ECON1193 bstat asm2 PDF

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BUSINESS STATISTICS Course

Econ1193B

Assignment 2

Individual case study

Lecturer

Nguyen Thanh Liem

Student name

Nguyen Thi Thanh Lan

Student ID

S3891619

Word count

2588

Lan Nguyen

Introduction 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

LI

MI

HI

Mean

31.20

17.24

2.12

Median

30.25

17.60

2.35

Mode

#N/A

#N/A

#N/A

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 highincome 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: Categories Variance Interquartile Range (IQR) Range Standard Deviation (SD) Coefficient of Variation (CV)

LI 20,79 8,55 10,5 4,56 14,62%

MI 77,05 14,7 26,3 8,78 50,92%

HI 0,65 1,5 2,1 0,81 38%

Figure 2: Measure of Variation of each income level on mortality rate neonatal (units: neonatal mortality per 1000 live births)

2

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 are drastically 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 Mortality rate (L)

High Mortality Rate (H)

Total

0

4

4

7

8

15

6

0

6

13

12

25

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) P(H) =

H 12 = =0.48 = 48% 25 25 P ( H ∩ LI ) 4 = =¿ 1 = 100% P (H|LI ) ≠ P ( H ) 4 P ( LI )  P(H∨MI )≠ P(H ) P ( H ∩ MI ) 8 P (H|HI ) ≠ P ( H ) = = = 0.53=53% 15 P ( MI )

P(H∨LI ) =

P(H∨MI )

P(H∨HI ) =

P ( H ∩ HI ) 0 = =0 = 0% 6 P ( 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. 3

With the calculation above, we have: P(H∨LI ) = 1 P(H∨MI )

= 0.53

P(H∨HI ) =

⇒P(H ∨HI )< P (H∨MI )< P(H ∨LI )

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

1−α ¿ ×100 % 95%

Population Standard Deviation Sample mean

�

´ X

Unknown 15,84 (per 1,000 live births)

s 11,63 (per 1,000 live births) n 25 Figure 5: Data summary In this case, we use the t table substitute for z table because the Population Standard Deviation ( σ ¿ is unknow. Confidence level: (1−α )× 100 %=95 % => Significant level: α =5 % Using tDegree of freedom :d . f =n−1=24 . Confident Interval: ´ ± t n−1 × s μ= X √n 11,63 11,63 ≤ μ ≤15,84 +2,063 × ⇒15,84−2,063 × √ 25 √ 25 Sample Standard Deviation Sample size

⇒11,04 ≤ μ ≤ 20,63 4

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 do not reject the Null Hypothesis ( H 0 ¿ and reject the Alternative Hypothesis ( H A ¿

7

Rejection region

Non-rejection region

Rejection i

Figure 7: rejection and non-rejection region 

Step 8: Make a managerial decision in the context of the problem. As we do not reject H 0 : 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: ´ ± t n−1 × s μ= X √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

ttest =

Xbar − μ S / √ n /2

¿

√

1 Xbar − μ × √n × 2 s

√

1 (Xbar 2 −μ > >

37,4 32,4 3,1

no outlier no outlier no outlier...