency in the procedures or their application to reproduce the results in order to determine whether they have been carried out correctly. This paper addresses concerns in sampling and analysis of data records by looking at the case of a specific audit of a medical practice carried out by a private insurer. If done properly, statistical audits can be a very useful tool, but often the methodologies are vague and the implementation is either wrong or not explained fully enough to reproduce and analyze

Auditing The Auditors In Medicare And Medicaid

Baker Surgical Supplies, a small company, went bankrupt after it could not repay a significant overpayment charge demanded by Medicare based on a statistical extrapolation of claims of overpayment. The case centered on whether the extrapolation process was justifiable and whether it was properly implemented. This paper provides a description of the extrapolation process used by Medicare and Medicaid and presents the data and sampling procedure offered by Medicare and the statistical arguments offered by Baker. The case demonstrates some potential misuses of statistics in the auditing process. In shedding light on this issue, the analysis in this paper could prove to be instrumental in prompting significant improvements to the auditing process of Medicare and Medicaid

Pooled Testing: Determining The Optimum Pool Size To Minimize The Total Number Of Tests

In light of the rapidly spreading COVID-19 virus, the FDA has suggested pooling of samples in order to reduce the cost of testing a large population. Under this approach, several samples are pooled, and the pooled samples are first tested. If the pool tests negative, then the lab would have successfully tested many samples while consuming only the resources needed for a single test. If the pooled sample tests positive, then each sample that comprised the pool is individually tested. In this context, an important question for people in the field is “Given a certain overall infection rate among the population, what is the optimum pool size so that we can minimize the overall number of tests for a given number of individual samples?” In this paper, we derive this number both empirically and analytically. We also address the related question “Given a certain pool size, what is the maximum infection rate for which we can still gain in terms of the number of tests?

The Effect Of Plus/Minus Grading On The GPA

In recent years, an increasing number of colleges and universities have been turning away from traditional letter grading systems that limit student grades to A, B, C, D, and F based on the presumption that grading systems with more flexibility are advantageous to both teachers and students. However, as with any rating system, before opting for a new grading system it is important to recognize that modifications may result in some, possibly unintended, consequences as well.  In this paper, we discuss theoretical effects that including plus and/or minus grades may have on Grade Point Average (GPA) and analyze data from a School that implemented such a change

The PBA vs Piscataway: A Case Study Statistics In The Workplace

The State of New Jersey Public Relations Employment Commission recently rendered a decision in a dispute over the Piscataway Police Department’s procedure for promoting individuals to the rank of sergeant. One important component of the case was how to properly interpret the results of a 1999 sergeant’s promotion exam. This paper gives a brief history of the promotional process and offers the data and statistical analysis submitted by both the Plaintiff (Patrolmen’s Benevolent Association- PBA) and the Police Administration. The case provides an excellent tutorial for beginners and practitioners on how to properly apply some elementary, but powerful, statistical concepts

Behavioural economics, motivating psycho-education improvements; a mobile technology initiative in South Africa

Here we report on a health behavioural support project, using incentivised behaviour on a mobile platform through M4JAM. This was a proof of concept study to support further developments, more specifically targeted at the management of Tuberculosis and Human Immunodeficiency Virus. The study reported here examines the impact of financial rewards and app towards improving mental health outcomes in South Africa. 136 participants were recruited from a database and dichotomized into self-determined and heteronomous groups based on self-report scores. Overall the findings highlighted that personal financial incentives have a role in motivating behaviour and that individuals with higher levels of self-determinate motivation. The findings are discussed in light of the usefulness of an incentivized mobile platform in real-world practice to encourage mental health improvements in a low to middle-income countries

Toxic effects of Pb2+ on growth of cowpea (Vigna unguiculata)

A concentration as low as 1 mu M lead (Pb) is highly toxic to plants, but previous studies have typically related plant growth to the total amount of Pb added to a solution. In the present experiment, the relative fresh mass of cowpea (Vigna unguiculata) was reduced by 10% at a Pb2+ activity of 0.2 mu M for the shoots and at a Pb2+ activity of 0.06 mu M for the roots. The primary site of Pb2+ toxicity was the root, causing severe reductions in root growth, loss of apical dominance (shown by an increase in branching per unit root length), the formation of localized swellings behind the root tips (due to the initiation of lateral roots), and the bending of some root tips. In the root, Pb was found to accumulate primarily within the cell walls and intercellular spaces. (C) 2007 Elsevier Ltd. All rights reserved

Naming Names: The Impact of Supreme Court Opinion Attribution on Citizen Assessment of Policy Outcomes

The manner in which political institutions convey their policy outcomes can have important implications for how the public views institutions\u27 policy decisions. This paper explores whether the way in which the U.S. Supreme Court communicates its policy decrees affects how favorably members of the public assess its decisions. Specifically, we investigate whether attributing a decision to the nation\u27s High Court or to an individual justice influences the public\u27s agreement with the Court\u27s rulings. Using an experimental design, we find that when a Supreme Court outcome is ascribed to the institution as a whole, rather than to a particular justice, people are more apt to agree with the policy decision. We also find that identifying the gender of the opinion author affects public agreement under certain conditions. Our findings have important implications for how public support for institutional policymaking operates, as well as the dynamics of how the Supreme Court manages to accumulate and maintain public goodwill