implying a strong negative relationship between the neonatal mortality rate and gross national income (GNI

Between 1990 and 2017, the global neonatal death rate dropped by 51% United Nations Inter-agency Group for Child Mortality Estimation 2018, however, it still remains high, with more coun

 BUSINESS STATISTICS 1 - ASSIGNMENT 2 - DATASET: 06 - MORTALITY RATE NEONATAL

BY LE NGOC HUE ID: s3892314

Word count: 2963

I Introduction.

Decreasing the neonatal mortality rate has become a huge concern in social policy, public health (Treiber 2017) Between 1990 and 2017, the global neonatal death rate dropped by 51% (United Nations Inter-agency Group for Child Mortality Estimation 2018), however, it still remains high, with more countries are predicted to fail the neonatal mortality target in 2030 (UNICEF n.d), because neonatal death in the highest-risk countries are 50 times more likely to occur than in the lowest mortality country, and it declined more slowly than under-five mortality (UNICEF n.d) Decreasing the neonatal mortality rate plays a crucial part in meeting the United Nations SDG 3 (The Global Goals n.d) because the neonatal death rate is an essential indication of a community's overall physical health (Treiber 2017) Furthermore, high neonatal death rates are frequently indicative of unfulfilled human health needs in hygiene, nutrition, healthcare, suggesting that the country's SDG 3 goal of guaranteeing healthy lives and promoting well-being for all ages remains unreachable (Treiber 2017)

According to UNICEF (n.d), neonatal mortality worldwide remains alarmingly high, especially

in the poorest countries, implying a strong negative relationship between the neonatal mortality rate and gross national income (GNI) (Neal & Falkingham 2014) GNI is a criterion

for classifying economies (Jalal, Khan & Younis 2016), whereas neonatal mortality rate is a helpful indication of a country's level of growth or health (Jalal, Khan & Younis 2016) It is stated that the average neonatal mortality rate in low-income nations is much higher than in high-income countries (UNICEF n.d) It is because residents of these wealthy nations can easily access cutting-edge medical facilities (Jalal, Khan & Younis 2016), improved contextual factors (income, sanitation) (Neal & Falkingham 2014), high coverage of excellent prenatal care as well

as timely health interventions (World Health Organization 2020), thus, they naturally have a lower neonatal mortality rate than those in less developed countries (Jalal, Khan & Younis 2016) Conversely, low and middle-income countries frequently account for the great majority of neonatal mortality (World Health Organization 2020) due to a lack of resources to invest in healthcare systems, resulting in a very high rate of impact of poor health, which in turn affects Gross National Income (Jalal, Khan & Younis 2016)

II Descriptive Statistics and Probability.

1 Probability.

Conditional probability, as defined by Berenson and Levine (2018), is when the likelihood of one incidence depends on the occurrence of others Specifically:

P(high rate): the probability of high mortality rate neonatal in 2017 P(nI): the probability of The Gross National Income made in three countries categories in 2017 The probability of mortality rate neonatal in each country category, P(high rate ∩ nI), will be divided by the marginal probability, P(nI), to establish if the Mortality rate neonatal is dependent

on the GNI or not Therefore, P(high rate|nI) is the probability of the nations' neonatal mortality rate If this P(high rate |nI) = P(high rate) equation holds true, the two events are considered independent (Holmes, Illowsky & Dean 2015) Otherwise, the neonatal mortality rate and the GNI are interdependent Use “DP1000LB” as the abbreviation for “deaths per 1,000 live births”

High mortality rate neonatal (>15 DP1000LB)

Low mortality rate neonatal (<15 DP1000LB )

Total

Low-Income

countries (LI)

Middle- Income

countries (MI)

High-Income

countries (HI)

Table 1: Contingency table of three countries categories in terms of mortality rate neonatal and

the gross national income

� (high rate) = ≈ 0,36

P(high rate | LI)= = = 1 → P(high rate|LI) P(high rate)

P(high rate |MI)= = ≈ 0.38 → P(high rate|MI) P(high rate)

P(high rate |HI)= = = 0 → P(high rate|HI) P(high rate)

Proven by the foregoing calculations, it can be concluded that neonatal mortality rates are fully dependent on GNI, since P(high rate|nI) P(high rate) Namely, the neonatal mortality rate of 2017 would mostly occur in the low-income countries with the highest probability of 100%, as opposed to the two remaining countries, where the chances of having a high infant mortality rate are only 0% to 38% Conversely, high-income countries, have the highest likelihood of a low neonatal mortality rate in 2017, with a probability of 100%, followed by middle-income countries with a probability of 62%

2 Descriptive Statistics

a) Central Tendency.

Min Comparison Low

thresh

thresh

Result

Low-Income

countries

0

outliers

Middle-Income

0

> 35.24 1 Outlier

High-Income

countries

Outliers

Table 2: Table of tests of outliers.

Measures of Central

Tendency

Low-income countries

Middle-income countries

High-income countries

Mean

26.12 DP1000LB 14.06 DP1000LB 2.25 DP1000LB

Median

2.2 DP1000LB

Table 3: Measures of Central Tendency of three countries categories on mortality rate neonatal.

Table 3 is calculated after the application of the IQR rules has determined that there are outliers

in the dataset since the maximums of both middle-income and high-income countries are larger than their upper bounds As seen in Table 3, all measures of low-income countries are greater than middle-income countries and high-income countries, demonstrating that the low-income group has witnessed the highest neonatal mortality rate Furthermore, the high-income countries’ median is the lowest, indicating the high-income countries’ 2017 neonatal mortality rate is pretty lower than that of the other 2 remanding However, Table 2 is demonstrated a total of 1 outlier in the middle-income group dataset and 2 outliers in high-income ones When there are outliers in the dataset, Manikandan (2011) believes that the median is preferable to the mean because it can compensate for the distortion caused by extreme values while the mean is stated to be sensitive

to extreme values (Manikandan 2011) Furthermore, the data's mode of low and middle-income countries is undetectable Therefore, the median is the ideal metric for assessing this data due to its ability to counteract the distortion of extreme values

b) Variation.

Measures of Variation Low-income

countries

Middle-income countries

High-income countries Range

12.40 DP1000LB 33.70 DP1000LB 3.80 DP1000LB

Interquartile Range

(IQR)

8.90 DP1000LB 10.83 DP1000LB 0.90 DP1000LB

Sample Variance

19.00 DP1000LB squared

69.21 DP1000LB

squared

Standard Deviation

4.87 DP1000LB 8.47 DP1000LB

1.28 DP1000LB

Coefficient of

Table 4: Measures of Variation of three countries categories on mortality rate neonatal.

Moving to table 4, it can be seen that all the middle-income countries’ measures of variation are the highest compared to those of both low and high-income countries, with the gap between them being fairly substantial The IQR is the optimum metric in this case since the data contain extreme values (Whaley III 2005) Its unaffected by extreme value makes IQR superior to the standard deviation and the range since both of them are sensitive to outliers (Manikadan 2011) Furthermore, the standard deviation represents the dispersion around the mean, hence, calculating the standard deviation when utilizing the median as a metric of central tendency is impractical (Whaley III 2005) Manikadan (2011) also noted that the middle half of all observations is described by the IQR This means that the lower a data value's IQR is, the closer

to the mean the center half of the data is, thus the less variance the data has (Whaley III 2005) Consequently, data from middle-income countries have a more fluctuated IQR than data from other remaining, implying that middle-income countries’ neonatal mortality rate is more spread out and dispersed

III Confidence interval (CI).

1 Calculate CI.

Confidence

level

( 1 ― )�

0.95

Significance level

�

0.05

0.025

standard

deviation

(� )

-Sample standard deviation

()

9.85

Population

mean (�)

-Sample mean ( )

12.51

Sample size

()

45

Degree of freedom

(d.f)

44

t-critical

value ( )t

± 2.0153

Table 5: Summary of Inferential Statistics of the dataset.

Since the population standard deviation is unknown, the sample standard deviations are utilized instead of the population standard deviations (Holmes, Illowsky & Dean 2015) Furthermore, Hartmann, Krois & Waske (2018) also noted that instead of using the normal distribution, the Student's t-distribution should be used as a consequence of the lack of population standard deviation Furthermore, a confidence level of 95% was used to determine the CI of given datasets, leading to the estimated significant level is 0.05 The needed values have been computed and shown in Table 5 sequentially Following that, the CI is calculated using the equations below:

⇒

9.55 15.47⇒

In conclusion, it is 95% confident that the population mean of global neonatal mortality rate is between 9.55 DP1000LB and 15.47 DP1000LB

2 Discussing assumptions.

As stated by Siegel (2016), according to the Central Limit Theorem (CLT), as the sample size is larger than 30, it will be approximately normally distributed regardless of the population

distribution Consequently, though the population standard deviation is unknown, no assumptions are required for the computation of the CI because the sample size is 45, which is greater than the standard of 30

3 Impact on the CI results.

Since the global standard deviation of each Mortality rate neonatal ( is given, the normal distribution would be used (Figure 2) (Hartmann, Krois & Waske 2018) Whether is known or unknown, the sample given would stay the same in both cases, therefore the sample mean and the sample size would be unchanged Using the same 95% of confidence level in the given scenario, the significance level value would be the same, therefore, the t-critical value would larger than the z- critical value since the t-distribution tend to have a fatter tail, accounting for the fact that the area for unlikely value is broader compared to the z-distribution (Hayes 2021), leading to decrease non-rejection region, then the CI would reduce when the is known However, it is not enough evidence to conclude because it is impossible to confirm the population standard deviation (σ) is smaller than the sample standard deviation (S) since a lot of samples could be chosen randomly due to the random sampling process Therefore, 3 assumptions are made to examine after concluding:

 Assumption 1:

In this scenario, all the value is unchanged except the critical values As stated above, the t-critical values would be larger than the z-t-critical values, leading to the CI would decrease when the is known.�

 Assumption 2:

With the t-critical value larger than the z-critical value, combined with the assumption which made the CI result even larger since and have a positive relationship (Figure 1), hence the CI would decrease when is known.�

 Assumption 3:

The t-critical value is larger than the z-critical value, however, with the assumption , it is impossible to conclude in this scenario

Figure 1: The formula of CI estimate with an unknown � (case 1).

Figure 2: The formula of CI estimate with a known �.

After three assumptions are considered, it is concluded that a decrease would be the possible impact on the CI result when the is given This will reduce the uncertainty, hence the accuracy is more enhanced (Nica 2013)

VI Hypothesis testing.

a) Hypothesis testing.

The global average neonatal mortality rate given was 18.6 DP1000LB, which is higher than the mean of the dataset (12.51 DP1000LB) However, due to the possibility of error of the random sampling, the 95% CI should be considered Still, when this mean is applied to the CI, the upper limit of the CI is likewise lower than the hypothetical mean (15.47<18.6) Thus, a decrease in the average neonatal death rate is predicted in the future Nine steps of hypothesis testing are conducted below:

Step 1: As the sample size (n = 45) is greater than 30, hence CLT is applicable and thus

sampling distribution of mean becomes normally distributed

Step 2:

H0:� 18.6 DP1000LB

H1:� DP1000LB

Step 3: The lower-tail test is conducted to test the statistical hypothesis since it comprises ′ < ′

and ′′

Step 4: Because of the unknown population standard deviation, a T-table is utilized in this

situation

Step 5:

The significance level: �=0.05

Sample size: n=45

T-critical value for lower-tail test: -1.680

Step 6:

=

Step 7: = -4.15 < -1.680, the test statistic falls into the rejection region Hence, the null

hypothesis, H is rejected and accepts H0, 1.

Step 8: As H0 is rejected, hence with a 95% level of confidence it can be concluded that the

global neonatal mortality rate is NOT increasing from 2016 to 2017 In other words, 95% confidence that the global average neonatal mortality rate will decrease in the future

Step 9: As the is H0 rejected, type I error may have been committed in this case This error means that it is concluded that the global average neonatal mortality rate will decrease in the future but actually it might increase

b) Discuss the possible impact on the hypothesis testing results when the sample size become half

Because the test statistic t1 is less than the t-critical value, the hypothesis testing outcome is that H0 is rejected It is stated that the significance level does not change when the sample size is cut

in half, but the degree of freedom changes This will increase the critical value of the lower-tailed test then broaden the CI since the sample size has an inverse relationship with the CI width (Hazra 2017), hence the rejection region would decline, limiting the precision in finding the true population mean's value (Mc Leod 2019) It can be seen in Figure 3 that the value of sample size

is inversely proportional to the sample standard deviation In other words, the greater the standard deviation, the smaller the sample size (Lumen 2017) As a result, if the sample size is reduced, the standard deviation will increase, and the test statistic will fall Now the equation for new test statistic with is:

Figure 3: The new test statistic formula.

As discussed above, the rejection region would be narrowed, and the test statistic value would fall when the sample size is cut in half, the is likely to stay rejected The outcome of the hypothesis will not change In other words, the worldwide average neonatal mortality rate is forecast to keep falling in the future Since it is impossible to determine which mean in the sampling distribution corresponds to the population mean, the sample means will cluster together using the sampling method, allowing the study to produce a very accurate estimate of the population mean (Mc Leod 2019) Consequently, the smaller the sample size is, the more the sampling error might be included, resulting in less reliable results with lower precision

V.Conclusion.

After analyzing all of the data using a variety of approaches, these specific results were obtained

to answer the case study question

First, the descriptive analysis revealed that the low-income group has experienced the highest neonatal mortality rate, with a median of 25 DP1000LB, while the high-income countries' median is the lowest, indicating the high-income countries’ 2017 neonatal mortality rate is pretty low, right after the middle-income countries' rate However, middle-income nations exhibit higher volatility in terms of neonatal death rate spread than the other two groups, which demonstrates that infant mortality rates in this category have fallen, but not as dramatically as in high-income nations

Secondly, the probability calculation illustrated that the neonatal mortality rates are fully dependent on GNI Namely, the low-income countries have suffered from the highest neonatal mortality rate in 2017, about 100%, compared with 38% of the middle-income countries and 0%

of the high-income countries This high rate has resulted from the low ability to access cutting-edge medical facilities (Jalal, Khan & Younis 2016), improved contextual factors of these low-income countries are still limited and unmet since they are lacking resources and money to invest

in healthcare more deeply, as stated in Part I On the other hand, high-income countries have more opportunities to improve the situation With the high GNI, these wealthy countries can ensure healthy lives and promoting timely health interventions for their citizens, especially women who are pregnant Therefore the neonatal mortality situation is barely occurring in this countries category

Finally, based on the hypothesis testing, there is 95% confidence that the worldwide average newborn mortality rate has decreased by 6.09 DP1000LB from 2016 to 2017 This indicates some positive signal that the global average neonatal mortality rate might continue to decrease in the future, therefore, making the United Nations SDG 3 more likely to be achieved However, there is still a 5% possibility that the global average neonatal mortality rate might increase in the future as more countries are predicted to fail the neonatal mortality target by 2030 (UNICEF n.d), hence, all nations in the world, particularly the low-income and middle-income ones, should accelerate their progress to meet the SDG 3 goals

In conclusion, because the infant mortality rate and GNI are inversely related, nations with low GNI are more likely to experience a high neonatal mortality rate than countries with high GNI

In other words, as each country's GNI declines, this rate appears to steadily rise While the global infant mortality rate is experiencing a slight decline, there is still a relatively small risk that this rate might increase and the GDS 3 target will be unmet in the future if countries around the world, especially low- and middle-income countries do not take appropriate measures to reduce infant mortality on time In addition, high-income countries should also strengthen effective treatments to remain low neonatal mortality rates

IV References.

Berenson, ML & Levine, DM 2018, Basic Business Statistics: Concepts and Applications, 5th edn, Pearson Education Australia, ProQuest Ebook Central database

Hartmann, K, Krois, J & Waske, B 2018, E-Learning Project SOGA: Statistics and Geospatial Data Analysis, Freie Universitaet Berlin, viewed 17 August 2021,