The aim of this investigation is to examine whether or not the number of people per doctor affects a countries average life expectancy Essays

The aim of this investigation is to examine whether or not the number of people per doctor affects a countries average life expectancy Essays The aim of this investigation is to examine whether or not the number of people per doctor affects a countries average life expectancy Essay The aim of this investigation is to examine whether or not the number of people per doctor affects a countries average life expectancy Essay The aim of this investigation is to examine whether or not the number of people per doctor affects a countries average life expectancy. The life expectancy of many lesser economically developed countries is lower than that of more economically developed countries. Generally, better-developed countries have a greater doctor to population ratio. So I wish to determine whether this is a factor that affects life expectancy. I choose this investigation, as Im interested in geography particularly travelling. I plan to take a gap year after my A-levels, prior to university and hopefully visit many areas of the world including less economically developed countries. This led me to an interest in the variation of death rates between countries and I decided to compare this data to the number of doctors per person and to see if this influences the death rate in anyway. DATA COLLECTION: Firstly, I collected a list of all the countries in the world and their doctor to patient ratio. I got my data from a school Atlas I acquired from the college library; I collected the data from the same source as it was obtained in the same year. The countries were listed alphabetically and assigned a number. Using a graphics calculator I generated a random number, using a random function and chose a sample of 50. However, some numbers were generated twice so I ignored it the second time and went on to the next number. 1 Data No. People per Dr. average life expectancy 1 7358 45 2 769 73 3 1250 69 4 555 83 5 14300 47 6 1316 75 7 370 73 8 298 71 9 455 78 10 385 77 11 257 70 12 709 74 13 9090 73 14 5000 58 15 885 76 16 244 68 17 885 76 18 10000 53 19 5825 61 20 57300 44 21 3448 69 22 909 75 23 1111 76 24 667 70 25 357 78 26 2000 52 27 5000 47 28 5556 45 29 2500 69 30 333 79 31 2500 63 32 6423 65 33 1667 62 34 588 78 35 625 70 36 6667 52 37 5000 86 38 20000 56 39 476 77 40 406 77 41 50000 45 42 476 77 43 33333 49 44 303 78 45 10000 68 46 435 73 47 699 72 48 556 70 49 375 81 50 14300 37 Total 123743 1712 2 Modelling Procedures: I decided to use Excel to input my data into a table format (shown above), from this table I used Excel to draw a scatter diagram of all the data. Scatter Diagram to Compare Life Expectancies to People Per Doctor For 50 Random Countries The scatter diagram gives a good diagrammatic representation of the data and shows how the data is spread in roughly an elliptical nature. From this I can make an initial conclusion/statement that both data variables are random and normally distributed. Due to the elliptical nature of the data it allowed me to produce a regression line from the data. The regression lines shows visually roughly how strong or weak the correlation of the data is and in this instance the data is a relatively strong negative correlation. The strength of the correlation can be calculated using Pearsons Product Moment Correlation. To do this I used Excel to set-up a table consisting of (xi, yi , xi2 , yi2 , xiyi ) and the sum of all columns (shown page. 5) 3 Data No. People per Dr. average life expectancy Xi^2 Yi^2 XiYi 1 7358 45 54140164 2025 331110 2 769 73 591361 5329 56137 3 1250 69 1562500 4761 86250 4 555 83 308025 6889 46065 5 14300 47 204490000 2209 672100 6 1316 75 1731856 5625 98700 7 370 73 136900 5329 27010 8 298 71 88804 5041 21158 9 455 78 207025 6084 35490 10 385 77 148225 5929 29645 11 257 70 66049 4900 17990 12 709 74 502681 5476 52466 13 9090 73 82628100 5329 663570 14 5000 58 25000000 3364 290000 15 885 76 783225 5776 67260 16 244 68 59536 4624 16592 17 885 76 783225 5776 67260 18 10000 53 100000000 2809 530000 19 5825 61 33930625 3721 355325 20 57300 44 3283290000 1936 2521200 21 3448 69 11888704 4761 237912 22 909 75 826281 5625 68175 23 1111 76 1234321 5776 84436 24 667 70 444889 4900 46690 25 357 78 127449 6084 27846 26 2000 52 4000000 2704 104000 27 5000 47 25000000 2209 235000 28 5556 45 30869136 2025 250020 29 2500 69 6250000 4761 172500 30 333 79 110889 6241 26307 31 2500 63 6250000 3969 157500 32 6423 65 41254929 4225 417495 33 1667 62 2778889 3844 103354 34 588 78 345744 6084 45864 35 625 70 390625 4900 43750 36 6667 52 44448889 2704 346684 37 5000 86 25000000 7396 430000 38 20000 56 400000000 3136 1120000 39 476 77 226576 5929 36652 40 406 77 164836 5929 31262 41 50000 45 2500000000 2025 2250000 42 476 77 226576 5929 36652 43 33333 49 1111088889 2401 1633317 44 303 78 91809 6084 23634 45 10000 68 100000000 4624 680000 46 435 73 189225 5329 31755 47 699 72 488601 5184 50328 48 556 70 309136 4900 38920 49 375 81 140625 6561 30375 50 14300 37 204490000 1369 529100 Total 123743 1712 3804969945 120078 6450387 5 Pearsons Product Moment Correlation Coefficient This is denoted by r r = Sxy Sx Sy Sx = Standard deviation of x = Sy = Standard deviation of y = Sxy = Covariance = 1/50 ?xi yi x y = 1/50 ?xi yi x y Sx Sy Sx = 11588.897 Sy = 12.312 Sxy = -87234.776 R = -0.624 Hypothesis Test Im going to test my data at a 5% significant level. p = Population Product Moment Correlation Coefficient, H0: p = 0 (no correlation between people per doctor and life expectancy) H1: p 0 (negative correlation between people per doctor and life expectancy) Im using a 1 tail test- as from the initial scatter diagram and Pearsons Product Moment Correlation Coefficient Im aware that the correlation (if significant will be negative). * n = 50 r = -0.624 r (critical value) = Therefore by using the tables of critical values for (r) when n = 50 it is evident that the value for r (-0.624) is greater than the critical value when n = 50 at a 5% significant level. H1: p ; 0 (negative correlation between people per doctor and life expectancy) can be accepted and H0 rejected. Thus showing that at a 5% significant level there is negative correlation between people per doctor and life expectancy. 6- Regression Line Using the equation for a regression line: y- y = Sxy (x -x) Sx2 Ive generated an equation to calculate the value of (x) from (y). * y 66.8 = -87234.776 (x- 5879.22) 11588.8972 * Conclusion The scatter diagram is a good initial indication of negative correlation between people per doctor and life expectancy, suggesting that for countries that life expectancy is low there will be a greater number of people per doctor- compared to a country with higher life expectancy. Pearsons Product Moment Correlation Coefficient determines the strength of correlation between data, i.e * if r = o (no correlation) * if r = -1 ( perfect negative correlation) * if r = 1 (perfect positive correlation) Because my calculation gave me the value of r equal to -0.624 it supported the initial interpretation of the data having negative correlation and indicated that the negative correlation was of a reasonable strength. I decided to carry out a Hypothesis test on the data. This was carried out by the comparison of r (-0.624) with the corresponding critical values of (r) from the tables- showing negative correlation between people per doctor and life expectancy at a 5% significance level. 7- Accuracy The accuracy of my raw data is likely to be of the highest accuracy due to the fixers being obtained from the CIA (Central Intelligence of America) web site- from this I can be certain that all data is recent and for my investigation reliable. The only error likely to occur is the ever changing patient to doctor ratio, although is accounted for before the raw data was published by the CIA. I found this the most accurate and up to date source of information available for my access. Within the calculations itself the results are also of my highest possible accuracy. I used Excel to initially calculate Pearsons Product Correlation Coefficient, Mean, Standard Deviation and Co-variance, that was then check by hand using a calculator and the formulas included within my investigation. I kept the data to 3signifcant figures as accuracy beyond this wasnt necessary for this particular investigation. The regression line was also drawn by Excel and not by hand as to be most accurate. The only inaccuracy that I felt might have effected my investigation is a particular significant outlier or anomal result: (a result over two standard deviations from the mean). This could have caused my standard deviation of X to increase and Y to decrease compared to all other data figures, leading to a possible inaccuracy to my Co-variance and Pearsons Product Correlation Coefficient. The anomaly is highlighted in my scatter diagram (including the regression line) as to show the change in the regression line to incorporate this outlier- another possibly affected factor in my investigation.