(TIỂU LUẬN) the studied countries in the provided data set would be divided into three categories based on their GNI condition and the exposure to air pollution

INF ER EN Dang Thi Thuc Quyen s3818318 Table of Contents Introduction 2 Descriptive Statistics and Probability 2.1 Probability 2.2 Descriptive statistics Confidence intervals .5 Hypothesis Testing Conclusion .8 References 10 Appendices: 11 Dang Thi Thuc Quyen s3818318 Introduction In recent decades, air pollution is obviously a highly topical issue that costs the academia and the media countless research papers and communication attempts Air pollution is defined as a harmful concentration of key air pollutants such as particulate matter, carbon dioxide, nitrogen dioxide, sulfur dioxide and ground-level ozone in outdoor and indoor environment (WHO n.d) Scientifically, particulate matter (PM) especially the fine one (PM2.5) with a diameter of 2.5 μm or less, can penetrate deep inside human lung and enter the blood system (WHO 2016) Even with a little contact with very low concentration, PM2.5 possibly causes cardiovascular, respiratory disease and cancer Therefore, WHO (2005) stated it is imperative to determine human exposure to air pollution for further research on health impacts and preventions Because of its health-damaging impacts among all other air pollutants, PM2.5 is the most used indicator for measurement of air pollution (WHO 2005) in terms of daily or annual mean concentrations of micrograms per cubic meter of air volume (μg/m3) Moreover, WHO (2005) promulgated a global guideline in response of air quality assessment and air pollution management WHO guidelines set the maximum safe level for annual average PM2.5 concentration is equal or less than 10μg/m3 However, WHO (2018) also reported that 91% of the world population were exposing to PM2.5 air pollution concentrations that exceeds the WHO safety limit According to The World Bank (2019), the exposure to air pollution occurs in both urban and rural areas but the world is witnessing the much higher level in developing cities/countries than in the developed ones (Appendix 1) This highlights a direct relationship between mean annual exposure to air pollution and the Gross National Income (GNI) As WHO (2005) stated that clean air is surely basic need of human health and well-being, air pollution is one of the crucial determinants for sustainable development and highly relevant to climate change The reason for this connection is that fossil fuel combustion, which results from transport activities and energy consumption, is classified as the main driver of climate change as well as contribution of air pollution (WHO n.d.) Hence, the effort on mitigating the air pollution will ease the effect of climate change, then support the global sustainability This objective perfectly aligns with the nature of the United Nations’ 17 Sustainable Development Goals, especially the Goal 13: Take urgent action to combat climate change and its impacts Therefore, considerable yet immediate actions need to be taken hand in hand by not only giant organizations but also every individual (UNDP 2020) Overall, this paper aims to examine the relation between the GNI and mean annual exposure to PM2.5 air pollution by using descriptive statistics, inferential statistics, and probability to analyze the data set of 38 countries Dang Thi Thuc Quyen s3818318 Descriptive Statistics and Probability 2.1 Probability Ott (1982, p.195) concluded that human exposure is ‘the occurrence of the event that a pollutant (at a particular concentration) comes into contact with the physical boundary of the individual’ Then, the average annual exposure to air pollution which is greater than 33 μg/m3 is considered as a high level of exposure (H) On the other hand, different GNI level will determine different income level of that country:    Low-income countries (LI): with a GNI less than $1,000 per capita Middle-income countries (MI): with a GNI between $1,00 and $12,500 per capita High-income countries (HI): with a GNI greater than $12,500 per capita The studied countries in the provided data set would be divided into three categories based on their GNI condition and the exposure to air pollution (Appendix 2) High mean annual exposure to air pollution (H) Not high mean annual exposure to air pollution (N) Total Low-income countries (LI) Middle-income countries (MI) High-income countries (HI) 3 16 22 10 Total 20 18 38 Figure 1: Contingency table for country categories in terms of income and mean annual exposure to air pollution (μg/m3) a To determine if income level and mean annual exposure to air pollution are statistically independent or not, conditional probability of two related variables from two categories must be considered In this case, these variables would be high-income countries (HI) and high mean annual exposure to air pollution (H) P ( HI )= 10 = 38 19 P ( HI ∧ H ) 38 = = P ( HI|H )= 20 20 P(H ) 38 ≠ ) , high income and high mean annual exposure to air pollution 19 20 are not independent events and one event has certain effect on the probability of the other As P ( HI ) ≠ P ( HI|H ) ( Dang Thi Thuc Quyen s3818318 Hence, a conclusion can be established that income and mean annual exposure to air pollution are statistically dependent b The chance of one country category have high mean exposure to air pollution would be compared based on the probabilities of the high mean annual exposure to air pollution given an income level P(H∧LI ) 38 = = =0.5∨50 % P ( H|LI )= P( LI ) 38 16 P(H ∧MI) 38 P ( H|MI ) = = = ≈ 0.727∨72.7 % 22 11 P(MI ) 38 P(H∧HI ) 38 = = =0.1∨10 % P (H| HI) = P (HI ) 10 10 38 ⇒P ( H|MI ) > P ( H| LI ) > P ( H |HI ) } The above calculations show that countries with middle-income level is likely to suffer from high mean annual exposure to air pollution with the highest probability of 72.7% In addition, the probability for high-income countries is the lowest, probably thanks to the positive relationship between social prosperity and air quality 2.2 Descriptive statistics Low-income Middle-income High-income countries (LI) countries (MI) countries (HI) Mean 49.95 27.08 13.60 Median 31.05 20.85 9.87 Mode #N/A #N/A #N/A Figure 2: Table for central tendency of mean annual exposure to air pollution (μg/m3) Extremely Extremely >,, 99.73 -63.26 < 21.3 MI 64.76 < 71.8 -15.09 < 7.8 HI 22.32 < 41.12 -1.35 < 5.96 Figure 3: Comparison between extreme value and maximum, minimum value of mean exposure to air pollution (μg/m3) As Figure shown, this data set contains outliers, the values are excessively greater than the rest of the data Therefore, Mean is not the ideal approach for analysis since it is sensitive to outliers Dang Thi Thuc Quyen s3818318 Moreover, these are numerical data and no Mode is detected in this data set as well, so Mode is also not suitable at all In this case, Median appears to be the most effective measure among other central tendency methods The low-income category accounts for the highest median (31.05μg/m3), just units lower than the safety level of air quality (33μg/m3) Incidentally, this exactly matches with the probability calculation: P ( H |LI )=0.5∨50 % , both of them saying that 50% of low-income countries would undergo more than 31.05μg/m3 in PM2.5 air pollution and possibly high exposure to air pollution On the other hand, the median of high-income countries’ exposure to air pollution (9.87μg/m3) is nearly three times lower than the figure for low-income countries (31.05μg/m3) and a half of the figure for middle-income countries (20.85μg/m3) As a result, countries with high-income level has the best air quality and the low-income ones are likely to endure a dangerous amount of PM2.5 in air Confidence intervals a Caculation In this case, 95% would be randomly chosen to be confidence level in order to estimate the confidence interval Population standard of deviation ( Unknown μg/m3 σ¿ Sample standard of deviation (S) 22.73 μg/m3 27.15 μg/m3 Sample mean ( X ) Sample size (n) 38 countries Confidence level (1-α) 95 % t-critical value ±2.03 Figure 4: Statistics summary table for mean annual exposure to air pollution As the sample size is 38 which is higher than 30, Central Limit Theorem (CLT) is applied and the sampling distribution becomes normally distributed Because the population standard deviation ( σ ¿ is unknown, the sample standard deviation (S) is substituted, and the Student’s t table would be used  Calculate confidence interval: ⇒μ=27.15 ±2.03 μ= X +t( S ) √n =27.15 ±7.49 ( 22.73 √ 38 ) ⇒19.66 ≤ μ≤ 34.64  Interpretation: With 95% of confidence, we can say that the world average of mean annual exposure to air pollution is between 19.66μg/m3 and 34.64μg/m3 b Assumption Dang Thi Thuc Quyen s3818318 In spite of missing the population standard deviation, there is no requirement for any assumption because the sample size is 38 which is higher than 30, therefore, Central Limit Theorem (CLT) is applicable and the sampling distribution is normally distributed c Supposing that world standard deviation of mean annual exposure to air pollution is known, implying that all the values in the entire population are collected and population mean is easily calculated Thus, there is no need to conduct inferential statistics to estimate the population mean, no standard error of the mean would be committed because there is no variation between sample to sample (Levine et al 2016) σ S ) and μ= X +t( ) , we can see that the √n √n major difference of knowing the world standard deviation is the use of the z-value instead of the t-value According to McEvoy (2013), because t-distribution shape looks flatter than the zdistribution one (figure 5), the t-value is slightly bigger than z-value when the sample size is small And when the critical value is larger, confidence interval becomes wider, violating in the inverse relationship: the narrower confidence interval width, the higher accuracy In addition, looking at the equations: μ= X +Z ( Figure 5: Adapted from A Guide to Business Statistics (McEvoy 2018) In short, using the world standard deviation of mean exposure to air pollution will reduce the confidence interval but the result will be more exact Hypothesis Testing a According to The World Bank (2020), during the 27-year period, the mean annual exposure to air pollution saw a rapid increase from 44.3μg/m3 (1990) and peaked 50.8μg/m3 (2011), then the figure gradually decreased to 45.2μg/m3 in 2016 Based on the calculated confidence interval above (19.66 ≤ μ ≤ 34.64) , the global mean annual exposure to air pollution is expected to decline in the future Population standard of deviation ( σ¿ Sample standard of deviation (S) Sample mean ( X ) Sample size (n) Confidence level (1-α) Unknown μg/m3 22.73 27.15 38 95 μg/m3 μg/m3 countries % Dang Thi Thuc Quyen s3818318 Figure 6: Statistics summary table, mean annual exposure to air pollution Hypothesis Testing (Critical Value approach) Step 1: Check for Central Limit Theorem (CLT) Since the sample size (n=38) is larger than 30, it is applicable to use CLT and the sampling distribution is normally distributed { The null hypothesis H ;μ ≥ 45.2 The alternativehypothesis H ; μ