INDIVIDUAL CASE STUDY ANALYSIS ASSIGNMENT 2 why is it critical to check to mean annual openness to air pollution

Table 1: country classifications by group dependent on Gross National Income in 2017 Unit: current US$ per capita Furthermore, there are two distinct groups which are defined by the mean

INDIVIDUAL CASE STUDY

ANALYSIS - ASSIGNMENT 2

Student: Tran Hoang Long S-ID: S3878257

Class group: SGS-G15 Lecturer: Ha Thanh Nguyen Semester: Semester B 2021

Word Count: 2998 (Excluding cover page, table of contents, references, appendices)

Sarkar, S., Chauhan, A., Kumar, R., &

Singh, R P (2019) Impact of deadly

dust storms (May 2018) on air quality,

meteorological, and atmospheric

parameters over the northern parts of

India GeoHealth, 3 , 6 7 –80

Sarkar, S., Chauhan, A., Kumar, R., &

Singh, R P (2019) Impact of deadly

dust storms (May 2018) on air quality,

meteorological, and atmospheric

parameters over the northern parts of

India GeoHealth, 3 , 6 7 –80

Table of Contents

I Introduction 2

II Descriptive Statistics and Probability 2

1 Probability 2

a Test of statistical dependence 3

b Country category identification 3

2 Descriptive Statistics 3

a Measure of Central Tendency 4

b Measure of Variation 4

III Confidence Intervals 5

1 Calculation 5

2 Discussion on assumptions 5

3 Discussion on the confidence interval results 6

IV Hypothesis Testing 6

1 Trend of the world average annual mean exposure 6

2 Hypothesis Testing 6

3 Discussion on hypothesis testing results 8

V Conclusion 9

VI References 10 VII Appendices 12

I Introduction

Global description: According to the World Health Organization 2016, over 90% of people

worldwide live in polluted air places (Pirlea & Huang 2019) The leading causes of ambient air pollution include vehicles, coal-fired power plants, industrial emissions, and human activity, based on the State of the Air 2019 report (Pirlea & Huang 2019) Besides, Sarkar et al (2019) found that air quality is also affected by dust storms, deserts and causes severe consequences for human health Especially, air pollution is the main reason for mortality in low-to-middle-income nations (Netula 2021) Nearly 60% of deaths in the WHO's Southeast Asia and Western Pacific areas are attributable to air pollution, with 90% of cases ascribed to cardiovascular illness, stroke, cellular breakdown in the lungs, and intense respiratory diseases (Geneva 2016) Dr Flavia Bustreo - an associate chief general of Who, states that women, youngsters, and seniors are the most vulnerable to the impacts of air contamination (Worland 2016)

Why is it critical to check to mean annual openness to air pollution? Monitoring exposure to

air pollution is essential for estimating health impacts and calculating disease burden from ambient air pollution (World Health Organization 2018) Therefore, concentrations in air

pollutants will significantly reduce, helping to reduce the health burden, greenhouse gas

emissions, and impacts of global warming (World Health Organization 2010) Furthermore, according to the UNFCCC, this is part of SDG 13, which is urgent action against climate change

to relieve poverty, prosper a healthy planet, and pass it on to the next generation (Figueres 2015) Hence, as a target of SDG, monitoring exposure to air pollution will considerably decrease the quantity of passings and diseases and adverse effects on the environment by 2030 (Elder 2016)

Relationship between GNI and mean annual exposure to air pollution: It tends to be a

significant association between atmospheric pollution levels, suicide rates, and climate change The change in GNI per capita has important implications for temperature, suicide, and future annual studies are needed to determine the link between suicide and air pollution (Heo, Lee & Bell 2021) According to World Health Organization 2019, most suicides are estimated to occur

in low-and center income nations According to the latest global data from WHO, air pollution kills 7 million individuals per year, mainly in emerging countries (Watts 2018) Dr Ghebreyesus,

a WHO's executive director, said that the poor suffer the most from air pollution (Watts 2018)

II Descriptive Statistics and Probability

1 Probability

The case study incorporates an aggregate of 44 nations, which are categorized into three

gatherings relying upon their Gross National Income (GNI)

Table 1: country classifications by group dependent on Gross National Income in 2017 (Unit:

current US$ per capita)

Furthermore, there are two distinct groups which are defined by the mean yearly exposure of this test, with 33 micrograms as norm The contingency table below presents the following figures:

High Mean Annual Exposure (H) Low Mean Annual Exposure (L) Total

Table 2: table of contingencies depending on income levels and regardless of whether

individuals are presented to air pollution in 2017

a Test of statistical dependence

Here is the mathematical proof to compare the elevation of income countries with mean annual exposure P(H/HI) and the rate of determination for all high altitude countries, which is P(H) The purpose of the work was to determine whether annual income and exposure were statistically dependent or independent

P (H/HI) = 1/11 = 0.09

P (H) = 11/44 = 0.25

Þ P (H | HI) P (H); (0.09

According to the above estimate, the probability of high mean annual exposure for high-income nations is not equal to high mean annual exposure for all countries Therefore, national income and average yearly exposure are statistically dependent events It indicates that the moderate yearly exposure has an impact on the worth of a country's income

b Country category identification

To determine the country categories most likely to be exposed to average annual air pollution, the study uses probabilities based on different proportions of three different country groups: high-income, middle-income and low-income

P (H / HI) = 1/11 = 0.09 = 9%

P (H / MI) = 9/28 = 0.32 = 32%

P (H / LI) = 1/5 = 0.2 = 20%

As the estimation above, countries with a middle-income have a 32% chance of being exposed to average air pollution per year This demonstrates that middle-income nations are more vulnerable

to air pollution than the other two categories of countries

2 Descriptive Statistics

Min >,<,= Lower Bound Max >,<,= Upper Bound Result

outliers

Table 3: outliers test of three country group in 2017 (unit: micrograms per cubic meter)

a Measure of Central Tendency

High-income countires Middle-income countries Low-income countries

-Table 4: table of contingencies depending on income levels and regardless of whether individuals are presented to air pollution (unit: micrograms per cubic meter)

Because there is no mode in all three categories of nations, mean and median are the two most effective replacements, according to table 4 However, there are two outliers in the above

calculation table (table 3); the mean will not be chosen because it is easily affected by outliers Therefore, the only suitable measure of central tendency is the median Table 4 shows that the median for middle-income nations is the highest, at 23.925 micrograms per cubic meter The median of low-income nations is lower than middle-income countries, although the difference is negligible (22.54 micrograms) Finally, high-income nations have just 13.43 micrograms, 1.78 and 1.67 times less than middle- and low-income countries, respectively Hence, a comparison of nations' medians illustrates that low-and center incomes countries are more probable than

P (H / MI) > P (H / LI) > P (H / HI)Þ

wealthy countries, particularly middle-income countries, to be harmed by air pollution Low- and middle-income nations should increase their per capita income (GNI) to decrease the danger of air contamination Moreover, the people's health and national economy are both seriously affected As a result, these governments may decrease loan interest rates and give financial support to low-income households, according to the United Nations Environment Programme (Steiner n.d.)

b Measure of Variation

High-income Middle-income Low-income

Table 5: Variation of each country category on Mean Annual Exposure in 2017 (unit:

micrograms per cubic meter)

There are outliers in all three groups where factors such as range, standard deviation, or the coefficient of variation are primarily sensitive to outliers IQR plays a vital role in determining if the data is truly an outlier, so it is the most suitable tool because of not being affected by any outliers (Taylor 2018) Regarding table 5, the IQR of middle-income countries accounts for 20.77 micrograms per cubic meter which is significantly more than low-income countries and high-income countries In particular, the IQR of middle-income countries is 9.14 times more than those of low-income countries and more than double that of high-income countries It indicates that air pollution has the most significant impact on middle-income countries' economic

activities, health care, or value of life concerns In addition to improving the average income for people, middle-income countries need to take measures to effectively consider moderate

exposure to the effects of climate change and air pollution These countries should conserve and sustainably manage the economic value of their forests and ecological services to address climate change (Steiner n.d.) Besides, the combination of technologies such as using wind, electricity in residential and industrial areas is also an ideal solution to air pollution (Jacobson 2009)

III Confidence Intervals

1 Calculation

To compute the confidence intervals for the global average of mean annual air pollution

exposure, 95% is assumed for the estimate The data table is below:

Table 6: Statistics summary table of normal mean yearly exposure to polluted air around the

world in 2017 (unit: micrograms per cubic meter)

As the population standard deviation is not provided, the sample standard deviation is

substituted In this situation, the student's t-Table is applied instead of the z-Table

● t-Table

Degree of freedom: d x f = n – 1 = 43

Significance level: a = 0.05

● Confidence Interval:

Þ 20.468 ≤ ≤ 31.103�

 The calculation indicates that that the worldwide ordinary of mean yearly openness to air pollution ranges between 20.468 and 31.103 micrograms per cubic with 95% confidence

2 Discussion on assumptions

Table 6 shows that the sample size (n) is 44, larger than the usual sample size of 30, implying that the Central Limit Theorem (LCT) is pertinent and the sampling distribution is ordinarily issued Hence, there is no assumption required despite the unknown population standard

deviation

3 Discussion on the confidence interval results

In cases where the population standard deviation is known, the z-value will be used because of having the appropriate sample size and population standard deviation We have the formula following the recognized population standard deviation:

The population and the standard deviation (S) measure change but still vary significantly from sample to sample They represent the distinction between parameter (population standard deviation) and statistical (sample standard deviation) Furthermore, the sample standard

deviation is more significant than the population because it has a sizeable sample-based

variability (Taylor 2019) Therefore, it leads to a lot of uncertainty in the statistical data

(Anderson 2014) As the confidence interval is smaller, the uncertainty also decreases because the confidence interval is a measure of tension and excludes other parameter values (Gelman & Greenland 2019) According to Hazra 2017, the critical z-value is determined by the level of confidence From the formula above, the confidence level is proportional to the z-value, which means that increasing the z value also widens the confidence interval, leading to less precise results On the other hand, the margin of error (e) is determined by the sample size, so the length

of the sample is considerable, then the width of the confidence interval will also be narrowed (Hazra 2017) Therefore, a lower confidence level will ensure more accurate results and more minor errors

Þ t-critical value: t = ± 2.0167

IV Hypothesis Testing

1 Trend of the world average annual mean exposure

As indicated by the World Health Organization 2016, the world standard yearly mean openness

to air pollution amounts to 45.2 micrograms per cubic meter, while the calculation from the previous part indicates that the yearly mean exposure ranged from 20,468 to 31,103 micrograms

in 2017 In comparing annual mean exposure levels between 2016 and 2017, there is a

substantial drop from 45.2 to the maximum confidence interval of 31.103, roughly 1.45 times Furthermore, according to the State of Global Air n.d., global average PM2.5 exposure declined marginally from 2010 to 2019 Therefore, we anticipate that world normal yearly mean openness

to air contamination will keep on falling later on, which is likewise a decent sign for worldwide wellbeing and the economy

2 Hypothesis Testing

Table 7: Statistics summary table of hypothesis testing (unit: micrograms per cubic meter)

Step 1: Check the CLT: the sample size n is 44 that is greater than the standard 30, so the Central

Limit Theorem is applicable, indicating that the sampling distribution of mean is normally distributed

Step 2: State null and alternative hypotheses:

Null hypothesis ; 45.2 �

Alternative hypothesis ; 45.2 (claim)�

Step 3: Choose rejection region: lower-tailed test is applied with the alternative hypothesis

containing “<”

Step 4: Choose table: since the population standard deviation is unidentified and the mean � sampling distribution is regularly distributed, we apply the t-Table

Step 5: Determine critical value (CV):

Degree of freedom: d x f = n – 1 = 43

Significance level: a = 0.05

Þ lower-tailed test, t = 1.681

Step 6: Calculate test statistic:

t’ =

Step 7: Make statistic decision:

With -7.363 (t’) < -1.681 < 1.681 (t), the test measurement lies in the non-rejection zone Hence,

we do not dismiss the (null hypothesis) and reject (alternative hypothesis)

The t-distribution graph is showed below:

-10 -8 -6 -4 -2 0 2 4 6 8 10

Step 8: Managerial decision

As the is not dismissed and with 95% degree of confidence, we may assume that the worldwide average yearly mean openness to air contamination in 2017 is under 45.2 micrograms per cubic meter leading to a further downtrend from this moment

Step 9: Identify the error type

In the instance of removing , we most likely made a Type II error () Although we believe there is insufficient evidence to suggest that the worldwide mean yearly openness to polluted air can raise, the fact is that this level of exposure is unlikely to fall entirely in the future years While using the power of hypothesis test P (type II error) = 1 - , increasing the sample size (n) or the significance level (α) are the two best approaches to optimize error removal To account for this solution, at the point when the null hypothesis is valid, increasing the level of α is regarded as the highest likelihood that the test statistic will fall into the rejection zone (Pernet 2016) However, increasing the sample size should be more leveraged because it would minimize the

unpredictability of the statistic in issue (Bill 2017), namely gathering data from just 44 nations out of a total of 195 throughout the world

3 Discussion on hypothesis testing results

Rejection region

t = -1.681

t’ = -7.363

Non-rejection region

Assuming the number of countries triples, the sample size and the degree of freedom will also increase because they are closely related (Frost n.d.) Amongst the most noteworthy features of the t-distribution is that the more degrees of freedom, the closer the t-distribution is to the

standard normal distribution (Anderson n.d.) This also implies that the t-distribution curve will

be higher and thinner, with a shorter gap between it and the standard typical allocation

Therefore, the larger the sample size, the greater the accuracy because the sample size is

inversely related to standard error (Ramsey 2016), resulting in a decrease in standard error as the number of nations (n) tripled Furthermore, the actual population mean is closer to the sample mean, then the standard deviation (S) is lowered since the data distribution is less varied (Salkind

& Frey 2019) With the formula t = , t and t' will come closer together (both in the rejection zone) as n increases and S gets smaller However, when the two critical values change, the data's test score cannot simply pass through the rejection district Subsequently, the statistical decision will stay unaltered while tripling the number of countries

V Conclusion

To conclude, this is a report that analyzes and compiles available data on average annual air pollution exposure from 44 countries Right from the first overview assessment, the Gross National Income (GNI) and the mean annual exposure (MAX) relate closely, as shown by the levels of exposure in relatively middle-income countries are higher than in high-income ones In addition, we estimate that the average exposure to dirty air decreases to a decrease in the future

We express these observations through three main vital findings

Our first finding is based on probabilistic computation, which includes two dependent events, MAX and GNI The contingency table further explains this calculation, generating various sampling models through multiple shapes and sizes (Fienberg 2005) Specifically, middle-income countries have the highest probability that their openness to air contamination is highest, trailed by low-paid nations Our following finding concentrates on measures of two factors, central tendency and variation, supported by descriptive statistics This finding implies that the median micrograms of low- and middle-income countries are almost half higher than those of high-income countries While the middle-income countries continue to lead the group of

countries exposed to air pollution with the median micrograms per cubic meter near 24 and the interquartile more than twice as high as the wealthy countries and almost ten times higher than the poor countries, further confirms the strong inverse relationship between MAX and GNI Our final finding is expressed from the confidence interval and the hypothesis test The calculation indicates that the worldwide normal of mean yearly openness to air contamination in 2017 lies in the range of 20,468 and 31,103 micrograms per cubic meter, which shows signs of decline compared to 45.2 micrograms of the world MAX 2016 In addition, the increase in the number of countries tripled, the outcomes are also more accurate However, while we have 95% confidence that this average exposure would decrease in the future, the reality remains uncertain

From the findings presented, the world normal of mean yearly openness to pollution of the air could become one of the issues that need to be considered and devised an effective improvement strategy in the Sustainable Development Goals (SDG) for 2030 of The United Nations Because pollution is considered the most dangerous threat to human health, which increases mortality (Netula 2021) Therefore, another deeper aspects such as the health system, social status,