with all nations aiming to decrease neonatal mortality to at least 12 deaths per 1,000 live births

In addition, according to UNDP, they address neonatal mortality in the Achievable Development Goals as one of Goal 3 is that by 2030, End avoidable deaths of newborns and children under

BUSINESS

STATISTICS

Assignment 2

Lecturer

Student name

Individual case study

Nguyen Thanh Liem

Nguyen Thi Thanh Lan

Lan Nguyen

The neonatal mortality rate (NMR) is the number of deaths occurring during the first 28 days

of life per 1000 live births in a particular year (WHO n d) According to UNICEF, in recent years, neonatal mortality rates have decreased globally with an average yearly rate of

reduction of 3.4% between 2012 and 2019 Neonatal mortality accounts for 47% of under-five deaths globally in 2019

On United Nations SDG 3 Goal: Good Health and Well-being (UN SDG 3 2020) The newest objective for Worldwide Good Health, according to The Global Goals (n.d., p 1), is to encourage healthy lifestyles, preventative measures, and modern, efficient healthcare for everyone The reduced neonatal mortality rate is also related to indentify the encouragement 'modern and efficient healthcare' during and after birth In addition, according to UNDP, they address neonatal mortality in the Achievable Development Goals as one of Goal 3 is that by 2030, End avoidable deaths of newborns and children

under the age of five, with all nations aiming to decrease neonatal mortality to at least 12 deaths per 1,000 live births and under-5 mortality to at least 25 deaths per 1,000 live births (UN.org) As a result,

it is critical to reduce the newborn mortality rate in order to achieve the United Nations Sustainable Development Goal 3 According to UNICEF, significant increases in child health spending, such as creating a full-coverage increased knowledge program, providing modern and efficient healthcare for mothers before and after giving birth would assist to reduce NMR Consequently, It is critical to decrease this rate since it is not only a measure of the quality and availability of medical technology and health services, but it also serves as an indication of public health (Amchp.org 2020).

According to WHO, Gross National Income (GNI) is considered to have a negative

association with neonatal death rate (appendix 1), which means that the higher level countries' income are, the lower neonatal mortality occurred According to Jalal et al 2016, when GNI per capita increases, the country's health probably improves and illnesses and death decrease Almost 99% of newborn deaths occur in low- and middle-income nations (WHO 2011) So, the lower income level of a country, the higher the newborn death rate This implies that high-income nations may 1

invest in medical advancements and increased health expenditures to improve people'

health (O’Hare et al 2013)

Descriptive Statistics and Probability:

1 Descriptive Statistics:

a Central Tendency:

Categories

Mean Median Mode

Figure 1: Central Tendency of Neonatal Mortality per 1,000 live births in three levels Income

countries (current US$).

In this case it does not have mode, so we consider using mean or median However, there is no outlier in this case (appendix 2), mean is chosen over median Additionally, the Median does not take the exact value of each observation into consideration and therefore does not use all

of the information included in the data as the Mean does (Manikandan, S 2011) So, Mean is the best measure of Central Tendency

As seen in the chart above, selected low-income nations have the highest average newborn death rate of 31.20 per 1,000 live births, while middle-income countries have a rate of 17.24 and high-income countries have a significant lower, just 2,12 This shows that the higher the income level of a country, the lower the newborn death rate It is actually the same as the information published by World Bank, that the mortality rate for the whole high income level countries always less than the lower ones (Worldbank.org report 2019)

b Measure of Variance:

Figure 2: Measure of Variation of each income level on mortality rate neonatal (units: neonatal

mortality per 1000 live births)

In this case, the IQR is not suggested because the common rule to use IQR is to identify

outliers (RMIT 2021), however, in this case, no outliers exist In addition, we can not use

Standard Deviation because the Mean of three levels of income is significantly different With

the Means of all three categories so different, the best measure of variation is Coefficient of

Variation (CV) because CV can be specifically designed for comparing several data sets even

if the means aredrastically different from one another (Adam, H 2021)

In this case, middle-income nations had the highest CV (50,92%), implying that its neonatal

mortality is less dispersed and concentrated more around an average value of 17,24 per 1,000

live births However, CV for LI and HI is slightly lower than MI, which is 14,62% and 38%

respectively Therefore, data of countries with middle GNI is quite dispersed around the mean

than the low and high-income category

2 Probability:

Categories

Low-Income countries

(LI) Middle-Income countries

(MI) High-Income countries

(HI) Total

Figure 3: Contingency table of country categories in terms of mortality rate,

neonatal (per 1,000 live births) and GNI per capita (current $US)

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P(H ∨LI )

P(H ∨MI )≠ P(H ) P(H ∨MI ) =

P(H ∨HI ) =

The different between the probability of countries having high neonatal mortality rate (H) and

the probability of H in each level of countries, indicating that Neonatal mortality rate and

income are statistically dependent events This implies that Gross Nation Income per capital

of a country has effect on its neonatal mortality rate

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With the calculation above, we have:

P(H ∨LI ) = 1

P(H ∨MI ) = 0.53 ⇒P(H ∨HI )<P (H∨MI )<P(H∨LI )

P(H ∨HI ) = 0

In this sample case, it is obvious that low-income nations had the highest neonatal mortality rate, with

a chance of 1 However, the probability of neonatal mortality rate for middle income and high-income are 0.53 and 0 respectively This means lower income nations may have higher neonatal mortality per 1,000 live births than other As a consequence, in this case, we can conclude that the lower the GNI per capita, the higher the Neonatal Mortality Rate.

Confidence Interval:

a Calculate the confidence interval of world average NMR:

Confidence level

Population Standard Deviation

Sample mean

Sample Standard Deviation

Sample size

In this case, we use the

Deviation ( σ ¿ is unknow

Confidence level:

=> Significant level:

Degree of freedom

Confident Interval:

⇒15,84−2,063 ×

⇒11,04 ≤ μ ≤ 20,63

So, we are 95% confidence that the world’s average of neonatal mortality in 2017 is

between 11,04 and 20,63 per 1,000 live births

b Since the population distribution is unkown and our sample size for selected countries

is less than 30 (25<30), The Central Limit Theorem is not applicable As a result, we

must assume the population is approxiate normally distributed and the mean sampling distribution will approxiate normally distributed in order to use the formuala

to calculate the Confident Interval

c Supposing that world Standard Deviation is known:

When the world Standard Deviation of each neonatal mortality per 1,000 live births is

known, the Z-distribution is used, instead of Student T-distribution

According two formulas above, we can see two differences that is the critical value change from t to z and the standard deviation change from � to S

The population standard deviation is defined as a parameter that is fixed across the population data collection (RMIT 2021) While the sample standard deviation is referred to as a statistic which is derived from a sample of the population, has more variability; which generates uncertainty while calculating the statistics (Taylor 2019) Therefore, when utilizing sample standard deviation to calculate the mean of a whole population is uncertainty and inaccuracy (Taylor 2019)

When the sample size is not considerable, critical z-values are lower than critical t-values for any given degree of confidence (McEnvoy 2018) Therefore, the width of Z-values would be narrower than that of t-value According to Giannoulis n d, the more precise the estimate when

the confidence interval is narrower, which means width of the confidence intervals decreases, resulting in a more accurate result.

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To conclude, when the worldwide standard deviation of newborn mortality rate is known, the confidence intervals for the global average of neonatal mortality rate will decrease, and the resulting confidence intervals will be more accurate

Hypothesis Testing

a From part 3a, we are 95% confident that the range of the world average neonatal mortality from 11.04 and 20.63 deaths per 1,000 live births in 2017 According to WHO, in 2016, the world average neonatal mortality rate is 18.6 deaths within a confidence interval Therefore, the rate is expected to remain unchanged

Confidence level

Population Standard Deviation

Sample mean

Sample SD

Sample size

Population mean

(

1−α ¿×100 %

�

´

X

s n μ

Figure 6: summary data

Step 1: Check CLT.

The Central Limit Theorem is not applicable in this case because the population distribution is unknown and our sample size is less than 30 (25<30) Therefore, we assume the population is approxiate normally distributed and then we can use both z or t table

Step 2: Determine hypothesis

It has been determined above that the neonatal mortality is expected remain unchange, so

we have the following result sign:

Null hypothesis H0

Alternative hypothesis

Step 3: Determine distribution.

Confidence level: ( 1−α ) × 100 %=95

% => Significant level: α=0.05

Sample size: n = 25 countries

Since the H A : µ ≠ 18.6 (deaths/1,000 live births), the sign “≠” means we use two tails test.

Step 4: Identify the type of table

Since the population standard deviation, σ is unknown, and sampling distribution is assumpt

appoxiate normally distributed Then, we use t table

Step 5: Determine Critical Value(s)

(CV). o Significance level: α=0 05

o Degree of freedom :d f =n−1=24

o T-table: two tails test

o Critical Value t = ± 2.063

Step 6: Calculate test statistic

Since we use the t-table, we will have a test statistic (

t

test

= Xbar −μ

S

Step 7: Make the statistical decision.

t1 <t test <t2 (-2.063 < -1.186 < 2.063)

=> t test fall in the non-rejection region.

=> do not reject the Null Hypothesis ( H

0 ¿ and reject the Alternative Hypothesis ( H

A ¿

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Figure 7: rejection and non-rejection region

Step 8: Make a managerial decision in the context of the problem

As we do not reject H0 : µ = 18.6 deaths per 1,000 live births, we are 95% confident that the average neonatal mortality rate per 1,000 live births might equal to 18.6 This means that the

neonatal mortality rate is expected remain unchanged.

=> This may not be the ideal scenario for achieving the 3 Sustainable Development Goal since SDG 3 seeks for a change, particularly a decrease to 12 deaths per 1,000 live births However, according to the results, the average newborn mortality rate per 1,000 live births

is expected remain unchange in the future

Step 9: Discuss the possible errors:

Since we failed to reject the Null Hypothesis, the type II error might commit This means

we can conclude not sufficient evidence that the average of world's neonatal mortality rate

is different than 18.6 death per 1,000 live births, but actually it may be different

b Standard deviation is unknown, we use the formula:

s

n−1 × √

n

When the sample size (n) is reduced, given the same anpha, the critical value move further

from 0 This also means that the critical value will increase, and the non-rejection region become larger Assume that the (Xbar) and (s) will not cause any large change because

when reducing only the sample size, we could not know the exactly value of (Xbar) and (s) Therefore, in this case the sample size is the only variable change We have the formula for test statistic:

8

√

t

μ=´ X ± t

Therefore, when sample size become half, the test statistic is only increase by √ 1

2

(Xbar −μ<0 ¿ The change of t test is extremely small while the non-rejection region is become larger, implying that the result is likely to still within the confidence interval which is

non-rejection region So, the statistical decision is likely to remain unchanged In addition, the

smaller sample size is, the higer margin of error occur (Dezil, C 2018) Therefore, the result is

less accurate when we reduce the sample size.

Conclusion

Some key findings from the calculations and analysis of the mortality rate for three income levels in 25 nations are listed below:

Firstly, as for the descriptive statistics, the average has been regarded as the most efficient statistic for examining mortality rates data at various income levels The low income countries witnessed the highest average of mortality rate compare to middle and high income countries This aslo indicate that the lower income level is, the higher neonatal mortality death occurred This is also link with part 1 is the city with the low level of income, they have less

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conditions to invest in companies modernizing equipment for the medical industry than in higher income countries, which leads to the higher neonatal death rate compare with higher income countries

The second finding is that GNI and NMR are statistically dependent events, which means that both of them have a strong relationship with other Furthermore, nations with a GNI per capita

of less than $1,000.are more likely to have the high neonatal mortality rate With higher income and lower rates, the United Nations may simply split the nations into numerous categories depending on their degree of income for more easy management and

administration Since there is a strong relationship between NMR and GNI, experts now recognize the importance of expanding the focus beyond just mortality to include additional and broader facets – socioeconomic issues They may focus intensely on develop the economy and key regional issues, such as health systems, and education From then, suitable steps to assist nations in decreasing the neonatal mortality rate to achieve the SDG 3

From part 4, it demonstrates that the average of newborn death rate will remain unchaged in the future There is 95% confidence that trend of the world average neonatal mortality rate will remain stable in the range of 11.04 and 20.63 deaths per 1,000 live births over the next year The unchanged NMR could bring disadvantages since SDG 3 seeks for a change, particularly a decrease to 12 deaths per 1,000 live births However, this result is based only on data from 25 nations As a consequence, the results may differ across samples

References:

Adam, H 2021, ‘Coefficient of Variation (CV)’, investopedia.com, viewed 18 August

2021, <https://www.investopedia.com/terms/c/coefficientofvariation.asp>

Dezil, C 2018, sciencing.com, ‘Effects small sample size limitation’, viewed 21 August

2021, <https://sciencing.com/effects-small-sample-size-limitation-8545371.html >