Assessment name individual case study inferential statistics

As well as the level of exposure to air pollution, in this case, countries that have a mean annual exposure to air pollution higher than 33 micrograms per cubic meter μg/m is considered

Inferential Statistics

Assessment 2

Course code and name: ECON1193 - Business Statistics 1

Assessment name: Individual Case Study - Inferential Statistics

Word count: 2572

Air pollution Dataset #4

PART 1: Introduction

According to the 2019 World Air Quality Report by IQAir, amongst the environmental health risks faced by the global population, air pollution constitutes the most imperative one WHO (2018) listed particulate matter (PM) as a common proxy indicator for air pollution due to its exceptionally detrimental health impacts In this case study, mean annual exposure to PM2.5 is the key focus of all calculation and prediction This pollutant’s effects to human health are the most disastrous Its microscopic size of 2.5 microns lets these particles penetrate the human body via breath, deeply absorbed into the bloodstream and cause far-reaching health effects The WHO noted that an annual mean exposure threshold of 10 μg/m can lessen the impacts of PM2.5, 3 however, there is no level of exposure to this pollutant that is safe for humans (IQAir 2019) Apart from its culpability in harming human health, PM2.5 also hurts the environment in

different ways, such as acid deposition, increased ozone levels and damage to marine lives and vegetation (IQAir 2021) In fact, the UNECE (n.d.) named particulate matter as one of the short-lived climate pollutants (SCLPs), which means that it is an air pollutant and is also climate-relevant Monitoring the Mean annual exposure to air pollution is aligned with the United Nation SDG 13 goal: Climate Change as is a global effort to keep track of the level of PM

concentrations in the air and ‘retaliate’ accordingly

Ritchie & Roser (2019) reported that the mean annual exposure of 95% of the world population transcends WHO limits, and this is applicable for both high and low-to-middle income nations Nevertheless, the majority of the population in most low-to-middle income countries is put at the risk of pollution levels above 35 μg/m (Appendix 1) Similarly, as reported by WHO (2006), the 3 highest levels of air pollution are to be found in the low- and middle-income countries of Asia

As Gross National Income (GNI) delivers a total measure of income (WHO n.d.), these

information somewhat indicates the relationship between mean annual exposure and GNI Overall, the purpose of this case study is to evaluate the relation bewtween mean annual

exposure and GNI of countries, as well as to estimate the mean annual exposure to air pollution value and rate, with the support of statistics

PART 2: Probability and Descriptive Statistics

1

a Probability

25 countries in the data set will be categorized based on their GNI, specifically:

 Low-Income countries (LI): GNI < $1,000 per capita

 Middle- Income countries (MI): GNI between $1,000 and $12,500 per capita

 High-Income countries (HI): GNI > $12,500 per capita

As well as the level of exposure to air pollution, in this case, countries that have a mean annual exposure to air pollution higher than 33 micrograms per cubic meter (μg/m ) is considered as 3

“High 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

Middle-income

High-income

Table 1: Contingency table of country category based on income and mean annual exposure to air pollution

 To figure out whether income and mean annual exposure to air pollution are statistically independent events or not, the conditional probability of high-income countries (HI) given that they have high mean annual exposure to air pollution (H) and the marginal probability of the high-income countries (HI) will be examined:

As two events are only statistical independent when them conditional probability equals to the marginal probability, this means that high income and high mean annual exposure to air

pollution are not Instead, they are dependent To conclude, income and mean annual exposure to air pollution are statistically dependent, which means that the income of a country influences its mean annual exposure to air pollution

 To determine which country categor have more chance of having high mean annual y exposure to air pollution, the conditional probability of high mean annual exposure to air pollution given the income level (high, middle, low) will be calculated:

It can be interpreted from the calculations above that no high-income countries face high mean annual exposure to air pollution This percentage is impressive as for low and middle-income countries, the situation is not so good Actually, for low-income countries, they have the highest chance of dealing with high mean annual exposure to air pollution

b Descriptive Statistics

Measures of central

tendency

Low-income countries (LI) >,<,=

Middle-income countries (MI) >,<,=

High-income countries (HI)

Table 2: Measures of central tendency of mean annual exposure to air pollution (μg/m )3

3

In this data set, there is no existence of outliers, hence Median cannot be utilized Furthermore, the Mode certainly cannot be used as they are not to be found in this data set Consequently, Mean is the most idealistic measure The fact that Low-income countries own the highest Mean (32.199 μg/m ) is conspicuous This indicate that these countries in general are on the verge of 3 reaching the high level of exposure to air pollution, which is 33 μg/m Middle-income countries’3 Mean, despite being smaller compared to Low-income countries’ one, is still concerning as it only 2.544 μg/m short from reaching the high level of exposure As for High-income countries, 3 their Mean overall are significantly smaller than the other two Actually, they are somewhat aligned with WHO’s annual mean exposure limit of 10 μg/m 3

Measures of variation Low-income

countries (LI)

>,<,= Middle-income

countries (MI)

>,<,

=

High-income countries (HI)

Interquartile Range 6.385 < 21.218 > 4.418 Standard Deviation 5.558 < 20.053 > 3.812 Sample Variance 30.893 < 402.142 > 14.536 Coefficient of Variation

(%)

Table 3: Measures of central variation of mean annual exposure to air pollution (μg/m )3

Albeit there are no outliers in the data set, the appearances of unequal Mean and SD as seen in table one and three make it certain that Coefficient of Variation (%) is the most appropriate measure The highest CV belongs to Middle-income countries (66%), which means that the countries in this category have the highest degree of mean annual exposure to air pollution disparity As for High-income countries, their CV suggests that their mean annual exposure to air pollution ratio experiences a moderate spread from the Mean value Lastly, Low-income

countries’ mean annual exposure to air pollution is the least disperse and tends to revolve around their average value of 32.199 μg/m 3

PART 3: Confidence intervals

a Calculation

The confidence level chosen to calculate confidence interval of mean annual exposure to air pollution is 95%

Population standard deviation ( unknown Sample standard deviation (S) 17.909 Sample mean () 25.932 Sample size (n) 25 Confidence level (1-α) 95%

The sample size is 25, which is smaller than 30, hence the Central Limit Theorem (CLT) cannot

be applied Besides, the distribution of the sample is unknown In this situation, the sampling distribution will be assumed that it is normally distributed Since the population standard deviation ( ) is unknown, sample standard deviation (S) will be used instead, which means the s Student’s t-table will be utilized

Degree of freedom: d.f = n-1=24

Significance level: α =0.05

Confidence interval:

With 95% of confidence, the mean annual exposure to air pollution of the world in 2017

is between μg/m and 33.321μg/m 3 3

b Assumption

5

t = ±2.063

Apart from the missing population standard deviation, the sample size of 25 is not sufficient to apply the CLT, which requires the sample size to be larger than 30 Therefore, the assumption that the sampling distribution is normally distributed have to be made in order to carry out the calculation

c If the world standard deviation (σ) of mean annual exposure to air pollution is available, the value will be used instead of t-value, which means replacing t-distribution with z-distribution This will minimize the degree of variability as standard normal distribution (z- distribution) has smaller standard deviation and variance compared to t-distribution (Anderson 2014) Confidence interval uses the variability of the data to judge the

estimated statistics’s accuracy, the less the degree of variability is, the more precise (smaller) it gets (NEDARC n.d.) As a result, the confidence interval in this case, will decrease

Generally, t-distributions shape is almost identical with normal distribution shape (bell-shaped and symmetric), however, it has a thicker tail (Greeni 2021) (Appendix 3) This is due to the fact that sample standard deviation (S) is used in t-distributions, as S is

mutable from sample to sample, it creates extra uncertainty (Greeni 2021) In contrary, the standard deviation (σ) used in z-distributions create more stability All of this

indicates that t-distributions possesses more uncertainty compared to the z-distribution Consequently, when z-value is used, confidence interval will be more accurate, as its distribution is more stable

PART 4: Hypothesis Testing

a Based on the data provided by The World Bank (2017) about the world mean annual exposure to air pollution, after reaching the peak of 50.8μg/m in 2011, it has started 3

to decline (whereas increase still resurfaces in some years) Then, in 2016, the mean annual exposure to air pollution dropped to 45.2μg/m With the confidence interval 3

of calculated in part 3a, the global mean annual exposure to air pollution is predicted

to decrease in the future

Population standard deviation ( unknown Sample standard deviation (S) 17.909 Sample mean () 25.932 Sample size (n) 25 Confidence level (1-α) 95%

Step 1: Check for CLT

The CLT is not applicable since the sample size is smaller than 30 (n=25) In this case, the sample is assumed to be normally distributed

Step 2: Determine hypothesis

Step 3: Since the , ’s sign is ‘<’, the lower-tailed test will be used

Step 4: Because the population standard deviation ( is unknown and the sampling distribution is normally distributed, T-table will be utilized

Step 5: Determine critical value

-1.71

Step 6: Calculate test statistic

Step 7: Make statistical decision

Since , the test statistic falls in Rejection Region, thus we accept and reject

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Step 8: Explanation

Because is rejected, therefore, with 95% level of confidence, we conclude that the mean annual exposure to air pollution will decline in the future

Step 9:

We can possibly commit Type I error, P (Type I) = = 0.05 = 5% as we reject Meaning that there

is a 5% chance that the mean annual exposure to air pollution will not decrease in the future

b If the number of countries in the dataset triples, the statistical decision will remain the same and even get more accurate

Looking at this formula: , it can be interpreted that as n increases, decreases In that case, would move further to the left (negative) side and still be in the Rejection Region, which in turn making the statistical decision remains correct and does not need to be changed

Technically, as the number of countries grows, it will raise the sample size (n) as well

as the degrees of freedom (d.f) Gradually, the t-distribution will get more and more identical to the z-distribution (Greeni, 2021) (Appendix 4) In fact, when n , normal distribution can be use in place of a t-distribution (jmp n.d.) And when z-distribution

is used, the degree of certainty increase Additionally, as stated by Budiu (2021), confidence interval is narrowed as sample size grows and is proportional to

variability Therefore, when the sample size (number of countries of the dataset) increases threefold, the results will get more precise

Part 5: Overall conclusion

There is a mutual message that part one and two deliver: Countries’ mean annual exposure to air pollution is associated with their income (GNI) As a matter of fact, the low-to-middle income

countries face the most severe levels of air pollution, whilst high-income ones experience lowest air pollution in decades (Ritchie & Roser 2019) These are technically proven by part two calculations:

 Firstly, the conclusion of statistical dependency between income and mean annual exposure to air pollution demonstrates the close relationship of those two factors of countries This is further supported by the conditional probability of high mean annual exposure to air pollution given the income level While high-income countries face no risk of high mean annual exposure to air pollution, middle- and low-income countries suffer from that tribulation greatly

 Secondly, the measures of central tendency and variation of mean annual exposure to air pollution together show that low-income countries’ mean annual exposure to air pollution value is the highest, and this applies to most countries in this category Furthermore, mean annual exposure to air pollution of middle-income countries is also alarming, although not all of these countries experience the same condition In contrary, high-income countries’ mean annual exposure to air pollution is the smallest

This circumstance can be explained by the fact that richer countries possess less polluting production technology, besides, wealthy consumers demand improved environmental quality (Carson, Jeon & McCubbin 1997) Contrarily, UNEP (2019) observed that laws in developing countries are either weak or not applied Furthermore, indoor combustion of wood, kerosene, charcoal, etc in these countries exacerbate air pollution

In part four, a prediction is statistically made: There is a 95% chance that the world's mean annual exposure to air pollution will decline in the future This prediction is backed by the calculated confidence interval It indicates that the range of 2017 world's mean annual exposure

to air pollution is 18.543μg/m3 to 33.321μg/m3, and is lower than that of the previous year (45.2μg/m3)

In order to fulfil this prediction and accomplish United Nation SDG 13 goal: Climate Change, actions need to be taken as there is a close link between climate change and poor air quality according to UNECE (n.d.) The y also noted that in 2012, the Gothenburg Protocol was to be the first legally binding agreement that consisted of obligations to lessen more short-lived climate pollutants varieties, especially fine particulate matter Clean air is not only a human right, but also the pre-condition to tackle climate change Combating 9