Business statistic 1 Assignment 2 Nguyen-Thuy-Trang -s3807874 PDF

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November20191. INTRODUCTION:According to Roser, Ritchie, and Dadonaite (2013), child mortality is the death of children under five years old. Therefore, the Child mortality rate (or “Under-five mortality rate”) is explained by UNICEF (n.) as the “probability of dying between birth and exactly five y...

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November 2019

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1. INTRODUCTION: According to Roser, Ritchie, and Dadonaite (2013), child mortality is the death of children under five years old. Therefore, the Child mortality rate (or “Under-five mortality rate”) is explained by UNICEF (n.d.) as the “probability of dying between birth and exactly five years of age expressed per 1,000 live births”. The United Nations have promoted the Sustainable Development Goals since 2015. As part of Goal 3 about Well-being and Good health, every country has set a target to decrease the Child mortality rate to 2.5% (WHO, 2019). The reduction will help uphold the rights of children and develop a thriving world because child mortality demonstrates the most vital human rights, which are the rights to health and life (United Nations, 2010). Indeed, child survival rates have plummeted by 59% from 1990 to 2018. However, the disparities in the Child mortality rates across regions and countries still exist. Also, in 2018, there were still 5.3 million children who died mostly because of preventable reasons (WHO, 2019), indicating that one child passed away every five seconds (UNICEF, 2019). Hence, the world as a whole needs to keep trying to achieve a lower rate. When it comes to the GNI, the wealthier countries often have better health outcomes and a lower Child mortality rate (O'Hare et al., 2013). To support the finding, Figure 1 shows that when the GNI per capita rose gradually from $9,400 to $10,600, the Child mortality rate went down marginally by about 13% between 2009 and 2017. Hence, we can conclude that these two figures are inversely proportional.

Figure 1: World’s Child Mortality Rate (per 10,000 live births) and GNI per capita (constant 2010 US$) from 2009 to 2017 (adapted from The World Bank, n.d.). 2

2. DESCRIPTIVE STATISTICS AND PROBABILITY:

Figure 2: Contingency Table of Child mortality rate and Country categories. From Figure 2: P(A) = P(High child mortality rate) = 23/38 = 0.6053 P(A|B) = P(High child mortality rate WITH Low income) = (4/38) / (4/38) = 1 P(A|C) = P(High child mortality rate WITH Middle income) = (18/38) / (19/38) = 0.9474 P(A|D) = P(High child mortality rate WITH High income) = (1/38) / (15/38) = 0.0667 We can see that P(A|B), P(A|C) and P(A|D) are all different from P(A). Therefore, income and Child mortality rates are statistically dependent events, implying that the GNI per capita of a country has effects on its Child mortality rate. From the calculation above, the probabilities of High under-five mortality rates in countries with middle income and low income are respectively 94.74% and 100%, which are more considerable than the figure of High-income countries (6.67%). Thus, Low-income and Middle-income countries usually bear High under-five mortality rates.

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Figure 3: Summary statistics of each country category’s Child mortality rate. Overall, Figure 3 shows the descriptive statistics of the Under-five mortality rate of each country category. As the statistics of high-income and middle-income countries have outliers, the most appropriate measure of central tendency is the median. In low-income countries, the average Under-five mortality rate is 70.75, which is four times higher than that of middle-income countries (17.7) and more than eighteen times higher than the number of high-income countries (3.9). Those medians indicate that the less developed countries often have higher Child mortality rates. When it comes to variation, the coefficient of variation is the best measure in the case of outliers because it can demonstrate the data dispersion precisely. Middle-income countries have a 91.57% coefficient of variation, which doubles the figures of low-income and high-income countries. Therefore, Under-five mortality rates in high-income and low-income countries are far more consistent than the rate in nations with middle income.

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Figure 4: The Box-and-Whisker plots show the Child mortality rate distribution of three country categories. In general, Figure 4 illustrates the Box-and-Whisker plots of the three-country categories. Lowincome countries have the most massive box, along with the highest rates of child mortality. The second biggest box is of middle-income countries. High-income nations have the smallest box and also the modest Child mortality rate. Therefore, the wealthier countries have more consistent data and fewer child deaths.

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3. CONFIDENCE INTERVALS: a. Calculate the confidence intervals for the world average of Child mortality rate:

Figure 5: Descriptive statistics of the world’s Under-five mortality rate. According to Figure 5: o Mean = World average Child mortality rate = 23.58 o Sample size: n = 38 countries o Sample standard deviation = 29.22 o Take the level of significance of 5%: α = 0.05 → α/2 = 0.025 Since we do not know the population standard deviation, we will use the t-table to determine the confidence intervals: o Degree of freedom: d.f = n - 1 = 38 – 1 = 37 o t37 = 2.0262 → Confidence intervals = 23.58 ± 2.0262

( 29.22 √ 38 )

→ 13.98 ≤ Child mortality rate ≤ 33.18

To conclude, we are 95% sure that, on average, the Under-five mortality rate per 1000 children 6

is between 13.98 and 33.18 in 2015.

b. Assumption: The Central Limit Theorem is applied because we have a sample size of 38 countries (larger than 30), suggesting that the sample has a normal distribution. Hence, there is no assumption needed to determine those confidence intervals.

c. Impact on the results of confidence intervals when we know the population standard deviation: Confidence interval formula when population standard deviation is unknown: X´

± tn-1

( √Sn ) Confidence interval formula when population standard deviation is known: X´

±Z

( √σn )

From the two formulas above, when the sample size (n) is constant, the change in confidence intervals depends on the standard deviation ( σ or S) the critical value (z-value or t-value). With the same confidence level of 95% and the sample size of 38 countries, the value of z is 1.96, smaller than the t-value of 2.0262. Moreover, when the sample size is more than 30, the tdistribution and z-distribution are roughly the same (see appendix 1 for more details); therefore, σ is equal to S. In conclusion, with t = 2.0262 > z = 1.96 and S = σ , the confidence interval will diminish if we know the population standard deviation, resulting in more accurate confidence intervals.

4. HYPOTHESIS TESTING: a. Test the hypothesis: From Part 3, the confidence intervals show that the average Under-five mortality rate ranges from 13.98 to 33.18 deaths per 1,000 children. However, according to World Bank data, there were 46 deaths per 1,000 children in 2013, which is far higher than the confidence intervals. Thus, there is a prediction that the Under-five mortality rate of the world will witness a decrease in the future. o Take 5% as the level of significance: α = 0.05 o The Under-five mortality rate is normally distributed because the sample size has 38 countries (CLT applied). Since we have no data about the population standard deviation, to test the hypothesis, we will use the t-value. The average Under-five mortality rate in 7

2013 is considered the sample mean = µ = 46. o Hypotheses:  H0 (null hypothesis): µ ≥ 46  H1 (alternative hypothesis): µ < 46 o Test statistic:  We have: n = 38; X = 23.58; µ = 46  d.f = n – 1 = 38 – 1 = 37  tcrictical = -1.6871  Sample standard deviation = 29.22 23.58 −46 29.22  tstatistic = = -4.7298 √ 38 o Critical region:

Figure 6: Critical region of hypothesis testing.  As tstatistic = -4.7298 < tcrictical = -1.6871, H0 is rejected. o Conclusion statement:  As a 5% level of significance is used, the average Under-five mortality rate is lower than 46 per 1,000 children.

b. Triple the number of countries in the dataset: We have

S=

√

∑ (x− x´ )2 n−1

According to the formula above, the sample size (n) triples will lead to a decrease in the sample standard deviation (S). Thus, there will be a narrower distance between the mean and the observations, which leads to the reduction in differences between the population parameter and the sample statistic. Consequently, the chance of error is lower so that we can still reject the null. To conclude, we still have the same statistical decision, and the hypothesis testing results will also be more accurate.

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5. REGRESSION ANALYSIS: a. Regression analysis: The Under-five mortality rate is the dependent variable. The independent variables are years of compulsory education, Measles immunization (% of children ages 12-23 months), GNI per capita, and the Domestic government health expenditure per capita. According to Figure 7 and Appendix 2, 3, and 4, although all the independent variables have p-values of less than α = 0.05, the Measles immunization has the smallest p-value of 0.000000207426. Therefore, the most significant variable is the percentage of 12-23-month-old children who immunize against measles.

Figure 7: Regression output of the Under-five mortality rate (per 1,000 live births) and Immunization, measles (% of children ages 12-23 months). According to figure 7, we have a simple linear coefficient equation: ^ Child mortality rate

¿ 201.13−1.9798 (Percentage of measlesimmunization)

The regression intercept b0 = 201.13 indicates that when no child from 12-23 months olds immunize against measles, the estimation of the Under-five mortality rate will be about 201.13 per 1,000 children. The regression slope coefficient b1 = -1.9798 demonstrates the predicted changes in the worldwide average Child mortality rate when the percentage of immunization adjust by a unit. Thus, it forecasts that when the portion of Measles vaccination of children increases by 1%, the Under-five mortality rate will reduce by 1.9798 deaths per 1,000 children. 9

Moreover, the coefficient of determination R square = 0.5318 illustrates that the portion of Immunization of measles for children from 12-23 months old affects 53.18% of the change in the mortality rate for child. Meanwhile, other factors influence 46.82% remaining. Hence, Child mortality rate and Measles immunization of children have a strong relationship with each other.

Figure 8: Scatter plot of the Under-five mortality rate (per 1,000 live births) and Measles immunization (% of children ages 12-23 months). Figure 8 shows a negative linear relationship between Measles immunization of children from 12 to 23 months old and Child mortality rate. Therefore, if more babies receive vaccination against measles, there will be a lower Child mortality rate. Moreover, when the immunization percentage is nearly 100%, the Under-five mortality rate can be as low as 2.4%.

b. Two other variables affecting the Under-five mortality rate: Two other variables affecting the Child mortality rate are the Prevalence of HIV and the Total fertility rate. First, HIV is transmitted to the child from an infected mother, after which they may die from other detrimental health problems because of the weakened immune system. Hence, the growth of HIV prevalence indicates a lower health level for the population, which can lead to a higher rate of Child mortality (Wheatley, 2015). Second, according to Roser (2014), Total fertility rate describes the average number of sons or daughters given birth by a woman. As a woman just has limited resources, having more children means that the resources per child will decrease. Therefore, a high Total fertility rate can result in a soar in the Under-five mortality rate 10

(Wheatley, 2015).

6. OVERALL CONCLUSION: In summary, numerous factors affect the child mortality rate. However, to determine if a variable influences the Child mortality rate, various tests have to be made. There are three main findings of the topic on Child mortality rate: First, GNI per capita can influence the Child mortality rate. As we have found and proved in Part 1 and Part 2, the more prosperous countries often have a lower Under-five mortality rate because those countries can invest more money in healthcare and technology. Hence, children in high-income countries can enjoy better healthcare conditions that will enable them to live longer. This finding has come in line with the research of Neal and Falkingham (2014), which states the existence of a robust negative relationship between the Under-five mortality rate of a country and its income level. Second, as proved in Part 3, the confidence intervals of 95% significance are 13.98 and 33.18. Therefore, we are 95% sure that the average Child mortality rate per 1,000 children of the world is between 13.98 and 33.18. However, we need to make more tests to come up with the most accurate result. Thus, in Part 4, with a sample of 38 countries, the null hypothesis that the average Under-five mortality rate will be more than 46 per 1,000 live births can be rejected. As a result, we can predict that the rate will be lower than 46 in the future. Third, from Part 5, we can conclude that numerous factors are affecting the Child mortality rate besides GNI per capita, such as Measles immunization, Compulsory education, and Domestic government health expenditure per capita. The most significant factor is the Measles vaccination of children between 12 and 23 months old because it affects 53.18% of the Child mortality rate. These two variables have a notable negative relationship as if the portion of Measles immunization decrease, the Child mortality rate will go up dramatically. Moreover, when no child has measles vaccination, the death rate of children can be as high as 201.13 per 1,000 children. Additionally, when the percentage of babies who immunize against measles grows by 1%, the Under-five mortality rate will drop by 1.9798 deaths. Furthermore, in today's world, various other factors can create impacts on the Under-five mortality rate, two of which are the Prevalence of HIV and the Fertility rate. The increases in both of those factors can lead to a boost in the average Under-five mortality rate of the world.

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References Neal, S., and Falkingham, J. (2014). Neonatal Death and National Income in Developing Countries: Will Economic Growth Reduce Deaths in the First Month of Life?. International Journal of Population Research, 2014, pp.1-6. O'Hare, B., Makuta, I., Chiwaula, L., and Bar-Zeev, N. (2013). Income and child mortality in developing countries: a systematic review and meta-analysis. Journal of the Royal Society of Medicine, 106(10), pp.408-414. Roser, M. (2014). Fertility Rate. [online] Our World in Data. https://ourworldindata.org/fertility-rate [Accessed 14 Dec. 2019].

Available

at:

Roser, M., Ritchie, H., and Dadonaite, B. (2013). Child & Infant Mortality. [online] Our World in Data. Available at: https://ourworldindata.org/child-mortality [Accessed 9 Dec. 2019]. Roth-Johnson, P. (2016). Confidence Intervals: Statistical Techniques. [image] Available at: https://www.visionlearning.com/es/library/Matem%C3%A1ticas-en-laCiencia/62/Confidence-Intervals/239 [Accessed 13 Dec. 2019]. The

World Bank (n.d.). World Development Indicators | DataBank. [online] Databank.worldbank.org. Available at: https://databank.worldbank.org/reports.aspx? source=2&series=SH.DYN.MORT&country= [Accessed 10 Dec. 2019].

UNICEF (2019). Levels and Trends in Child Mortality - UNICEF DATA. [online] UNICEF DATA. Available at: https://data.unicef.org/resources/levels-and-trends-in-child-mortality/ [Accessed 9 Dec. 2019]. UNICEF (n.d.). UNICEF Definitions. [online] Unicef.org. Available https://www.unicef.org/infobycountry/stats_popup1.html [Accessed 9 Dec. 2019].

at:

United Nations (2010). Millennium Development Goals. [ebook] Cepal, p.1. Available at: https://www.cepal.org/MDG/noticias/paginas/6/40006/MDG4_CHILD_MORTALITY_FACT_S HEET.pdf [Accessed 9 Dec. 2019]. Wheatley, L. (2015). Factors affecting child mortality. [ebook] Honors Theses, pp.11-12. Available at: https://scholar.utc.edu/cgi/viewcontent.cgi?article=1026&context=honorstheses [Accessed 14 Dec. 2019]. WHO (2019). Children: reducing mortality. World Health Organization. [online] Available at: https://www.who.int/news-room/fact-sheets/detail/children-reducing-mortality [Accessed 9 Dec. 2019].

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Appendices

Appendix 1: Normal distribution (z distribution) vs. t distribution (Roth-Johnson, 2016).

Appendix 2: Regression output of Child mortality rate (per 1,000 live births) and Domestic general government health expenditure per capita, PPP (current international $).

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Appendix 3: Regression output of Child mortality rate (per 1,000 live births) and Compulsory education duration (years).

Appendix 4: Regression output of Child mortality rate (per 1,000 live births) and GNI per capita, Atlas method (current US$).

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