Assignment 2 Business stats 1 PDF

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Course Code Business Statistics- ECONCampus RMIT University Vietnam, SaigonStudent name & ID Nguyen Le Thien Quynh- sLecturer Ms. Greeni MaheshwariClass time Thursday 8AM-11AMWord count 3137 wordsDate of submission 15 th December 2019ContentsBusiness Statistics 1Assignment 2Individual Case Study...

Description

Course Code

Business Statistics- ECON1193

Campus

RMIT University Vietnam, Saigon

Student name & ID

Nguyen Le Thien Quynh- s3777295

Lecturer

Ms. Greeni Maheshwari

Class time

Thursday 8AM-11AM

Word count

3137 words

Date of submission

15th December 2019

Business Statistics 1 Assignment 2

Individual Case Study

Contents 1

1. Introduction………………………………………………………….3

2. Descriptive Statistics and Probability……………………………...4

3. Confidence Intervals………………………………………………...7

4. Hypothesis Testing…………………………………………………..7

5. Regression Analysis………………………………………………….9

6. Conclusion……………………………………………………………11

7. Reference…………………………………………………………….12

Part 1: Introduction

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State what experts say about child mortality under the age 5 Global description: Child mortality is known as the death of child who under the age of five (Max R, Hannah R and Bernadeta D 2013). According to World Health Organization (2019), the total number of under-five child mortality has dropped by 7.3 million in 2018. On average, only 15,000 of child under-5 die per day when compared with 34,000 in 1990. The mortality rate has deducted approximately by 59% leading to the reduction of 39 deaths per 1,000 live births in 2018. Although the world mortality rate of child has declined significantly, there are others country and regions still account for high rate in this figure. In particularly, Sub-Saharan Africa has the highest under-5 mortality rate in the global, with 1 in 13 infants who suffers with the death before having his or her fifth birthday celebrations (WHO 2019). Why is it important to decrease the child mortality rate The most frequently causes of mortality in child under-5 were pneumonia (18%), preterm birth complications (14%),diarrhoea (11%) and malaria (7%) (UNICEF 2012). The death of child is an enormous tragedy, therefore it is critical to decrease the mortality rate. Hence, the goals of United Nation SDG 3 are to diminish the newborn mortality rate to at least 12 per 1,000 births in each nation and lower the under-5 mortality rate to the minimum 25 per 1,000 births (WHO 2019). Therefore, urgent action is needed to reduce the mortality rate in order to reach the SDG targets by the end of 2030. There are 121 out of 195 countries have achieved the goals on under-five mortality (WHO 2019). The protection of child right to live will lead to the requirement of solving inequities, disparities in maternal and infant health, thus ensuring a great knowledge about what causes child mortality to help planning and guiding policymaking. As part of SDG targets, decreasing mortality rate will also contribute in building a more sustainable future, therefore addressing the problems that facing globally (United Nations n.d) Relationship between GNI and child mortality rate There is a relationship between the Gross National Income (GNI) and the child mortality. It is believed that wealthier people will be healthier as described by the life expectancy and child deaths within the nations, additionally the higher income levels connect closely with better health outcomes for the countries (Preston 1975 & Pritchett, Summers 1996). In contrast, other study claims that in 1990, approximately 0.5 million child deaths could lead to a poor economic performance (Pritchett & Summers n.d). Although improving the health system is a significant factor to reduce the mortality rate, number of studies show that socioeconomic factors, which are affected by the increase of GNI, have been an important element of mortality diminishing over the last few decades. For instance, experts stated that there is no “magic bullet” in deducting the under-5 child mortality rate, but elements such as women’s education and literacy will promote the real average per capita, particularly household income, environmental conditions (Rutstein, Cornia & Mwabu n.d).Other finding reflects that the decline in mortality rate depends on the development of effective maternal and primary health care services, which are still lacking in several developing regions (Sarah Neal & Jane Falkingham, 2014). Therefore, we cannot deny that there is a connection between GNI and mortality rate of child who under-5, meaning higher GNI figures of the nation will lead to the reduction in death rates.

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Part 2: Descriptive Statistics and Probability A.Categories:

Year

Country name

2015 2015 2015 2015

Malawi Mali Rwanda Senegal

Year 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015

Year 2015 2015 2015 2015 2015 2015 2015 2015

Low income countries (LI), GNI < $1000 GNI per capita, Atlas method (current US$) 340 790 710 980

Middle income countries (LI), GNI $1000-$12,500 Country name GNI per capita, Atlas method (current US$) Argentina 11.6 Colombia 15.8 Cote d'lvoire 95.1 El Salvador 15.5 Indonesia 27.3 Iran 15.7 Lao PDR 66.1 Mongolia 18.8 Morocco 28 Myanmar 52.7 Russian 8 Samoa 17.7 Serbia 6.2 Timor-Leste 51.6 Turkey 13.6 Vietnam 22

High income countries (LI), GNI > $12,500 Country name GNI per capita, Atlas method (current US$) Austria 47630 Bahamas 27920 Belgium 44230 Croatia 12950 Estonia 18380 France 40730 Germany 45790 United Kingdom 43720

Probability Contingency Table Low-income 4

Middle-income

High-income

Total

High child mortality rate under 5 (H) Low child mortality rate under 5 (L) Total P(LI/H) = 4/19 P(LI)= 4/28

countries (LI) 4

countries (MI) 14

countries (HI) 1

19

0

2

7

9

4

16

8

28

P(MI/H) =14/19 P(MI)=16/28

P(HI/H) =1/19 P(HI)=8/28

As can be seen from the table, the probability of the under-5 child mortality rate in lowincome (LI) countries is 4/19, while the probability of LI countries in total presented at 4/28. Therefore, these figures are considered as dependent events. Similarly, with the figures in MI and HI countries, the probabilities of mortality rate and total are different, which leading to the dependent events. Additionally, the total probability of LI and MI countries is 15/19 that is higher than when compared with the figure of HI countries, thus the high child mortality under 5 often occurred at developing countries such as LI and MI. B. Compare and Analysis i. Measurement of Central Tendency LI MI HI Mean 65.825 29.1 4.8375 Mode No mode No mode 3.9 Median 54.3 18.25 3.95 Figure 2.4: Measurement of Central Tendency of under-5 child mortality rate in low, middle- and high-income countries In fact, there is no best measure in central tendency. Besides, it depends on the data types, such as nominal or continuous. According to the table above, there is “no mode” in low and middle-income countries, therefore mean and median are the best alternative choices. However, since the mean is easily affected by the outliers, I decided to choose median which will be more suitable and supportive for the comparation and analysis. Regarding the table 2.4, we can see that the median of low-income countries (54.3) is almost triple the figure of middle-income countries (18.25) and much higher than when compared with high-income nations (3.95). Therefore, it shows that the developed countries are healthier because of the investment in health care system, which leading to the lower child mortality rate. ii. Measurement of Variation LI MI HI Range 73.7 88.9 7.9 IQR 25.625 18.875 0.675 Standard Deviation 33.13 6.17 0.89 Coefficient of Variation 33.13 24.68 2.54 Figure 2.5: Measurement of Variation of under-5 child mortality rate in low, middle- and high-income countries The coefficient of variations illustrates the extension of variables of data in a mean of population (Adam Hayes, 2019). The higher the CV, the more risks will occur. In this scenario, the coefficient value of LI and MI are 33.13 and 24.69 respectively, which are much 5

higher than HI. This means in these countries; the child mortality rate is greater than highincome nations. This happens because the developing countries might be lack of health-care systems. Additionally, the reason why I choose coefficient for the analysis is because coefficient variation provides the accessibility to estimate the risk and prediction. Hence, it is believed to be the most reasonable measurement. iii. Min Q1 Median Max Q3

Box-and-whisker plots: LI MI HI 40.5 6.2 3.1 47.25 15.025 3.825 54.3 18.25 3.95 114.2 95.1 11 72.875 33.9 4.5 Figure 2.6: Box and whisker plots of under-5 child mortality rate in low, middleand high-income countries

According to the shape, it can be notice that the right box of under-5 child mortality in lowincome countries is 18.575 (Q3-Q2) > 7.05 (Q2-Q1) and right whisker 41.325 (Max-Q3) > left whisker 6.75 (Q1-Min) and hence the shape of the distribution is right-skewed. Similarly, with other countries in middle and high-income, the shape of distribution is also rightskewed. Part 3: Confidence Intervals a. Calculate confidence intervals for the world average of Child mortality rate under the age of 5 (per 1,000 live birth) o o o o o 6

Level of significance: α=0.05 =5% Level of confidence: 1- α = 1-0.05=0.95=95% Sample size: n=28 Sample mean: X : 27.42 Standard Deviation: S= 28.87

o α=0.05 , degree of freedom= n-1=27 o Use T-online calculator: t= = 2.0518 s o => μ= X : +/- t*( )= 16.23 ≤ μ ≤ 38.6 √n o With 95% level of confidence, we can say that the world average of child mortality rate under the age of 5 (per 1,000 birth) is between 16.23 and 38.6. b. Discuss whether and why the assumptions are required or not to calculate these confidence intervals As population distribution is unknown and sample size is 28< 30 then CLT is not applicable and hence we assume that population is normally distributed and standard deviation of ¯ X is normally distributed. c. Suppose the world standard deviation of each variables is known. Discuss the possible impact on the confidence interval results. σ ) √n 2 zσ W= √n

μ= X + z (

The confidence intervals are affected by 4 components including X , z , standard deviation and sample size. Hence, the relationship between confidence intervals and sample size is indirect. By looking at the formula, we can see that if the sample size “n” increases, the width of confidence intervals will be narrowed. Therefore, as the spreading level is lower, the outcomes will become more accurate and less error occurs. On the other hand, as the sample size and confidence level are direct relationship, meaning the rising in z value will lead to the expansion of confidence intervals. As a result, the outcomes turn out to be less accurate. Part 4: Hypothesis Testing A. Regarding the report from WHO 2013, the world average child mortality rate is 46 deaths per 1,000 birth, whereas from the confidence intervals calculated in previous part, the child mortality rate is between 16.23 and 38.6 deaths per 1,000 birth. Nonetheless, the figure of child mortality rate has decreased significantly from 42.4 in 2015 to 38.6 in 2018 (World Bank 2018). Therefore, we can say that the world average child mortality will continue to decrease, which is the good signal for the world. Hypothesis testing:  μ=46( deaths )  n=28  X =27.42  S=28.87  α =0.05=5 %  CL: 95%=0.95

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1. As population distribution is unknown and sample size is 28< 30 then CLT is not applicable and hence we assume that population is normally distributed and sampling distribution of X is normally distributed. 2. Ho; μ ≤ 46 (claim) ; H1; μ>46 3. As population SD is unknown, we use t-table 4. Upper tail 5. At the significant level of 0.05 and degree of freedom 27, CV(t)=> t=2.0518 X−μ =¿ s -3.41 6. Test statistic: t= √n 7. As test statistic falls in non-rejection region, hence we do not reject Ho.

Ho

-3.41

0

2.0518

8. As we do not reject Ho, hence with 95% level of confidence, we can say that the world child mortality rate in 2015 is less or equal 46 deaths per 1,000 births. 9. As we do not reject Ho, we might have committed type II error, we can say that the world average child mortality is no more than 46 deaths per birth, but actually the world average child mortality can be more than 46 deaths per birth. There are two approaches to eliminate the errors, which are accumulating the significant level or the sample size. Nonetheless, in this scenario, extending the sample size is considered to be more reasonable and acceptable among other methods. The reason is because there are 195 countries in total, whereas the sampling gathered data only from 28 nations.

B. The possible impact on the hypothesis testing result when the number of countries of the data set will triple Assume that the number of countries is triple, and other data remain the same, as the sample size is triple => n=28*3= 84 X−μ s Applying this formula to calculation new critical value: t= = -5.989 √n Compare: t(n=28) = -3.41> t(n=84) = -5.989 We can see that the new critical value is also outside the rejection region, hence we do not reject Ho.Therefore, we can conclude that when expanding the sample size to triple, the 8

statistical decision still remains unchanged. In conclusion, as the results stay the same, the increasing of sample size leads to more accurate outcomes. Part 5: Regression Analysis A. By observing the scatter plot 2, it is clear that the data is declining and is on a negative trend. This explains that the investment in measles immunization could lead to the deduction in child mortality rate. Moreover, the data set concentrated closely at the end of the trendline, meaning the R square will be higher leading to less error occurs, also stronger relationship between under 5 child mortality rate and the measles immunization.

Motality rate, under 5 (per 1,000 birth)

Immunization, measles (% of children ages 12-23 months) 120 100 80 Predicted 11.6 Linear (Predicted 11.6)

60 40 20 0 65

70

75

80

85

90

95

100

105

Immunization, measles (% of children ages 12-23 months)

Scatter plot 2: The relationship between under-5 child mortality and immunization measles Dependent variables: Mortality rate, under-5 (per 1,000 live births) Independent variables:  Domestic general government health expenditure per capita, PPP (current international $)  Immunization, measles (% of children ages 12-23 months)  Compulsory education, duration (years)  GNI per capita, Atlas method (current US$)

P-VALUE

Domestic general government health expenditure per capita, PPP (current international $)

Immunizatio n, measles (% of children ages 12-23 months)

Compulsory education, duration (years)

GNI per capita, Atlas method (current US$)

0.0027

0.0002

0.0599

0.0023

Figure 5.1: The P-value of 4 variables

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The table above shows the p-value of four factors that affect the mortality rate of low, middle and high-income countries. It is noticeable that the p-value of immunization measles is the lowest (0.0002) when compared with three other factors. Additionally, the significant level is 0.05, which are greater than p-value of immunization measles. This means the two variables have the relationship with each other. To conclude, as the immunization measles has the lowest p-value indicates the most significant variable.

 Simple Linear Regression Equation: ^ Y =

b0 +

b1 X

 Under 5 child mortality = b0 + b1 x % of measles immunization (children ages 12-23 months)  = 199.198 – 1.918 x % of measles immunization (children ages 12-23 months)  Interpret the regression coefficient (slope): 

b0 =¿ 199.198 shows the value of child mortality when there is no immunization measles because the regression line cuts the y-axis where x=0. This means when the percentage of immunization measles is zero, the average of child mortality rate is around 199.198 deaths per 1,000 birth.



b1=−1.918 presents the average decline by 1.918 (per 1,000 birth) in the child mortality rate when the immunization measles increases by 1 percent of total output.

 Interpret the coefficient of determination (R-square) 

R2 = 42.8% (0.428). This means that the 42.8% of variation in child mortality can be explained by variation in immunization measles and remaining (100-42.8%) 57.2% of variation in child mortality an may be due to other factors.

B. Two other variables that will affect the child mortality rate. In general, levels of child mortality rate have dropped considerably over the last century due to the improvement in healthcare system, especially in high-income countries. However, there are several countries whose under-five child mortality rate are still alarmingly high, specifically in developing categories countries. According to 10

Gordon (2009) study shows that there is a relationship between mother’s years of education and the mortality rate. It claimed that the better levels of maternal education could lead to the reduction of the probability of a child’s death before the age of five. Inversely, the increase in mother’s age also spurring the mortality rate. Similarly, Demographic and Health Survey (DHS) programme found that components such as “environmental health factors” also contribute in changing the trend of mortality rate. Removing contaminants from the living environment of the children is a crucial means of preventing the elements of health that might lead to death. In most of developed countries, the decline in mortality rate has come from the improvement in environmental health, particularly water purification, trash and garbage collection and diminishing in food contaminations (Bulletin of the World Health Organization 2000). Part 6: Conclusion Overall, we can see that high-income countries tend to have higher under-5 child mortality rate when compared with others developing countries, especially low-income categories. To be more precise, we can take a look at the mean (average) of LI, MI and HI countries, at 65.8, 29.1, 4.8, respectively. Clearly, the figure for HI countries is the lowest (4.8), meaning the child mortality rate of developed countries is not rising alarmingly. Meanwhile, the figure of LI is the highest (65.8), particularly in Sub-Sahara area, the child mortality is increased significantly (WHO 2019). Therefore, certain actions need to be applied to help reduce the mortality rate and achieve the SDG goals. Additionally, the hypothesis testing shows that the mortality rate is less than or equal 46 deaths per 1,000 birth. The results indicate that the rate is on the decline trend, meaning in the long-term, the data might keep decrease or remain constant. This is the good signal for the world since the mortality rate is not rising rapidly like it was in the past. Last but not least, regarding the outcomes of regression analysis, we can say that there is still a relationship between child mortality and the variables such as education, GNI, as well as the immunization measles. Higher-income countries with higher GNI, education can lead to the reduction in mortality rate. This happens because these countries provide the residents with better living standard due to the high GNI rate, and advance health-care system for the infant. These factors also considered as an important criterion to determine the mortality rate. Moreover, there is a strong relationship between under-five child mortality rate and the immunizati...