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

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

INF ER EN

Table of Contents

1 Introduction 2

2 Descriptive Statistics and Probability 2

2.1 Probability 3

2.2 Descriptive statistics 4

3 Confidence intervals 5

4 Hypothesis Testing 6

5 Conclusion 8

6 References 10

7 Appendices: 11

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1 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 μmmor less, can penetrate deep inside human lung and enter the blood system (WHO 2016)

Evenwith 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 (μmg/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 10μmg/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

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2 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 μmg/

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)

pollution (H) air pollution (N) Low-income

countries (LI)

Middle-income

countries (MI)

High-income

countries (HI)

Figure 1: Contingency table for country categories in terms of income and

mean annual exposure to air pollution (μmg/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

= 5

38 19

1

P HI|H )= P (HI ∧H )

= 38 = 1

38

As P (HI )≠ P ( HI|H )( 5 ≠ 1

) , 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

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

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P ( H|LI )= P(H∧LI )= 38= 1 =0.5∨50 %

38 16

}

P (H|MI )=P(H ∧MI)

≈ 0.727∨72.7 %

38 1

P (H|HI) =

=0.1∨10 %

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

Figure 2: Table for central tendency of mean annual exposure to air pollution (μmg/m3)

Extremely

>,<,= Maximum Extremely >,<,= Minimum

Figure 3: Comparison between extreme value and maximum, minimum

value of mean exposure to air pollution (μmg/m3)

As Figure 3 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.

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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 (31.05μmg/m3), just 2 units lower than the safety level of air quality (33μmg/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 31.05μmg/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

(9.87μmg/m3) is nearly three times lower than the figure for low-income countries (31.05μmg/

m3) and a half of the figure for middle-income countries (20.85μmg/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

3 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 (

σ ¿

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= X

+t

( S )

√n

(22.73 )

⇒μ=27.15 ±2.03 √38 =27.15 ±7.49

⇒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 19.66μmg/m3 and 34.64μmg/m3

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)

In addition, looking at the equations: μ=X+Z( σ ) and μ= X +t( S ) , we can see that the

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 z-distribution 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

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

4 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 44.3μmg/m3 (1990) and peaked 50.8μmg/m3

(2011), then the figure gradually decreased to 45.2μmg/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 ( Unknown μg/mg/m 3

σ ¿

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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 0 ;μ ≥μ ≥ 45.2

Step 2: Determine hypothesis

The alternativehypothesis H 1 ;μ ≥ μ<45.2(claim)

Step 3: Based on the alternative hypothesis above, H1 contains ‘<’, thus lower-tailed test would be used

Step 4: Because there is no population standard deviation ( σ ¿ provided and the

sampling distribution is normally distributed, we use the T-table

Step 5: Determine critical value

Level of significance α=0.05

}⇒t=−1.69

Degrees of freedom d f =37

Lower−tailed test

Step 6: Calculate test statistic

Step 7: Make statistical decision.

As t ' (−4.895 )<t (−1.69 ) , the test statistic falls in Rejection Region, hence we reject H

0 and accept H

1

Step 8: Explanation

As we reject H0 , hence with 95% level of confidence, we can say that the mean annual

exposure to air pollution will decrease in the future

Step 9:

As we reject H0 , we might have committed Type I error, P(Type I) = α = 0.05 = 5% This

means there is still 5% of chance that the mean annual exposure to air pollution will decrease

in the future but actually it might not decrease in the future

b Tripple sample size

Supposing the number of countries in the data set will triple, the aforementioned

hypothesis testing conclusion remains unaffected, yet more precise

Actually, the increase in the number of countries will directly lead to the increase in the sample size (n) and the degrees of freedom (d.f) As a result, the t distribution gradually comes nearer the standardised normal distribution, then the larger the sample size, the more identical these distribution shape (Figure 7) When the sample size is big enough, there will be a little difference between t and Z distribution, therefore, the population standard deviation would be more accurately estimated (Berenson 2015)

Figure 7: Standardised normal distribution and t distribution for 5 degrees of freedom,

adopted from Basic Business Statistics EBook (Berenson 2015).

According to Bowerman, Froelich and Duckworth (2018), bigger sample size can decrease the margin of error in the confidence interval By increase the sample size, we can gather more information about the studied population, hence we can make better estimation This will narrow the confidence interval, we can gain more statistical power and greater precision (Littler 2015), reducing the uncertainty and enhancing the accuracy

5 Conclusion

After calculating and analyzing the relevance of income and the mean annual exposure to air

pollution, the above inferential statistics gives us some key findings discussed as below.

Firstly, income level of a country is strongly associated to its mean annual exposure to air pollution, meaning that low-income countries with GNI of lower than $1,000 per capita will face higher

concentrations of key pollutants such as PM2.5, while high-income countries with GNI of higher than

$12,500 is likely to have better air quality Specifically, richer consumers tend to

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demand better quality products with more environmentally friendly features, which acts as

an incentive for the suppliers to induce better technology to reduce factory air pollutants (Carson, Jeon & McCubbin 1997) Another reason might lie on the lack of regulations on waste management while doing industrial activities in developing countries at the expense

of environmental justices (Hajat, Hsia & O’Neill 2015)

Secondly, it is calculated that 50% of low-income countries have a higher possibility of

experiencing harmful air condition of 31.05μmg/m3 On the other hand, the mean annual

exposure to air pollution of middle-income countries tends to vary around (20.85μmg/m3) Moreover, countries with high-income level have the lowest median of mean annual

exposure to air pollution at (9.87μmg/m3) These figures again strengthen the income-pollution relationship stated in the previous paragraph

Thirdly, we are 95% confident that the world mean annual exposure to air pollution will decrease in the future As calculated above, the global mean exposure to air pollution in 2016

is significantly higher than the confidence interval for 2017 figure, therefore, we could come

to conclusion that global mean annual concentration of PM2.5 is likely to decline in the future based on the hypothesis testing result

To make these predictions become reality, some measures need to be taken to achieve

sustainable future In accordance with the Paris Agreement aiming to maintain the global temperature rise below two-degree Celsius above pre-industrial level, the UN encourages all countries to regulate financial flows, adopt new technology framework to enhance its ability

to deal with climate change (UNDP 2020) With the increasing concerns about the planet sustainability in long run and the impacts of climate change on the poor, especially air

pollution in this case, it is important to balance the economic development and the natural capital (Lange, Wodon & Carey 2018) Furthermore, Pope, Ezzati and Dockery (2015)

suggested that there is no tradeoff in economic growth and air pollution reduction, meaning that all countries can attempt to have better air quality while develop their economic health Individually, everyone should prepare better environmental awareness and actively protect themselves from long term exposing to air pollutant

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