Math ia final


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Math ia final

  1. 1. What is the Relationship between the annual per capita wealth of a country and the Male Suicide Rate Per 100000 people?<br />Introduction<br />In 2004 Japan saw 24 deaths in the span of 2 months where groups of people died in forms of “group suicides”. Investigations rooted back this phenomenon to communities on the internet where men and women overcome with depression organize groups to commit suicide in groups (Harding). Such occurrences are still not rare in Japan and remains one of the nation’s most serious issues. While many Japanese decide to take the path of suicide, nationals of Egypt, Peru, Belize and Jamaica are almost strangers to suicide with suicide rates that are over 25 times less that that of Japan’s. So what causes this large gap? The direct causes of suicide are often left under the covers, but the general backgrounds of suicide victims can say much about the lifestyle and, possibly, the cause of suicide of the person. Hawaii University’s Thomas W. Young examined this concept through the comparison of suicide and wealth in Kansas City, Missouri. Named the “The Richard Cory Phenomenon”, he found that there was a positive correlation in the association of suicide and wealth in the 4 years worth of data of the city (Young). Could this theory hold true, then, for the causes of suicide of people in different countries with different wealth? In this investigation, this theory will be put to the test; what is the relationship between a country’s GDP per capita and the male suicide rate per 100000 people?<br />Statement of Task<br />The main purpose of this investigation is to determine whether there is a relationship between a country’s Gross Domestic Product (GDP) per capita and its male suicide rates per 100000 people. The GDP per capita is the value of all final goods and services produced within a nation in a given year divided by the average population for the same year. The male suicide rate per capita is the number of males who committed suicide per 100,000 people in that nation in its most recent year. In order to perform the investigation, data was collected from the Nation Master website. <br />Plan of Investigation<br />Following the data collection, a number of mathematical processes were used to analyze the data; standard deviation, least square regressions, Pearson’s correlation coefficient and the Chi-Square test.<br />Collected Data<br />Table 1: GDP and Male Suicide Rates for 39 Countries <br />#CountryGDP ($ per capita)Male Suicide Rate (per 100,000 people)1Lithuania8,770.0981.92Russia6,932.3374.13Latvia8,79771.44Estonia12,236.6064.65Belarus3,802.5455.76Hungary11,226.7055.57Sri Lanka1,363.9246.98Slovenia18,674.2145.19Finland39,855.9343.310Kazakhstan5,045.5039.711Ukraine2,278.4738.212Belgium37,384.3437.313Croatia9,611.6834.614Austria39,131.3734.215Luxembourg89,563.6330.816France36,546.7230.417Switzerland51,032.6629.518Moldova849.7529.519Czech Republic13,877.0228.120Bulgaria4,089.2225.321Japan34,022.942522Egypt1,425.580.123Jamaica3,954.330.524Peru3,287.740.725Azerbaijan2,374.400.826Belize4,094.421.127Kuwait31,860.602.128The Bahamas17,497.162.429Albania2,911.902.930Turkey5,521.473.831Armenia2,130.133.932Nicaragua1,022.814.333Mexico8,051.924.534Brazil5,659.744.635Bahrain17,773.384.936Colombia2,981.744.937Panama5,205.49538Tajikistan422.655.439Ecuador3,041.855.7<br />Table 1: Table 1 displays the data that was collected from the Nation Master website for the GDPs and the Male Suicide Rates per capita. The countries shown were the 21 countries with the highest Male Suicide Rates, along with the 18 counties with the lowest Male Suicide Rates. <br />Data Analysis/Mathematical Processes<br />We will start by looking at an Excel generated scatter plot of the collected data. <br />Graph 1 shows the GDP (y-axis) vs. Male Suicide Rates (x-axis) plotted on a scatterplot. <br />Standard Deviation Calculations<br />Standard Deviation measures the variability/dispersion of the particular variables (in this case, of GDP and Male Suicide Rates). We need the standard deviations of x and y in subsequent calculations <br /> <br />23.68 is the standard deviation of x, the Male Suicide Rates. <br />18122.92514 is the standard deviation of y, the GDP.<br />Least Squares Regression<br />Least Squares regression calculations identify the relationship between the independent variable, x, and the dependent variable, y. The least squares regression is given by the following formulae:<br /> where <br />y = 122.1159x +11148.69<br />y = 122.1159x +11148.69 is the equation of the least squares regression line for this particular set of data. <br />Pearson’s Correlation Coefficient<br />Pearson’s Correlation Coefficient indicates the strength of the relationship between the two variables (per capital income and male suicide rates). It is given by the following formula:<br />r = 0.1597<br />We can compare this to a standard table of coefficients of determination like the one on page 581 of our math textbook and see that an <br /> value or 0.255 represents a “very weak” correlation (Coad).<br />Chi-Square Test<br />Chi-Square test measures the independence of the two variables.<br />The following formulas are used:<br />Observed Values: <br />B1B2TotalA1aba+bA2cd c+dTotala+cb+dN<br />Calculations of Expected Values:<br />B1B2TotalA1a+bA2c+d Totala+cb+d N<br />Degrees of freedom measures the number of values in the calculation that can vary: <br />Df = (r - 1)(c – 1)<br />r; row c; column <br />Null Hypothesis: GDP and Male Suicide Rates are independent.<br />Alternative Hypothesis: GDP and Male Suicide Rates are not independent.<br />Male Suicide Rates (per 100,000 people)Table 2: Observation Values<br /> GDP ($ per capita)<br />0.1-20.5520.55 - 4141 – 61.4561.45 – 81.9Total 422.65-22707.89176533122707.89 – 44993.141410644993.14 – 67278.380100167278.38 – 89563.6301001Total18126339<br />There are too many zeros in this table, thus making it relatively unreliable for finding the results. <br />Table 3: Calculation of Expected Values<br />Male Suicide Rates (per 100,000 people)<br /> GDP ($ per capita)<br />0.1-20.5520.55 - 4141 – 61.4561.45 – 81.9Total 422.65-22707.893122707.89 – 44993.14644993.14 – 67278.38167278.38 – 89563.631Total18126339<br />Table 3 shows the individual calculations for each of the expected values<br />Table 4: Expected Values<br />Male Suicide Rates (per 100,000 people)<br />0.1-20.5520.55 - 4141 – 61.4561.45 – 81.9Total 422.65-22707.8914.3079.5384.7692.383122707.89 – 44993.142.7691.8460.9230.461644993.14 – 67278.380.4610.3070.1540.077167278.38 – 89563.630.4610.3070.1530.0771Total18126339<br />Df = (4-1)(4-1) = 9 9 degrees of freedom <br />For a significance level of 5% the critical value for 9 degrees of freedom is 16.919. <br />Since the chi square value for this investigation is over the critical value, the null hypothesis is confirmed. This indicates that male suicide rates and relative individual wealth of males in a country are independent. <br />Conclsion:<br />Table 5 : Interpretation of the Pearson’s Correlation CoefficientThe many tests done in this investigation point to the same conclusion; that the GDP per capita and Male Suicide Rate per capita of a country has no connection with eachother. The first mathematical evidence is the result of the Pearson’s Correlation Coefficient test which was 0.0255 as seen in Table 5, the result - which is remarkably close to 0.0 – shows no correlation. <br /> The chi square result, which was 8.1451, is also <br />CorrelationNegativePositiveNone−0.09 to 0.00.0 to 0.09Small−0.3 to −0.10.1 to 0.3Medium−0.5 to −0.30.3 to 0.5Large−1.0 to −0.50.5 to 1.0<br />significantly below the critical value which is 16.919, indicating that the null hypothesis is correct. <br />Limitations:<br />In analyzing the validity of the conclusion, a few important factors could be raised that could be limitations to the reliability of the data. <br />For one, the validy of the data collected from could be questioned. Although all data on NationMaster are backed by legitimate sources, recorded data is not always an accurate reflection of the actual situation in that nation. The method of collecting data varies in each nation and in many cases, many pieces of data go by unrecorded/misrecorded. An example of this is the statistics of the suicide rates in Egypt; as Dr. Mohamed Rakha, a psychiatric physician at Abbasiya Hospital states that many cases of suicide are not officially documented (Charbel). <br />“Very often families of suicide victims seek to cover-up, or to avoid mentioning that a family member has taken their own life.” He added that there are serious moral and religious stigmas involved: “Families do not want people to remember that their son or daughter died as a so-called apostate. Covering up a suicide is often perceived as the only way to preserve the reputation of the deceased, and the reputation of the family.” As Rakha states, each piece of evidence is merely the data that the government was able to surface and collect; they are not always reality.<br /> <br />Sources:<br />Charbel, Jano. “Egyptian suicide rate on the rise”. Al-Masry Al-Youm. 9 Oct <br />2010. 5 Nov 2010.<br />Coad, Mal. “Mathematics for the international student”. Adelaide Airport: Haese and Harris <br />Publications: 2004. <br />“Economy Statistics > GDP (per capita) (most recent) by country”. NationMaster. Web. 2010. 5 Nov <br />2010.<br />Harding, Andrew. “Japan’s Internet ‘suicide clubs’”. BBC. Web. 7 Dec 2004. 25 Nov 2010. <br />“Health Statistics > Suicide rate > Males (most recent) by country”. NationMaster. Web. 2010. 5 Nov <br />2010.<br />Young, Thomas W. “The Richard Cory Phenomenon: Suicide and Wealth in Kansas City, Missouri”. <br />Forensic Science Journal 50.2 (2003). Hawaii University. Web. 25 Nov 2010. <br />