Math Studies I.A
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Introduction
Introduction
This mathematics project will be examining many countries’ life expectancy and GDP per capita and see which one is independent. Firstly, numbers that are of reliable resources from the internet will be found and will take the countries’ life expectancy and GDP per capita (PPP).
This experiment will be using correlation coefficient and the regression line to verify our results. Firstly, numbers will be taken from GDP per capita and overall life expectancy of both gender and using systemic sampling the data will be collected. The countries will only be collected at every odd
My Null Hypothesis is that life expectancy is dependent to the country’s GDP whereas my Alternative Hypothesis is that life expectancy and GDP are independent. The countries will be chosen in systematic sample of every odd number from a list of countries from The World Fact Book (see page:0 ). Then, the overall average of both sexes will be taken by adding both men and women’s life expectancy and divided by 2, because I do not desire to see if GDP affects one of the sexes. Furthermore, the sex ratio of the total population will be looked at if there is much difference or not. Sex ratio is the ratio of males to females in a population. In addition, life expectancy only tells us the life expectancy of either male or female and by taking the average of both sexes one would have to take sex ratio into account or acknowledge that this can also cause some variations to the final result.
Then, xy, ,𝑦-2.,, 𝑥-2. will be calculated so to put it in the Pearson’s correlations coefficient formula (r ) and to get ,𝑟-2.. This will identify the strength of the relationship between the life expectancy and GDP per capita.
Middle
213034
8410000
5396.3716
Yemen
2,400
62.5
150000
5760000
3906.25
Zimbabwe
200
39.5
7900
40000
1560.25
Total=
1707100
7914.39
130013258
51470030000
559261.8111
r = ,,𝑆-𝑥𝑦.-,,𝑆-𝑥 .𝑆-𝑦 ..
,𝑆-𝑥𝑦.=∑𝑥𝑦,,∑𝑥.,∑𝑦.-𝑛.
,𝑆-𝑥𝑦.is known as the covariance of X and Y.
,𝑆-𝑥 .= ,-∑,𝑥-2.−,,(∑𝑥)-2.-𝑛..
,𝑆-𝑥 .is called the standard deviation of X.
,𝑆-𝑦 .= ,-∑,𝑦-2.−,(∑,𝑦-2.)-𝑛..
,𝑆-𝑦 .is the standard deviation of Y.
r=,∑𝑥𝑦− ,,∑𝑥.,∑𝑦.-𝑛.-,-∑,𝑥-2.−,,(∑𝑥)-2.-𝑛..,-∑,𝑦-2.−,(∑,𝑦-2.)-𝑛...
So, r =,130013258−,,1707100.(7914.39)-115.-,-51470030000−,,(1707100)-2.-115..,-559261.8111−,,(7914.39)-2.-115...
=,12529300.01-161645.4262 ×120.7778847.
= ,12529300.01-19523192.65.
=0.6417649118
,𝑟-2.=0.4119
Interpretation of Results
Possible explanation for outliners (errors)
Correlation does not mean that there is a relation in GDP per capita to life expectancy because countries with low life expectancy are usually with some form of crisis. One would rarely see these in the higher life expectancy countries. Therefore, outliers are from the developing countries that are not only low in GDP but also other factors affecting it, such as war, disease, ‘brain drain’, economy crisis and so on. Even though the low GDP may be a contributing factor to the problem mentioned the impact that these crisis have on the countries are more pronounced in the life expectancy compared to GDP alone.
This form of GDP is used because… overall life expectancy rather than life expectancy at birth is used because…
One can see that the outliers of life expectancy 30-50 years old are usually from the developing countries such as Afghanistan, Zimbabwe, Rwanda, Ethiopia, Namibia, Niger, Nigeria and South Africa are of some trouble. For example,
Since the late 1970s Afghanistan has suffered continuous and brutal civil war in addition to foreign interventions in the form of the 1979 Soviet invasion and the 2001 U.S.-led invasion that toppled the Taliban government.
Following the September 11 attacks the United States launched Operation Enduring Freedom, a military campaign to destroy the Al-Qaeda terrorist training camps inside Afghanistan.
Zimbabwe is experiencing a severe hard-currency shortage, which has led to hyperinflation.
In 2002, Zimbabwe was suspended from the Commonwealth of Nations on charges of human rights abuses during the land redistribution and of election tampering.
Zimbabwe's current economic and food crisis, described by some observers as the country's worst humanitarian crisis since independence, has been attributed in varying degrees, to the government's price controls and land confiscations, the HIV/AIDS epidemic, and a drought affecting the entire region.
Ethiopia has one of the fastest growing economies in the world, according to The Economist. Ethiopia has showed a fast growing annual GDP and it was the fastest growing non-oil dependent African nation in 2007 and 2008.
Although the bloody border war between Ethiopia and Eritrea (1998-2000) and food crisis.
Nigeria
The Nigerian health care system is continuously faced with a shortage of doctors known as 'brain drain' due to the fact that many highly skilled Nigerian doctors emigrate to North America and Europe. In 1995, It was estimated that 21,000 Nigerian doctors were practicing in the United States alone, which about the same as the number of doctors working in the Nigerian public service. Retaining these expensively-trained professionals has been identified as one of the goals of the government.
Swaziland
Like many subsaharan African countries Swaziland is severely affected by the HIV and AIDS pandemic. In 2004, Swaziland acknowledged for the first time that it suffered an AIDS crisis, with 38.8% of tested pregnant women infected with HIV (see AIDS in Africa). Prime Minister Themba Dlamini declared a humanitarian crisis due to the combined effect of drought, land degradation, increased poverty, and HIV/AIDS.
Sudan
clashes occurred in the western region of Darfur in the early 1970s between the pastoral tribes.
In July 2007, many parts of the country were devastated by flooding,
First Sudanese Civil War 1955 – 1972
Second Sudanese Civil War 1983 - 2005
Botswana
Congo, Republic of the
Gabon
Guinea-Bissau
Kenya
Lesotho
Mozambique
Somalia
Tanzania
Uganda
All these countries have some form of crisis or history of crisis such as war internally or externally, “brain drain”, HIV/AIDS, extreme poverty, hyperinflation, economic crisis, food crisis due to economy of natural disasters, geological location of the country being not very productive and so on.
Validity
The choice of sampling is systemic sampling because it avoids human nature of emotion and bias. Other form of sampling such as simple random sampling, stratified sampling, convenience sampling and so on are not used. When simple random sampling is used human emotions can interfere while choosing countries, although one may say they chose it in random there is always some form of bias. Furthermore, while choosing randomness of selection can result in a sample that doesn’t reflect the makeup of population or unlucky error. Stratified sampling is not used because it is difficult to categorise countries based on any characteristics. Convenience sampling is not used as it is not very scientific or systematic and human emotion interference causing bias.
The assumption made is that there is a linear correlation. However, the value of r turns out to be not very strong. During the interpretation of results the weak correlation was partially explained by factors such as war, food shortage, economic crisis, epidemic of diseases, and so on. I addition, it could well be that there is a non linear correlation instead. Furthermore, this method is extremely difficult and hence unable to test it.
Sex ratio is used to find if there is a significant difference in either population. This is to keep the result as accurate as possible although it may vary the result a little as there is some difference in gender in most countries.
Reference
http://www.president.gov.af/
http://uk.oneworld.net/guides/zimbabwe/development
http://www.state.gov/r/pa/ei/bgn/2859.htm
http://www.crisisgroup.org/home/index.cfm?id=1229
https://www.cia.gov/library/publications/the-world-factbook/geos/ni.html
http://www.gov.sz/
Human Development Index (HDI)
HDI uses GDP as a part of its calculation and then factors in indicators of life expectancy and education levels.http://en.wikipedia.org/wiki/Gross_domestic_product
https://www.cia.gov/library/publications/the-world-factbook/fields/2004.html?countryCode=AF&rankAnchorRow=#AF (GDP? per capita (PPP))
http://unstats.un.org/unsd/demographic/products/indwm/tab3a.htm (life expectancy)
http://www.photius.com/rankings/population/sex_ratio_total_population_2006_1.html (sex ratio)
http://hdr.undp.org/en/statistics/faq/question,72,en.html (why GDP per capita (PPP))
http://en.wikipedia.org/wiki/List_of_countries_by_life_expectancy
Country | GDP - per capita (PPP) |
Afghanistan | $800 (2008 est.) |
Albania | $6,000 (2008 est.) |
Algeria | $7,000 (2008 est.) |
American Samoa | $8,000 (2007 est.) |
Andorra | $42,500 (2007) |
Angola | $8,800 (2008 est.) |
Anguilla | $8,800 (2004 est.) |
Antigua and Barbuda | $19,000 (2008 est.) |
Argentina | $14,200 (2008 est.) |
Armenia | $6,400 (2008 est.) |
Aruba | $21,800 (2004 est.) |
Australia | $38,100 (2008 est.) |
Austria | $39,200 (2008 est.) |
Azerbaijan | $9,000 (2008 est.) |
Bahamas, The | $28,600 (2008 est.) |
Bahrain | $37,200 (2008 est.) |
Bangladesh | $1,500 (2008 est.) |
Barbados | $19,300 (2008 est.) |
Belarus | $11,800 (2008 est.) |
Belgium | $37,500 (2008 est.) |
Belize | $8,600 (2008 est.) |
Benin | $1,500 (2008 est.) |
Bermuda | $69,900 (2004 est.) |
Bhutan | $5,600 (2008 est.) |
Bolivia | $4,500 (2008 est.) |
Bosnia and Herzegovina | $6,500 (2008 est.) |
Botswana | $13,300 (2008 est.) |
Brazil | $10,100 (2008 est.) |
British Virgin Islands | $38,500 (2004 est.) |
Brunei | $53,100 (2008 est.) |
Bulgaria | $12,900 (2008 est.) |
Burkina Faso | $1,200 (2008 est.) |
Burma | $1,200 (2008 est.) |
Burundi | $400 (2008 est.) |
Cambodia | $2,000 (2008 est.) $1,900 (2007 est.) |
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