# Math Studies I.A

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. Furthermore, by plotting a scatter graph one can see that if the graph is more towards +1, -1 or 0.  We cannot say what strong or weak correlation is because everyone describes it differently. Hence, we can only measure the degree of correlation in terms of a numerical value. We will then test the significance of the value based on our selected data.

Background information

Systemic

Information/Measurement

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. ...