Critically discuss the role of the nures in the promotion of Essay

Critically discuss the role of the nures in the promotion of continence in older people - Essay Example ically evaluate this role played by the nurse while linking incontinence to the ageing process, examining attitudes to it, the impact it has on older persons and their family, and looking at the strategies used in health promotion and rehabilitation as well as the steps taken by the National Service Framework for Older People. Most people assume that incontinence is a part of ageing. However in reality this is far removed from the truth. The human body as it ages, invariably shows signs of wear and tear and bodily functions tend to become slow and rusty. Therefore older people are more vulnerable to numerous ailments and such illnesses weaken the body further. And yet, â€Å"None of these age-related changes cause incontinence, but they do predispose the elderly to it† (DuBeau, 2002 p.12). Therefore a brief study of the anatomy and physiology will help in understanding the age-related factors that pre-empt incontinence. The urinary system has a vital part in maintaining health in the human body. And it is on the urinary system that the inexorable process of ageing takes its toll. The kidney is the chief organ in the excretory system and as it ages it is unable to function as before. In the words of Nazarko (2002 p.134), â€Å"the weight of the average kidney decreases from 250 grams to 200 grams between the ages of 20 and 80†. There is reduced blood flow to the kidney, further hampering its functioning. Studies have shown that with increasing age there is marked reduction in the glomerular filtration rate. Therefore according to Addison (1999), â€Å"†¦ there is less efficient response to water depletion and older people tend to continue to produce more urine which is also less concentrated than that produced by a younger person†(cited in Wilson 2003 p.142). This situation particularly when further exacerbated by illness may lead to incontinence. As the person ages there is reduced bladder capacity coupled with reduced sensitivity. The former condition is brought

Learing protfolio Essay Example | Topics and Well Written Essays - 1500 words

Learing protfolio - Essay Example We did majority of the work but he was the one on the limelight and this made him take all the success for himself and not acknowledging the team. He tried charming customers with his looks once the team disintegrated but he only received failure reports after that as only looks alone do not work to gain success. Research by (Judge, Hurst & Simon, 2009) indicates that success of leaders is an accumulation of different attributes from the physical appearance to the mental ability as well as their core self-evaluation which basically deal with the confidence level of the leader. What this means is that without all these attributes mentioned above which are integrate with team work, a leader cannot be successful. When a leader is unaware of the factors that make him or her successful, when failure come s along, the leader is unlikely to rise back to the success domain again as he took the success as purely a fundamental attribute. The other thing highlighted by the article by (Gino & Pisano, 2011) that is mentioned in the topic is that overconfidence is one of the main impediments of learning about success and failure as a leader. An overconfident leader tends to be overshadowed by biasness as well as the fundamental attribution error. This therefore leads them to failing to ask for guidance or assistance even when they are on the verge of plunging into failure. What these does is that is leads the organization into eminent failure and underperformance that they cannot recover from to reach their levels of success once again. The topic basically is full of advice on how a leader should behave and what attributes to consider and remember when they are successful so that they can use them in case of any failure. The tips on success depending largely on mental ability, physical attractiveness and self-evaluation will really come in handy in future when I will have a chance to be a leader or even now in case I am chosen as a group

Corporate governance and ethical decision ion making Essay

Corporate governance and ethical decision ion making - Essay Example The board of directors, as the top management team, therefore plays a major role in defining a company’s corporate governance as well as the governance’s effectiveness in achieving the company’s objectives. Subject to legal provisions and a company’s memorandum, the directors guide their organizations through offering directives as the top managerial decision making organ. Simpler forms of businesses such as partnerships or limited liability partnerships and companies may have their top management roles vested in teams or persons (Kazmi, 2008). The roles and responsibilities of an organization’s top management centers on making macro organizational decisions that are then passed to line managers for implementation. One of the roles of the top management is developing an organization’s missions and values that define the organization’s overall direction. The management also determines major strategies to be adopted and lays down operational plans. Similarly, the top management acts as a supervisory body to â€Å"monitor and control† the organization’s managers and other officers besides evaluating the organization’s position and making recommendations to owners and other stakeholders (Kazmi, 2008, p. 398). In a small laundry repair business where a father is the technician and his son is the administrator, the son assumes top management responsibilities to make strategic decisions, communicate the decisions, and supervise the father and other employees, and report recommendations to the stakeholders (Kazmi, 2008). An organization’s top management, whether board of directors or individuals, are in their roles faced with social responsibility, which is the moral obligation to maximize benefits of all stakeholders to a strategic decision. The management’s decision should therefore consider possible adverse â€Å"economic, legal,

The Virtual Learning Environment Education Essay

The Virtual Learning Environment Education Essay Is the Internet only about social networking sites. How does it relate to a whole new dimension of E-learning, what are its effects on traditional teaching methods? Virtual learning environments (VLEs) are prevailing in education nowadays and are effectively used to deliver training materials and assist the progress of communication within a module. There has been a comprehensive study which aimed at exploring the task- technology for two main groups namely trainers and students with the help of VLE WebCT. It has been apparent that students task technology usage, user satisfaction, perspective towards the usage and expected consequences of use were higher than trainers. Trainers had higher perceptions of social rules and regulations with higher perceptions of promoting conditions than students. However, there has been no difference in the level of practice of the VLE between the trainers and students. VLE had more impact on the learning of students rather than trainers in the whole learning process. These outcomes suggest that in spite of high levels of support approved by the tutors, they may still be confused about the benefaction of VLEs to their teaching. Introduction Higher education has been increasingly influenced by the progress of information and technology. The core training requirements in Universities and other institutes involve e-learning processes. Distance education has been possible with the introduction to new innovative courses due to the World Wide Web and online education is now available to in numerous students and lecturers for their training purposes (Peffers and Bloom 1999; Alexander 2001; Chen and Dwyer 2003). Information Technology has introduced new terms and forms which are further categorized into different segments. Some of these are e- learning, distributed learning and technology- mediated learning. The term e- learning has been extensively used to define education and training which is supported by the Internet. A virtual learning environment (VLE) simplifies e-learning by supporting an information system. Teaching and learning is carried out through communication support, broadcasting educational material, storage and processing of the VLEs. In spite of the omnipresence of VLEs in teaching, much of the proof to support their use is unreliable or inefficiently established. The usage of VLEs by instructors and how they signify student learning has been a topic of debate for many researchers. They believe that an extensive theory should be available which is reliable and rigorous in order to authorize the usage and its complexities (Alavi and leidner 2001; Poccoli et al 2001). This dissertation will mainly focus on the difference between Knowledge which has become more accessible on the Internet and the process of teaching and learning which has changed, but not always improved due to Information Communication Technologies (ICTs). Furthermore, it will also discuss about the information society in a wider context. The title global auction warns that the info society anticipated in the 1980s has failed to generate jobs, instead computer programs are used to substitute for skilled workers (in accountancy, education, law, manufacturing and other occupations) who become unemployed. This is partly because the internet facilitates outsourcing of jobs from the West to China and India, so globalization is another issue which will be discussed. Virtual learning Environment Virtual learning environment (VLEs) are defined as computer based environments that are relatively open systems, allowing interactions and encounters with other participants and delivering a huge database (Wilson 1996, p 8). Furthermore, he suggests that VLEs differ from computer micro-worlds and classroom based learning environments where we use technologies as tools or in micro-worlds where students help themselves by entering a self- contained computer based learning environment. Computer aided instruction (CAI) or computer micro-worlds have many similarities with VLEs. For instance, materials can be fetched or accessed individually by learners; different paths can be followed through them and can be utilized in material displays discrepantly. Although we see, that the VLE concept is much different and broader than the CAI as it adds new dimensions to individual learning. Electronic interaction and discussion, building up new infrastructure for widely available network are some of the things encouraged by the VLEs (Wilson 1996). In a broader context, VLEs augment the progress of an individual not only in the corporate sector but also enable him or her to connect and share experiences with a larger learner-learner and instructors group. Chapter 2 Introduction It has been observed that e-learning or VLEs had been the central supporting system for the formal countenance of learning by enhancing predefined formats and learning objectives. Although, it has been in the human nature to learn informally on the unconscious level which is essentially not based on traditional exams or curricula, as a part of education to some extent. The learning outcome can largely be depended upon VLEs which support and guide the learning system. E-learning and technology enhanced learning are provided with support and recognition with the growth of Social media with their probabilities to communicate to a larger group, reflect, relate and collaborate. Research Review On a global frame, it has been examined that social media have excessive potential influence on e-learning and technology- enhancing learning, mostly within the framework of contemporary learning methods (Baird and Fisher, 2006). This impact is however partly technologically derived. The whole truth is, with the concept of web 2.0, learning is influenced technically as well as socially. They encircle the strong alliance of informal environments, the desire to engage with the learning groups beyond the classroom environment. Technologies like instant messaging (chat), wikis and weblogs are considered to be social media which enable users to publish and be a part of online communities as well as manage them in a broader scale (Schaffert, 2006). The publication and exercising of content is cheaper and more flexible unlike traditional media. Precisely, social media aims to connect with a broader mass by forming and supporting user groups and communities. This dissertation focuses on the usage of social media in teaching and acquiring knowledge in higher education. The promotional culture of social media highlighted the shift of contents from producer generated to user generated content within the Web 2.0 framework. The standard change in the context of technology-enhanced learning symbolized the shift from traditional e-learning, established upon courses and the phenomenal of learning module to an active cooperation of the learners and their support as a community for general interest. So much so, social media is predestined to augment traditional learning and also e-learning environments. In a typical university curriculum, promotion or cultivation of informal learning with formal one is not done but Social media makes this possible. Informal learning has had a parallel shift from pedagogical standards from behaviourism to constructivism. It has been suggested that informal learning was held valuable due to its characteristics of be ing passively progressive outside the so-called traditional teaching. For example, Workplace coordinated learning, where the amount of information is sought in a permanent basis. (Tochermann and Granitzer, 2008) Research Questionnaires and Outcomes I had taken an online survey which was responded by 100 people from different countries for this thesis which focuses on the articulation, development, application and evaluation of implemented situations for social media in the background of higher education. These implemented situations are designed to answer the most crucial questions listed below for my research questions. Subsequently, the outcomes for each are precisely summarized under the respective questions. Are you familiar with the applications and technologies under Web 2.0 i.e Social Networking sites, Blogging, Web content Voting, Tagging, and Bookmarking? Can you tell me which of these do you use or used for your education? This research question drew the fact that most of the students were familiar with the applications of Web 2.0 but had little knowledge about their impact on the society as a whole and how social media trends keep changing in a profound way. Most of them used Social Networking sites, completely unaware of publishing data. Moreover, this was used as the base to confirm their intent to use the internet. Were you introduced to E-learning during your education? Library Catalogues, E-books, E-journals? Do you communicate with your lecturers via mail? This question was also conducted for research amongst students to test their attitude towards e-learning. Except Wikipedia most of them had little or no interest in other user contents for education. How do you think the concepts of E-learning 2.0 be applied to your education, if you are a software development or software engineering student? While from the above answer it is apparent that most of them used Wikipedia as their learning source, weblogs also counted as the second application crucial to the implementation of e-learning 2.0. Weblogs had been newly introduced in the software development education as learning logs dated back in the 1990s when it was used as blogs only. HTML and FTP was used to publish web content. How do you think Peer Review or Self Reflection helps you when you get feedback online about your assessment or work? The concept of Peer Review has been augmented to provide better assessment of software development students for themselves as well as their peers. In this way, a new adaptation meant better work as they now became familiar to faster feedbacks and more collaborative online components. How do you think the concept of Social media can be used to refer to a larger audience globally? Can we think of distance learning without social media? If no then why? Use examples to support your answer. These questions aim to externalize knowledge and were used as an online mind mapping tool. Probing how they use visualization of information to their maximum abilities. This is the traditional way of new features in the social media education arena which enhances students to determine the possible outcomes of e-learning. Possible use of situations for education have been improvised and evaluated. What do you think about mobile learning in higher education? Does scrolling down a map while youre outside help you? You can explain what you think about location based services. Mapping materials provided possible mashups for location based services as it has been seen as the renaissance in the previous years. To support successful expedition in higher education, a collaborative system essentially location based and lightweight had been developed. Structure and Methodology The methodology applied to the analysis presented in this thesis is constructed on the notions of situations and services denoted to itemize the crucial topic of social media to clarify concrete problems and enable learning in definite situations. Situations or Plots Situations or schemes are the devices for improving our perception. A problem becomes insightfully manageable and can be better mastered by putting a composite set of events and relationships into a story. (Van der Heijden, 1997) A plot is an idealized but detailed description of a specific scenario (Young and Barnard, 1987). Furthermore, a plot is an informal approach widely used in provisional engineering (Alspaugh and Anton, 2008). One of the critical advantages is the comfort of the designer to predict outcomes before trying to specify them, making necessities more proactive in the advancement. (Carroll et al., 1998) These situations can be used to define and identify details of individual research investigation. Furthermore, developing evaluation situations for individual investigative goals can be used efficiently after research. In the scenario of education, the OECD puts forth the definition of situations for the research of expected education in order to administer a basis for stakeholders from different fields to establish long-term strategies. (OECD Publishing, 2006) In technology- enhanced learning, situations or schemes are used in the parameter of an activity-based instructive theory. In this instructive model, learning situations are described as a series of activities, a list of associated user roles, system tools which are applied, and the tutorial content (Helic, 2005). These schemes provide the fundamental assembly of the learning process within this methodology. In the background of this research, situations were used firstly to define the individual issue domains for specific aspects of social media to be adapted to education and thus, by providing concrete scenarios, simplify the possible influence on the learning process. Secondly, these situations describe a test of cases with the help of which the suggested solution can be evaluated to examine the validity of the access.

Marranos: A Lost People :: essays research papers

Marranos: A Lost People Some people might call them New Jews, some New Christians, and others call them Marranos. The majority of the world population has no idea who the Marranos are. To begin to explain these secret people, one must first receive a lesson in World History. We will begin in the 1492. In school, we are brainwashed to connect the year 1492 with the year that Columbus discovered the New World. Yet, if we look at the year 1492, there are other occurrences which are noteworthy. For instance, in the year 1492, Spain, the country which sent Columbus to America, decided to officially expel the Jews from Spain. The Jews were forced to either leave Spain, convert to Catholicism, or be put to death. This was not a surprise to the Jews of Spain. Since 1931, there had been anti-Jewish riots throughout Spain. For years, the Jews had been converting to Christianity to escape religious persecution. These Jews were called conversos. The twist to this tale is that these conversos actually were only putting on a front. They still considered themselves Jews. They practiced in secret.1 The Spanish made every attempt to search out and punish these conversos. Some Jews chose not to convert and they moved to Portugal. . Unfortunately, Portugal, in 1497, expelled the Jews from its borders as well. Anti-semitism was growing in Western Europe and the Jews needed to escape. The prime choice seemed to be so obvious. The Jews went to the New World. The immigration of the Marranos to the new world might have begun with none other than Christopher Columbus. This, of course, is not definite, but there has been research which has shown that Columbus was indeed a Marrano. Apparently his parents were Marranos.2 Even though there are some disagreements about this fact, there is strong evidence to support the claim that Columbus was Jewish. As the Marranos arrived in the New World, they were not able to reveal their secret identities and practice as Jews. This was because the Spanish government established inquisition offices in the New World. These office's sole responsibility was to hunt down Marranos and bring them to justice. The inquisitors had to visit every town once a year and gather evidence of "non- believers" of the church. They would reward anyone who came forth with information. The information could be days old or forty years old, it made no difference to the Inquisitors. The punishments for being caught were varied, never merciful. The mildest form of punishment was Scourging. This was when the victim was forced to strip to the waist in public and receive hundreds of lashes.

Determine Disinfectant and Antiseptic Effectiveness Using Zone Inhibition Method

Lab Report Title Page: Determine Disinfectant and Antiseptic Effectiveness Using Zone Inhibition Method Prepared for: By: Date: Introduction Page: Abstract This study is to examine the effects of different types of disinfectants by disk diffusion method using common agents such as Betadine, Clorox, Crest, Kiss My Face, Listerine, and Lysol. Wound care and general cleaning of home surfaces is a part of daily activity for many of the general population. Knowing which agents are effective against the bacteria that most commonly cause infection, disease, and illness allows educated decisions on which agents to use. We compared the bactericidal effectiveness of 6 common agents widely used by the general public against 3 common bacterial organisms. Introduction Sterilization kills all organisms in or on an object or substance. Disinfectants and antiseptics do not sterilize since many types of organisms and spores are not killed. Disinfectants are described as antimicrobial agents that are used on inanimate objects such as an instrument or structural surfaces. The term antiseptic is usually applied to antimicrobial agents that are used on living tissue such as skin and throat mucosa. A disinfectant must be capable of killing pathogens while it is in contact with them, so that they cannot grow again when it is removed. This action is said to be cidal (lethal), and it is described according to the type of organisms it kills as bactericidal, sporicidal, fungicidal, virucidal, etc†¦ If the antimicrobial substance merely inhibits the organisms while it is in contact with them, they may be able to multiply again when it is removed. In this case, the agent is said to have static activity and may be described as bacteriostatic, fungistatic, etc†¦ Microorganisms of different groups are not uniformly susceptible to chemical disinfection due to the structures of their cell walls. As an example, Mycobacterium are more resistant than most other bacteria because of their waxy cell walls. Of all microbial forms, bacterial endospores display the greatest resistance to both chemical and physical agents of disinfection. The efficacy claimed for a given disinfectant in killing vegetative bacterial species may have no bearing on its ability to destroy bacterial or fungal spores, mycobacteria, some viruses or prions. A number of factors must be considered when choosing a disinfectant besides type of organism. These include exposure time, concentration of the antimicrobial agent, temperature, optimal pH activity of the antimicrobial agents, the concentration of the microorganisms present, and the toxicity of the agent for skin or its effect on materials to be disinfected. Here we will test the effectiveness of various antimicrobial substances by inoculating culture plates with the test organisms and then applying the disinfectant/antiseptic to the inoculated plate by a filter paper disk that has been dipped into the disinfectant/antiseptic. This is a disk diffusion method that is similar to the method used to test the effectiveness of various chemotherapeutic agents. We will then measure the zone-of-inhibition. With this method, the presence of such a clear zone (lack of growth) surrounding the chemical shows either the cells have been killed or that their growth has been inhibited. A zone of inhibition does not discriminate between bacterio-static and bactericidal chemicals. The 6 agents we will be testing are: Betadine (B) – A povidone-iodine preparation used mainly for skin disinfection and wound treatment. Kills a wide range of disease-causing organisms including bacteria, fungi, many viruses, and most micro-organisms. Does not affect hydrophilic viruses such as polyomavirus and PBFD. Clorox (C) – A biguanide preparation of Sodium Hypochlorite used mainly for surface cleaning in various environments such as homes and hospitals to kill microorganisms. Bleach is effective as a disinfectant and kills many micro-organisms, but is not a viable solution to the spread of tuberculosis, bacterial spores and Chlamydia. Crest (Cr) – A widely used antimicrobial for oral bacteria and biofilms. Especially useful on Gram-negative micro-organisms such as Aggregatibacter actinomycetemcomitans, Campylobacter rectus, Eikenella corrodens, and Fusobacterium nucleatum. Kiss My Face (Kf) – An organic alternative to typical alcohol based mouthwashes using aloe vera as antimicrobial agent and grapefruit extract as a polyphenol. Proven useful with Trichophyton mentagrophytes and Staphylococcus aureus. _ _. Listerine (Li) – An alcohol based antiseptic mouth rinse containing the active ingredient ethanol which is toxic to bacteria at concentrations of only 7%. Reduces dental carries, plaque and gingivitis. Lysol (Ly) – A O-phenylphenol preparation of cresols used for surface cleaning in various environments such as homes and hospitals to kill microorganisms such as fungi, Tuberculosis, certain viruses,_ staphylococcus_ and Pseudomonas bacteria. Does not kill nonenveloped viruses, such as _parvovirus, polyomavirus, papillomavirus, adenovirus and reovirus_, nor will they kill all bacteria types. The three common bacteria we will be testing against are: Pseudomonas aeruginosa – An ubiquitous environmental organism associated with whirlpools whereby infection is caused by immersion in contaminated water. Staphylococcus aureus – A normal flora organism on the skin surfaces of most healthy humans. Escherichia coli – A large and diverse group of organisms associated with fecal remnants that have been ingested causing infection. Materials and Methods Page: Materials and Methods T-Soy plates (TSA) – Lawn spreading method Sterile swabs Forceps Sterile filter paper disks Disinfectants/Antiseptics We will follow the specific instructions to carry out this experiment as noted in Lab 16 p90 of Symbiosis by Pearson. Results Page: Results and Discussion This experiment was conducted to show how different disinfectants and antiseptics kill bacteria. The results of our experiment under normal room conditions on the TSA agar were as follows: Conclusion Page: Conclusion Previous research has shown that if an antiseptic disinfectant agent does not kill bacteria, the risk of infection is significantly higher. We used a Gram-negative (P aeruginosa), a Gram-positive (S aureus), and a Gram-negative (_E. coli_) bacterium for bactericidal testing procedures. We allowed the TSA agar to mature over a 7 day period and then noted our results by viewing and measuring the zone inhibition (mm). Findings were that while all had an effect, there were differences among how effective each agent was against each strain of bacterium used. Surface cleaning agents – Lysol was most effective against S. aureus and E. Coli, while Clorox did significantly well with all three bacterium. It appears from our findings that Clorox is the most effective disinfectant and antimicrobial of the six agents tested. Oral care agents – The effects of Listerine were less than stealer, while the organic product Kiss My Face was more effective with all three types of bacteria. Crest rated low as an effective agent for all three types of bacteria. It is important to note that the standard deviation rose as high as 7. 8, which is a significant difference in the resulting data accuracy. Literature Cited Pearson, 2010. Symbiosis Lab 16 Disk Diffusion Assay to Determine Disinfectant and Antiseptic Effectiveness, pp. 89-91. Pearson Custom Publishing Vicki S. Rabenberg, Christopher D. Ingersoll, Michelle A. Sandrey, and Mary T. Johnson. The Bactericidal And Cytotoxic Effects Of Antimicrobial Wound Cleansers. 2002. Centers for Disease Control and Prevention http://www. cdc. gov/nczved/divisions/dfbmd/diseases/ecoli_o157h7/index. html#spread Violet I. Haraszthy, DDS, MS, PhD; Joseph J. Zambon, DDS, PhD;Prem K. Sreenivasan, PhD. The Antimicrobial Efficacy of Commercial Dentifrices Featured in General Dentistry. 2010 Agarry O. , Olaleye M. T, and Bello-Michael, C. O. Comparative antimicrobial activities of aloe vera gel and leaf. African Journal of Biotechnology Vol. 4 (12), pp. 1413-1414, 2005. ZDENKA CVETNI, ANDA VLADIMIR-KNE. Antimicrobial activity of grapefruit seed and pulp ethanolic extract. Department of Microbiology Faculty of Pharmacy and BiochemistryUniversity of Zagreb in conjunction with the Croatia and Department of Pharmacognosy Faculty of Pharmacy and Biochemistry University of Zagreb, Croatia. 2004.

The Relationship Between Life Expectancy at Birth and Gdp Per Capita

The relationship between Life Expectancy at birth and GDP per capita (PPP) Candidate: Teacher: Candidate number: Date of submission: Word Count: 2907 Section 1: Introduction In a given country, Life Expectancy at birth is the expected number of years of life from birth. Gross domestic product per capita is defined as the market value of all final goods and services produced within a country in one year, divided by the size of the population of that country. The main objective of the present project is to establish the existence of a statistical relation between Life Expectancy (y) at birth and GDP per capita (x).First, we will present in Section 2 the data, from an official governmental source, containing Life Expectancy at birth and GDP per capita of 48 countries in the year 2003. We will put this data in a table ordered alphabetically and at the end of the section we will perform some basic statistical analysis of these data. These statistics will include the mean, median, modal cl ass and standard deviation, for both Life Expectancy and GDP per capita. In Section 3 we will find the regression line which best fits our data and the corresponding correlation coefficient r.It is natural to ask if there is a non-linear model, which better describes the statistical relation between GDP per capita and Life Expectancy. This question will be studied in Section 4, where we will see if a logarithmic relation of type y=A ln(x+C) + B, is a better model. In Section 5 we will perform a chi square test to get evidence of the existence of a statistical relation between the variables x and y. In the last section of the project, other than summarizing the obtained results, we will present several possible directions to further investigation. Section 2: Data collectionThe following table shows the GDP per capita (PPP) (in US Dollars), denoted xi, and the mean Life Expectancy at birth (in years), denote yi, in 48 countries in the year 2003. The data has been collected through an online website (2). According to this website it represents official world records. Country| GDP – per capita (xi)| Life Expectancy at birth (yi)| 1. Argentina| 11200| 75. 48| 2. Australia| 29000| 80. 13| 3. Austria| 30000| 78,17| 4. Bahamas, The| 16700| 65,71| 5. Bangladesh| 1900| 61,33| 6. Belgium| 29100| 78,29| 7. Brazil| 7600| 71,13| 8. Bulgaria| 7600| 71,08| 9. Burundi| 600| 43,02| 10. Canada| 29800| 79,83| 1. Central African Republic| 1100| 41,71| 12. Chile| 9900| 76,35| 13. China| 5000| 72,22| 14. Colombia| 6300| 71,14| 15. Congo, Republic of the| 700| 50,02| 16. Costa Rica| 9100| 76,43| 17. Croatia| 10600| 74,37| 18. Cuba| 2900| 76,08| 19. Czech Republic| 15700| 75,18| 20. Denmark| 31100| 77,01| 21. Dominican Republic| 6000| 67,96| 22. Ecuador| 3300| 71,89| 23. Egypt| 4000| 70,41| 24. El Salvador| 4800| 70,62| 25. Estonia| 12300| 70,31| 26. Finland| 27400| 77,92| 27. France| 27600| 79,28| 28. Georgia| 2500| 64,76| 29. Germany| 27600| 78,42| 30. Ghana| 2200| 56,53| 31. Greece| 20000| 78,89| 32. Guatemala| 4100| 65,23| 33.Guinea| 2100| 49,54| 34. Haiti| 1600| 51,61| 35. Hong Kong| 28800| 79,93| 36. Hungary| 13900| 72,17| 37. India| 2900| 63,62| 38. Indonesia| 3200| 68,94| 39. Iraq| 1500| 67,81| 40. Israel| 19800| 79,02| 41. Italy| 26700| 79,04| 42. Jamaica| 3900| 75,85| 43. Japan| 28200| 80,93| 44. Jordan| 4300| 77,88| 45. South Africa| 10700| 46,56| 46. Turkey| 6700| 71,08| 47. United Kingdom| 27700| 78,16| 48. United States| 37800| 77,14| Table1: GDP per capita and Life Expectancy at birth in 48 countries in 2003 (source: reference [2]) Statistical analysis: First we compute some basic statistics of the data collected in the above table.Basic statistics for the GDP per capita: Mean: x=i=148xi48 = 12900 In order to compute the median, we need to order the GDP values: 600, 700, 1100, 1500, 1600, 1900, 2100, 2200, 2500, 2900, 2900, 3200, 3300, 3900, 4000, 4100, 4300, 4800, 5000, 6000, 6300, 6700, 7600, 7600, 9100, 9900, 10600, 10700, 11200, 12300, 13900, 15700, 16700, 19800, 20000, 26700, 27400, 27600, 27600, 27700, 28200, 28800, 29000, 29100, 29800, 30000, 31100, 37800. The median is obtained as the middle value of the two central values (the 25th and the 26th): Median= 7600+91002 = 8350 In order to compute the modal class, we need to split the data in classes.If we consider classes of USD 1000 (0-999, 1000-1999, †¦) we have the following table of frequencies: Class| Frequency| 0-999| 2| 1000-1999| 4| 2000-2999| 5| 3000-3999| 3| 4000-4999| 4| 5000-5999| 1| 6000-6999| 3| 7000-7999| 2| 8000-8999| 0| 9000-10000| 2| 10000-10999| 2| 11000-11999| 1| 12000-12999| 1| 13000-13999| 1| 14000-14999| 0| 15000-15999| 1| 16000-16999| 1| 17000-17999| 0| 18000-18999| 0| 19000-19999| 1| 20000-20999| 1| 21000-21999| 0| 22000-22999| 0| 23000-23999| 0| 24000-24999| 0| 25000-25999| 0| 26000-26999| 1| 27000-27999| 4| 28000-28999| 2| 29000-29999| 3| 30000-30999| 1| 31000-31999| 1| 32000-32999| 0| 3000-33999| 0| 34000-34999| 0| 35000-35999| 0| 36000-36999| 0| 37000-38000| 1| Table 2: Frequencies of GDP per capita with classes of USD 1000 With this choice of classes, the modal class is 2000-2999 (with a frequency of 5). If instead we consider classes of USD 5000 (0-4999, 5000-9999, †¦) the modal class is the first: 0-4999 (with a frequency of 18). Class| Frequency| 0-4999| 18| 5000-9999| 8| 10000-14999| 5| 15000-19999| 3| 20000-24999| 1| 25000-29999| 10| 30000-34999| 2| 35000-40000| 1| Table 3: Frequencies of GDP per capita with classes of USD 5000 Standard deviation: Sx=i=148(xi-x)248 =11100Basic statistics for the Life Expectancy: Mean: y=i=148yi48 = 70,13 As before, in order to compute the median, we need to order the Life Expectancies: 41. 71, 43. 02, 46. 56, 49. 54, 50. 02, 51. 61, 56. 53, 61. 33, 63. 62, 64. 76, 65. 23, 65. 71, 67. 81, 67. 96, 68. 94, 70. 31, 70. 41, 70. 62, 71. 08, 71. 08, 71. 13, 71. 14, 71. 89, 72. 17, 72. 22, 74. 37, 75. 18, 75. 48, 75. 85, 76. 08, 76. 35, 76. 43, 77. 01, 77. 14, 77. 88, 77. 92, 78. 16, 78. 17, 78. 29, 78. 42, 78. 89, 79. 02, 79. 04, 79. 28, 79. 83, 79. 93, 80. 13, 80. 93. The median is obtained as the middle value of the two central values:Median= 72,17+72,222 = 72. 195 To find the modal class of Life Expectancy we consider modal classes of one year. The table of frequencies is the following Class| Frequency | 41| 1| 42| 0| 43| 1| 44| 0| 45| 0| 46| 1| 47| 0| 48| 0| 49| 1| 50| 1| 51| 1| 52| 0| 53| 0| 54| 0| 55| 0| 56| 1| 57| 0| 58| 0| 59| 0| 60| 0| 61| 1| 62| 0| 63| 1| 64| 1| 65| 2| 66| 0| 67| 2| 68| 1| 69| 0| 70| 3| 71| 5| 72| 2| 73| 0| 74| 1| 75| 3| 76| 3| 77| 4| 78| 5| 79| 5| 80| 2| Table 4: Frequencies of Life Expectancy at birth with classes of 1 year It appears from the table above that there are three modal classes: 71, 78 and 79 (with a frequency of 5).Standard deviation: Sy=i=148(yi-y)248 =10. 31 The standard deviations Sx and Sy have been found using the following table of data: Country| GDP| Life exp. | (x – x? ) | (x – x? )2| (y – ? y)| (y – y? )2| (x – x ? )(y – y ? )| Argentina| 11200| 75. 48| -1665| 2770838| 5. 35| 28. 64| -8907. 60| Australia| 29000| 80. 13| 16135| 260351671| 10. 00| 100. 03| 161374. 34| Austria| 30000| 78. 17| 17135| 293622504| 8. 04| 64. 66| 137790. 17| Bahamas. The| 16700| 65. 71| 3835| 14710421| -4. 42| 19. 53| -16947. 75| Bangladesh| 1900| 61. 33| -10965| 120222088| -8. 80| 77. 42| 96474. 63| Belgium| 29100| 78. 29| 16235| 263588754| 8. 16| 66. 1| 132501. 29| Brazil| 7600| 71. 13| -5265| 27715838| 1. 00| 1. 00| -5271. 16| Bulgaria| 7600| 71. 08| -5265| 27715838| 0. 95| 0. 90| -5007. 93| Burundi| 600| 43. 02| -12265| 150420004| -27. 11| 734. 88| 332477. 52| Canada| 29800| 79. 83| 16935| 286808338| 9. 70| 94. 11| 164294. 71| Central African Republic| 1100| 41. 71| -11765| 138405421| -28. 42| 807. 63| 334334. 75| Chile| 9900| 76. 35| -2965| 8788754| 6. 22| 38. 70| -18443. 41| China| 5000| 72. 22| -7865| 61851671| 2. 09| 4. 37| -16446. 81| Colombia| 6300| 71. 14| -6565| 43093754| 1. 01| 1. 02| -6638. 43| Congo. Republic of the| 700| 50. 02| -12165| 147977088| -20. 1| 404. 36| 244614. 57| Costa Rica| 9100| 76. 43| -3765| 14172088| 6. 30| 39. 71| -23721. 58| Croatia| 10600| 74. 37| -2265| 5128338| 4. 24| 17. 99| -9604. 66| Cuba| 2900| 76. 08| -9965| 99292921| 5. 95| 35. 42| -59301. 73| Czech Republic| 15700| 75. 18| 2835| 8039588| 5. 05| 25. 52| 14322. 40| Denmark| 31100| 77. 01| 18235| 332530421| 6. 88| 47. 35| 125482. 46| Dominican Republic| 6000| 67. 96| -6865| 47122504| -2. 17| 4. 70| 14887. 57| Ecuador| 3300| 71. 89| -9565| 91481254| 1. 76| 3. 10| -16845. 62| Egypt| 4000| 70. 41| -8865| 78580838| 0. 28| 0. 08| -2493. 16| El Salvador| 4800| 70. 62| -8065| 65037504| 0. 9| 0. 24| -3961. 73| Estonia| 12300| 70. 31| -565| 318754| 0. 18| 0. 03| -102. 33| Finland| 27400| 77. 92| 14535| 211278338| 7. 79| 60. 70| 113249. 07| France| 27600| 79. 28| 14735| 217132504| 9. 15| 83. 75| 134847. 48| Georgia| 2500| 64. 76| -10365| 107424588| -5. 3 7| 28. 82| 55644. 86| Germany| 27600| 78. 42| 14735| 217132504| 8. 29| 68. 74| 122175. 02| Ghana| 2200| 56. 53| -10665| 113733338| -13. 60| 184. 93| 145025. 00| Greece| 20000| 78. 89| 7135| 50914171| 8. 76| 76. 76| 62515. 17| Guatemala| 4100| 65. 23| -8765| 76817921| -4. 90| 24. 00| 42935. 50| Guinea| 2100| 49. 54| -10765| 115876254| -20. 59| 423. 0| 221629. 32| Haiti| 1600| 51. 61| -11265| 126890838| -18. 52| 342. 94| 208606. 00| Hong Kong| 28800| 79. 93| 15935| 253937504| 9. 80| 96. 06| 156187. 00| Hungary| 13900| 72. 17| 1035| 1072088| 2. 04| 4. 17| 2113. 54| India| 2900| 63. 62| -9965| 99292921| -6. 51| 42. 36| 64856. 98| Indonesia| 3200| 68. 94| -9665| 93404171| -1. 19| 1. 41| 11488. 77| Iraq| 1500| 67. 81| -11365| 129153754| -2. 32| 5. 38| 26351. 63| Israel| 19800| 79. 02| 6935| 48100004| 8. 89| 79. 05| 61664. 52| Italy| 26700| 79. 04| 13835| 191418754| 8. 91| 79. 41| 123290. 86| Jamaica| 3900| 75. 85| -8965| 80363754| 5. 72| 32. 73| -51288. 2| Japan| 28200| 80. 93| 15335| 235 175004| 10. 80| 116. 67| 165641. 67| Jordan| 4300| 77. 88| -8565| 73352088| 7. 75| 60. 08| -66386. 23| South Africa| 10700| 46. 56| -2165| 4685421| -23. 57| 555. 49| 51016. 52| Turkey| 6700| 71. 08| -6165| 38002088| 0. 95| 0. 90| -5864. 06| United Kingdom| 27700| 78. 16| 14835| 220089588| 8. 03| 64. 50| 119146. 94| United States| 37800| 77. 14| 24935| 621775004| 7. 01| 49. 16| 174828. 44| Table 5: Statistical analysis of the data collected in Table 1 From the last column we can compute the covariance parameter of the GDP and Life Expectancy: Sxy =148 i=148(xi-x)(yi-y)= 73011. 6 Section 3: Linear regression We start our investigation by studying the line best fit of the data in Table 1. This will allow us to see whether there is a relation of linear dependence between GDP and Life Expectancy. The regression line for the variables x and y is given by the following formula: y-y  ? =SxySx2(x-x ) By using the values found above we get: y= 62. 51 + 0. 5926*10-3 x The Pearson's correlati on coefficient is: r = 0. 6380 The following graph shows the data on Table 1 together with the line of best fit computed Figure 1: Linear regression. The value of the correlation coefficient r ~ 0. , is evidence of a moderate positive linear correlation between the variables x and y. On the other hand it is apparent from the graph above that the relation between the variables is not exactly linear. In the next section we will try to speculate on the reason for this non-linear relation and on what type of statistical relation can exist between GDP per capita and Life Expectancy. Section 4: Logarithmic regression As explained in reference [3], â€Å"the main reason for this non-linear relationship [between GDP per capita and Life Expectancy] is because people consume both needs and wants.People consume needs in order to survive. Once a person’s needs are satisfied, they could then spend the rest of their money on non-necessities. If everyone’s needs are satisfied, then any increase in GDP per capita would barely affect Life Expectancy. â€Å" There are various other reasons that one can think of, to explain the non-linear relationship between GDP per capita and Life Expectancy. For example the GDP per capita is the average wealth, while one should consider also how the global wealth is distributed among the population of a given country.With this in mind, to have a more complete picture of the statistical relation between economy of a country and Life Expectancy, one should take into considerations also other economic parameters, such as the Inequality Index, that describe the distribution of wealth among the population. Moreover, the wealth of the population is not the only factor effecting Life Expectancy: one should also take into account, for example, the governmental policies of a nation towards health and poverty. For example Cuba, a country with a very low GDP per capita ($ 2900), has a relatively high Life Expectancy (76. 8 years), mostly due to the fact that the government provides basic needs and health assistance to the population. Some of these aspects will be discussed in the next section. Let’s try to guess what could be a reasonable relation between the variables x (GDP per capita) and y (Life Expectancy). According to the above observations we can consider the total GDP formed by two values: x= xn + xw, where xn denotes the part of wealth spent on necessities, and xw denotes the part spent on wants.It is reasonable to make the following assumptions: 1. The Life Expectancy depends linearly on the part of wealth spent on necessities: y=axn + b, (1) 2. The fraction xn/x of wealth spent on necessities, is close to 1 when x is close to 0 (if one has a little amount of money he/she will spend most of it on necessities), and is close to 0 when x is very large (if one has a very large money he/she will spend only a little fraction of on necessities). 3.We make the following choice for the function xn= f(x) sa tisfying the above requirements: xn= log (cx + 1)/c, (2) where c is some positive parameter. This function is chosen mainly for two reasons. On one hand it satisfies the requirements that are describe in 2, indeed the corresponding graph of xn/x = f(x) = log (cx + 1)/cx: Figure 2: Graph of the function y= log (cx + 1)/cx, for C=0. 5 (blue), 1 (black) and 10 (red). The blue, black and red lines correspond respectively to the choice of parameter c= 0. 5, 1 and 10.As it appears from the graph in all cases we have f(0)= 1 and f(x) is small for large values of x. On the other hand the function chosen allows us to use the statistical tools at our disposal in the excel software to derive some interesting conclusion about the statistical relation between x and y. This is what we are going to do next. First we want to find the relation between x and y under the above assumptions. Putting together equations (1) and (2) we get: y= aclncx+1+b, (3) which shows that there is a logarithmic depende nce between x and y.Equation (3) can be rewritten in the following equivalent form: if we denote A=a/c, B= b+(a/c)ln(c), C=1/c, y=Aln(x+C)+B . (4) We can now study the curve of type (4) which best fits the data in Table 1, using the statistical tools of excel spreadsheet. Unfortunately excel allows us to plot only a curve of type y= Aln(x) + B (i. e. equation of type four where C is equal to 0). For this choice of C, we get the following logarithmic curve of best fit together with the corresponding value of correlation coefficient r2. Figure 3: Logarithmic regression.To find the analogous curve of best fit for a given value of C (positive, arbitrarily chosen) we can simply add C to all the x values and redo the same plot as for C= 0 with the new independent variable x1= x + C. We omit showing the graphs containing the curve of best fit for all the possible values of C and we simply report, in the following table, the correlation coefficient r for some appropriately chosen values of C. C| r| 0. 00| 0. 77029| 0. 01| 0. 77029| 0. 1| 0. 77028| 1| 0. 77025| 10| 0. 76991| 100| 0. 76666| Table 8: correlation coefficient r2 for the curve of best fit y= Aln(x+C) +B, for some values of C. The above data indicate that the optimal choice of C is between 0. 00 and 0. 01, since in this case r is the closest to 1. Comparing the results got with the linear regression (r ~ 0,6) and the logarithmic regression (r ~ 0,8) we can conclude that the latter appears to be a better model to describe the relation between GDP per capita and Life Expectancy, since the value of the correlation coefficient is significantly bigger. From Figure 3 one the data is very far from the curve of best fit and so we may decide to discuss it separately and do the regression without it.This data is corresponds to South Africa with a GDP per capita of 10700 and a Life Expectancy at birth of 46. 56 (much lower than any other country with a comparable GDP). It is reasonable to think that this anomaly is due to the peculiar history of South Africa which, after the end of apartheid, had to face an uncontrolled violence. It is therefore difficult to fit this country in a statistical model and we can decide to remove it from our data. Doing so, we get the following new plot. Figure 4: Logarithmic regression for the data in Table 1 excluding South Africa. The new value of correlation coefficient r~ 0. 3 indicates that, excluding the anomalous data of South Africa, there is a strong positive logarithmic correlation between GDP per capita and Life Expectancy at birth. Section 5: Chi square test (? 2? test) We conclude our investigation by making a chi square test. This will allow us to confirm the existence of a relation between the variables x and y. For this purpose we formulate the following null and alternative hypotheses. H0: GDP and Life Expectancy are not correlated. H1: GDP and Life Expectancy are correlated * Observed frequency: The observed frequencies are obtained directly from Ta ble 2: | Below y? | Above y? | Total|Below x| 14| 1| 15| Above x| 16| 17| 33| Total| 30| 18| 48| Table 6: Observed frequencies for the chi square test * Expected frequency: The expected frequencies are obtained by the formula: fe = (column total (row total) / total sum | Below y? | Above y? | Total| Below x| 9. 375| 5. 625| 15| Above x| 20. 625| 12. 375| 33| Total| 30| 18| 48| Table 7: Expected frequencies for the chi square test. We can now calculate the chi square variable: ?2? = ( f0-fe)2/fe = 8. 85 In order to decide whether we accept or not the alternative hypothesis H1, we need to find the number of degrees of freedom (df) and to fix a level of confidence .The number of degrees of freedom is: df= (number of rows – 1) (number of columns –1) = 1 The corresponding critical values of chi square, depending on the choice of level of confidence , are given in the following table (see reference [4]) df| 00. 10| 00. 05| 0. 025| 00. 01| 0. 005| 1| 2. 706| 3. 841| 5. 024| 6 . 635| 7. 879| Table 7: Critical values of chi square with one degree of freedom. Since the value of chi square is greater than any of the above critical values, we conclude that even with a level of confidence = 0. 005 we can accept the alternative hypothesis H1: GDP and Life Expectancy are related.The above test shows that there is some relation between the two variables x (GDP per capita) and y (Life Expectancy at birth). Our goal is to further investigate this relation. Section 6: Conclusions Interpretation of results Our study of the statistical relation between GDP per capita and Life Expectancy brings us to the following conclusions. As the chi square test shows there is definitely some statistical relation between the two variables (with a confidence level = 0. 005). The study of linear regression shows that there is a moderate positive linear correlation between the two variables, with a correlation coefficient r~ 0. . This linear model can be greatly improved replacing the linear dependence with a different type of relation. In particular we considered a logarithmic relation between the variable x (GDP) and y (Life Expectancy). With this new relation we get a correlation coefficient r~ 0. 7. In fact, if we remove the data related to the anomalous country of South Africa (which should be discussed separately and does not fit well in our statistical analysis), we get an even higher correlation coefficient r~ 0. . This is evidence of a strong positive logarithmic dependence between x and y. Validity and Areas of improvement Of course one possible improvement of this project would be to consider a much more extended collection data on which to do the statistical analysis. For example one could consider a large list countries, data related to different years (other than 2003), and one could even think of studying data referring to local regions within a single country.All this can be found in literature but we decided to restrict to the data presented in this project because we considered it enough as an application of the mathematical and statistical tools used in the project. A second, probably more interesting, possible improvement of the project would be to consider other economic factors that can affect the Life Expectancy at birth of a country. Indeed the GDP per capita is just a measure of the average wealth of a country and it does not take in account the distribution of the wealth.There are however several economic indices that measure the dispersion of wealth in the population and could be considered, together with the GDP per capita, as a factor influencing Life Expectancy. For example, it would be interesting to study a linear regression model in which the dependent variable y is the Life Expectancy and with two (or more) independent variables xi, one of which should be the GDP per capita and another could be for example the Gini Inequality Index reference (measuring the dispersion of wealth in a country).This would have been very interesting but, perhaps, it would have been out of context in a project studying GDP per capita and Life Expectancy. Probably the most important direction of improvement of the present project is related to the somewhat arbitrary choice of the logarithmic model used to describe the relation between GDP and Life Expectancy. Our choice of the function y= Aln(x+C) +B, was mainly dictated by the statistic package at our disposal in the excel software used in this project.Nevertheless we could have considered different, and probably more appropriate, choices of functional relations between the variables x and y. For example we could have considered a mixed linear and hyperbolic regression model of type y= A + Bx + C/(x+D), as it is sometimes considered in literature (see reference [4]). Bibliography: 1. Gapminder World. Web. 4 Jan. 2012. ;lt;http://www. gapminder. org;gt;. 2. â€Å"GDP – per Capita (PPP) vs. Infant Mortality Rate. Index Mundi – Country Facts. W eb. 4Jan. 2012. <http://www. indexmundi. com/g/correlation. aspx? v1=67>. 3. â€Å"Life Expectancy at Birth versus GDP per Capita (PPP). † Statistical Consultants Ltd. Web. 4 Jan. 2012. <http://www. statisticalconsultants. co. nz/ weeklyfeatures/WF6. html>. 4. â€Å"Table: Chi-Square Probabilities. † Faculty & Staff Webpages. Web. 4 Jan. 2012. <http://people. richland. edu/james/lecture/m170/tbl-chi. html>.