Assessment 2 individual case study on inferential statistics DESCRIPTIVE STATISTICS AND PROBABILITY

ECON1193 – BUSINESS STATISTICS Assessment #2: Individual case study on Inferential Statistics Course code ECON1193 Course name Business Statistics Campus Sai Gon South Campus File submitted Word and Excel Student name Nguyen Duong Minh Hieu Student ID S3878647 Student email S3878647@rmit.edu.vn Lecturer Hieu, Nguyen Huynh Trong Assignment due date December 13 - 2021 Word Count 2914 Table of content ABBREVIATION I INTRODUCTION: II DESCRIPTIVE STATISTICS AND PROBABILITY: PROBABILITY: a Statistically dependent events’ experiment: b The clarification of three country categories: DESCRIPTIVE STATISTICS: a Measure of Central tendency: b Measure of Variance: c Measure of Shape: III CONFIDENCE INTERVALS: CALCULATION: ASSUMPTION FOR CALCULATION: DISCUSSION IV HYPOTHESIS TESTING: TREND OF WORLD ADOLESCENT BIRTH RATIO HYPOTHESIS EXAMINATION PROCES: DISCUSSION V CONCLUSION: VI REFERENCES: VII Appendices: Abbreviation (Notice: Some acronyms are also contained with their explanation in the report) GNI – Gross National Income AFR – Adolescent Fertility rate SDG - Sustainable Development Goals UN – United Nations UNICEF – United Nations Children Fund WHO – World Health Organization CLT - The Central Limit Theorem I Introduction In recent decades, sustainable development has become a hot topic globally, with the primary goal of ensuring human happiness by balancing social, economic and environmental factors, bringing prosperity to both present and future generations (UNDP, 2021) In consequence, the United Nations (UN) has developed a list of 17 Sustainable Development Goals (SDG) (Figure 1), with the third SDG (Figure 2) placing a high premium on maintaining healthy lives and fostering humanity's well-being (United Nations, 2020) The adolescent fertility rate (AFR) is one of the most important markers of the quality of teenage sexuality and can be used to quantify the UN's goal; therefore, diminishing adolescent fertility and treatment of underlying issues are crucial to improving teens' sexual and reproductive health, as well as their social and economic well-being (United Nation Statistical Division, 2021) The adolescent fertility rate is defined as the number of births per 1,000 women aged 15 to 19, and it serves as a basic indicator of reproductive health for vulnerable young women (WHO, 2020) Based on the UN report (2019), AFR has dropped by half in the last 20 years (from 55 births per 1000 female teens in 1995 to 25 births per 1000 female teens in 2015) (Figure 3) Whilst, out of 900 million teenage females worldwide, around 12 million 15–19-year-old girls gave birth in evolving nations (WHO, 2021) The objective is to reduce the adolescent birth rate by 2030 by providing universal access to reproductive health care and schooling, but there are still enormous factors preventing it from being measured accurately adolescent birth rate, such as actual adolescent births, are not published precisely due to large populations and remote locations (WHO, 2021) Resultantly, despite the efforts of several international organizations to reduce adolescent pregnancy rates, issues remain that must be addressed in order to ensure that no female citizens are left behind Adolescents understand and broaden their viewpoints and life skills during this vulnerable stage of human development in order to adjust to significant changes in their health (UNICEF, 2021); especially for women, who may face the possibility of early pregnancy if no help or schooling is provided in preparation Fortunately, according to (WHO, 2017), Due to education on modern contraceptive measures, the AFR in 2015 was just 44.1% per 1000 girls When compared to non-teaching countries, Latin American countries have approved legislation requiring sex education in schools, and the AFR has dropped by a statistically significant 6.73 points (Leung, 2019) Thence, education plays a key role in addressing this troubling issue, but it necessitates regular funding, which has become a major cause of concern for developing countries In fact, approximately 95% of adolescent births occur in low- and middle-income countries, for example, Yaya (2020) reported 110 births per 1000 female teenagers compared to the global average of 47 births Hence, in addition to schooling, differences in AFR between nations are caused by differences in gross national income (GNI) According to Schultz (2005); the average income index is inversely related to the fertility rate, indicating that socioeconomic factors can increase or reduce this ratio In actuality, the Africa region's teen fertility rate is the highest in the world in both 2000-2005 and 2015-2020 (Figure 4) (UNICEF, 2021), which can be attributed to a lack of facilities as well as investment in educational programs Figure 5, contrastly, illustrates that developed areas such as North America, Europe, and Asia have a lower AFR (24% of births per 1000 female teenagers) than developing areas (53%) (United Nations, 2013) Due to this, that testimony suggests a reversal of the link between the two variables AFR and GNI Using four computational approaches: probability, descriptive statistics, confidence intervals, and hypothesis testing; this report will explore and analyze the relationship between AFR and GNI in 35 countries in order to elucidate AFR trends in each country category II Descriptive Statistics and Probability Probability The adolescent birth rate statistics separate the 35 sample countries of the third sustainable development goal (Table 1) into three distinct categories based on gross national income provisions: Low-income countries GNI less than $1,045 per capita Middle-income countries GNI between $1,045 and $12,736 per capita High-income countries GNI greater than $12,736 per capita Besides, the AFR was divided into two classes to examine the dissimilarity between each nation group, with low and high ratios demonstrating low and high dissimilarity A country with an AFR greater than 30 has a high adolescent birth rate (H), while a country with an AFR less than or equal to 30 has a low adolescent birth rate (L) The contingency table below is generated by counting the number of countries that meet both of the requirements of each cell, assisting in the calculation of the next probability High Adolescent fertility rate (H) > 30 Low Adolescent fertility rate (L) ≤ 30 Total Low-income countries (LI) Middle-income countries (MI) 14 17 High-income countries( HI) Total 23 12 35 Table 2: Contingency table of each country category on Adolescent Fertility Rate (2015) a) Statistically dependent event’s experiment Apply a conditional probability formula to determine if GNP and AFR are statistically dependent or independent events in countries with low AFR(L) under conditions where the income event occurred low-income (LI) and then compare the probability of a low AFR, similarly with (L) in middle-income (MI) and high-income (HI) countries: The previous calculation indicated that the probability of low AFR (L) occurring under LI, MI and HI conditions is not equal to the probability of low AFR (L), given that GNI and AFR are statically dependent occurrences Therefore, adolescent fertility is directly affected by national income level and vice versa b) The clarification of three countries categorizes: When using conditional probability, the probability of the common events of high adolescent birth rates and each country's income divided by that country's income type, is the ideal metric for evaluating Which income category by country group has the greatest impact on AFR: According to the statistics above, low-income countries have the highest rate of adolescent childbearing, with an estimated 89 percent possibility This suggests that in low-income countries, 89 percent of nations will attain a hegemonic AFR Descriptive Statistics Min >,, 1,04 173,04 < 179,92 No outlier Middle-income countries 13,31 > -16,9775 111,22 < 112,3625 No outlier High-income countries 3,19 > -2,485 58,68 > 16,795 Upper Outlier Table 2.2: Examination of outliers in each country category on Adolescent Fertility Rate (unit: births per 1,000 women ages 15-19) A test of outliers is performed to ensure the accuracy of three measures in descriptive statistics According to the preceding test table, there is one existing upper outlier in the highincome category a) Measure of central tendency Low-income Mean Median Mode 91,133 90,15 #N/A 52,493 51,74 #N/A 12,18 6,21 #N/A countries Middle-income Countries High-income countries Table 2.3: Central Tendency of three country categories on Adolescent Fertility Rate (2015) (unit: births per 1,000 women ages 15-19) The Median is considered the greatest tool for examining differences in this circumstance because it is not inflated by the aforementioned outliners in this observation Low-income countries have the greatest adolescent fertility rate, with 90,15 births per 1000 girl teenagers, according to the table above More than half of low-income countries will have an AFR of more than 90.15 per 1000 adolescent girls, according to the statement Middle-income countries ranked second, with 51.74 per 1000 women aged 15-19 years, half as low as the low-income group but still outperforming the high-income group, with only 6.21 per 1000 women aged 15-19 This segment is 14 times below average for low-income earners and times below average for middle-income earners As a result, the Median comparison shows that the higher the economic level, the lower the fertility rate per 1000 adolescent girls b) Measure of Variance Range Interquartile Range Variance Standard Deviation Coefficient of Variation Low incomecountries 145,2 44,72 1621,273 40,271 44% Middle-income countries 97,91 32,335 602,156 24,539 47% High-income countries 55,49 4,82 308,8382 17,5738 144% Table 2.4: Measure of variation of three country categories on Adolescent Fertility Rate (2015) (unit: births per 1,000 women ages 15-19) The coefficient of variation is a useful statistic for comparing the variable degree of one data series to another, even when their means are considerably different (Frost, 2020) This technique is very beneficial in this circumstance because the Mean values of the three groups are so diverse Table 2.4 shows that the low-income countries with the lowest coefficient of variation (44%) show less frequent fluctuations in the adolescent fertility rate and are more concentrated on the average of 91,133 births births per 1000 female adolescents, while middle-income countries have a coefficient of variation of 47% and high-income countries have a coefficient of variation of 144%, implying that both countries all have a higher dispersion of AFR data than the low-income segment c) Measure of Shape Figure 6: Measure of shape of three country categories on Adolescent Fertility Rate (2015) (unit: births per 1,000 women ages 15-19) The box and whisker plots of three categories of country income revealed a number of noticeable outlier discrepancies In part because their Mean value is bigger than their Median value, all three nations are right-skewed or positively skewed, as seen in Figure However, in high-income countries, the right box is longer than the left, whereas in low- and middleincome countries, the right box is shorter It could be explained by the presence of an upperbound outlier in the group of high-income countries, causing the Mean value to be higher than it is The whiskers of the three types of countries, on the other hand, are longer to the right, meaning that more than half of the adolescent birth fertility ratio is concentrated more on the right sides of these three types III Confidence Intervals Calculation For the purpose of determining a confidence interval for the worldwide mean fertility rate for women aged 15-19 years, the significance level (� ) is assumed to be 0.05, meaning that the confidence level will be calculated as - 0.05 = 0.95 in the table below: Abbreviation Data Significance Level α 5% Confidence Level (1-α) *100% 95% Population standard deviation σ unknown Sample Standard Deviation S 39,5326 Sample Mean 52,06 Sample Size n 35 Table 3: Confidence intervals computational units (unit: births per 1,000 women ages 15-19) Because the population standard deviation is unknown, the sample standard deviation can be used, suggesting that the Student t distribution be employed instead of the normal distribution:  Consequently, the real worldwide mean of the childbearing ratio among women aged 15 to 19 is between 38,48 and 65,64 births per 1000 female adolescents has a 95% confidence level Assumption for calculation Even if the population standard deviation is unknown, the sample size of all observations is sufficiently large (n = 35) to meet a mandatory condition for applying the Central limit theorem (CLT) That is, regardless of the population's structure, this sampling distribution is almost normal, hence no assumptions are required Discussion The z-value table will be used if a population standard deviation is found because it has both a suitable sample size and a population standard deviation One advantage of using a Z-value table to calculate confidence intervals is that it is normalized from actual population data (Mcleod, 2019); and in the student-t distribution, the sample mean and standard deviation can vary significantly from one sample to the next, leading to many uncertainties in statistical work (Ranjan Rout, 2020) In principle, confidence intervals are used to assess the degree of uncertainty or certainty in a sampling process; the smaller the confidence interval, the lower the degree of ambiguity (Bevans, 2020) At the same period, when the sample size is small, critical z-values are smaller than critical t-values for any given degree of confidence (Cummung, 2008) The width of confidence intervals narrows as critical values are reduced, validating our hypothesis that using a population standard deviation in narrower confidence intervals Reduced confidence interval width, on the other hand, reduces the margin of error 10 (e), which is defined as a factor to assess the proportion of a collection of data that can generate errors, ensuring correct calculations results (KhanAcademy, 2017) ⟹ In a nutshell, when the population standard deviation is known, the width of the confidence interval narrows for higher certainty, yielding in more precise confidence intervals IV Hypothesis Testing Trend of world adolescent birth ratio According to the WHO statistics, female adolescent fertility rate in 2014 was 46 births per 1000 women, which easily falls within 38,48 and 65,64 of the preceding calculation, indicating that the average global adolescent birth rate will be in 2015 It's difficult to predict if this ratio will rise, fall, or stay the same in the long run The point estimate of a sample mean in 2015 is much higher (52,06 > 46) than the world average in 2014 As a result, it can be assumed that the rate of adolescent childbirth will rise in the coming years, and this prediction will be confirmed through the hypothesis testing that follows Hypothesis examination process Abbreviation Data Significance Level α 5% Confidence Level (1-α) *100% 95% Population standard deviation σ unknown Sample Standard Deviation S 39,5326 Population Mean μ 46 52,06 Sample Mean Sample Size n 35 Table 4: Hypothesis testing units (unit: births per 1,000 women ages 15-19) Step 1: Normal distribution inspection: The mean sample distribution is normally distributed because it meets the central limit theorem (CLT) criterion of n > 30 Step 2: Determine null and alternative hypothesis: Null hypothesis: H0: 11 Alternative hypothesis: H1: Step 3: Specify the kind of tail side Step 4: Deciding the kind of table to utilize: The t-table is appropriate since the sample mean is normally distributed and the population standard deviation is unknown Step 5: Determining Critical Value (CV): Step 6: Calculating test statistic t: Step 7: Making statistical decision: The non-rejection zone of the statistic t-test is 0.097 (t ') > -1.691 (t) As a result, not rule out the null hypothesis (H0), but rather reject the alternative hypothesis (H1) Step 8: Generating a managerial decision: Because H0 is not refuted, it may be concluded with 95 percent certainty that the global teenage fertility ratio would rise in the future Step 9: Determining the possible errors: If we not reject Ho, we may have committed a Type II error ( β) P (Error Type II) = – Test power Although we expect the adolescent fertility rate to climb in the future, this ratio may not rise in the near future Type II error, on the other hand, can be lowered by increasing the sample size (n), the 12 significance level (α), or decreasing the population standard deviation ( σ), because the larger, the more likely the null hypothesis will be rejected when it is genuinely true Discussion If the number of nations in the data set is cut in half, the degree of freedom (n - 1) reduces as well, resulting in a substitution in the t-distribution graph by decreasing the tail and shifting the crucial t value further away from the mean (Maindonald, 2008) Synchronously, as the number of countries decreases, the sample mean becomes increasingly distinct and distant from the real population mean, causing the standard deviation S to increase (Faber & Fonseca, 2014) From examining the formula t=(X  -μ)/(S⁄√n), the relationship between the three indices t, S, and n can be visualized If n is lower and S is bigger, t' will have a smaller value, meaning that t' will move further away from t-values As a result, the t' and t values will be wider apart in this situation, resulting in the statistical choice above being constant Theoretically, decreasing the sample size reduces accuracy because the standard error formula e=σ/√n has the sample size (n) as the denominator, which is inversely proportional to the standard error (e) (Frost, 2021) According to Fotini (2013), as a result of decreasing the number of countries, the standard error increases, making the statistical results less reliable and the sample less representative of the entire population Eventually, as the sample size grows larger, the test's strength (1-β) will increase, providing us with less information and increasing the amount of uncertainty, resulting in a higher risk of Type II error (Bhandari, 2021) V Conclusion In sum, this research found that gross national income (GNI) and adolescent fertility rate (AFR) are closely linked, as evidenced by the Probability and Descriptive Statistics sections, based on data from 35 countries on adolescent fertility rate (AFR) aged 15-19 years Furthermore, according to Hypothesis Testing, the maternal mortality ratio is expected to increase in the future As a result, in the following paragraph, we'll look at three major results from the data analysis method The first finding is that GNI and AFR are two statistically dependent events, implying that the probability of a country having a high or low AFR is dependent on its gross national income The likelihood for all low AFR nations in the contingency table is completely different from 13 that for low-income and low-AFR countries Surprisingly, the likelihood of having a child in adolescence is higher and even higher in middle-income nations than in low-income countries, most likely because it is examined in 17 countries, compared to in low-income countries The second discovery indicated that there is a strong inverse association between AFR and GNI, based on the application of three descriptive statistics measurements: central tendency, variation, and shape If countries have greater GNI levels (Table 2.3 - Median), the teenage birth rate might decline from 90,15 to 6,21 births per 1000 female teens, implying that the higher the national wealth, the lower the adolescent fertility rate In addition, using coefficients of variation and box plots, the AFR gap between middle- to low-income countries and high-income countries is well defined As seen in Figure 5, industrialized countries with a high GNP generally have the lowest AFR, whereas moderate to low-income nations have the highest AFR, validating the premise that GNP and AFR have an inverse relationship Finally, according to that sample, the global average adolescent fertility rate in 2015 was between 38.48 and 65.64 births per 1000 women aged 15-19 years, with point estimates (sample mean) lower than the 2014 global AFR average And, after working on the theory, we are 95% certain that the global adolescent birth rate will soar in the coming years; however, this percentage may actually decrease in the future Given the foregoing, these findings could be important assets for strategic planning aimed at achieving global SDG target Because adolescent pregnancy can be harmful to both the mother and the baby, increasing the risk of maternal death and preterm birth Hence, to increase people's access to education, gender equality, reproductive health, sexuality, and family planning should all be undertaken by the government From that point, low-income countries will benefit from realistic and precise strategies that will help them avoid excessive adolescent birth rates VI References: Bevans, R 2020, “Confidence Interval | Definition, Formulas, Examples,” Scribbr, viewed December 2021, Bhandari, P 2021, “Type I & Type II Errors | Differences, Examples, Visualizations,” Scribbr, viewed December 2021, 14 Cumming, G 2008, 'Replication and p Intervals: p Values Predict the Future Only Vaguely, but Confidence Intervals Do Much Better', Perspectives on Psychological Science, vol 3, no 4, pp 286–300 Faber, J & Fonseca, LM 2014, “How Sample Size Influences Research Outcomes,” Dental Press Journal of Orthodontics, vol 19, no 4, pp 27–29, viewed December 2021, Fotini, T 2013, “Alternative Approaches – Effects on Variance and Tracking Performance of the Consumer Confidence Indicator,” 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UNDP 2021, “Background of the Sustainable Development Goals,” UNDP, viewed December 2021, UNICEF 2021, “Early Childbearing,” UNICEF DATA, viewed December 2021, United Nations 2013, Adolescent Fertility since the International Conference on Population and Development (ICPD) in Cairo, viewed December 2021, United Nations Statistical Division 2021, SDG Indicator Metadata, viewed December 2021, WHO 2017, “Almost Half of All Deaths Now Have a Recorded Cause,” www.who.int, viewed December 2021, WHO 2020, “Indicator Metadata Registry Details,” www.who.int, viewed December 2021, WHO 2021, “Indicator Metadata Registry Details,” www.who.int, viewed December 2021, Yaya, S 2020, “Inequality in Fertility Rate among adolescents: Evidence from Timor-Leste Demographic and Health Surveys 2009–2016,” Archives of Public Health, vol 78, no 1, viewed2December 2021, VII Appendices 16 Figure 1: 17 Sustainable Development Goals (United Nations n.d) 17 Figure 2: The third sustainable development goal (United Nations, 2021) 18 Figure The fertility rate for female adolescents by Hispanic origin and race 1960-2016 ( Child Trends, Teen Births, 2019) Figure Adolescent Fertility Ratio Estimates (Unicef, Early childbearing, 2019) 19 Figure Birth rates of adolescents by development groups and regions in 2005-2010 (United Nations, Adolescent Fertility since the International Conference on Population and Development (ICPD) in Cairo, 2013) Country Name Country Code Norway Switzerland Sweden Netherlands Canada Germany France Italy Seychelles NOR CHE SWE NLD CAN DEU FRA ITA SYC Argentina Malaysia Brazil Mexico ARG MYS BRA MEX Adolescent fertility rate (births per 1,000 women ages 15-19) High Income 5.77 3.19 5.31 4.18 10.17 7.15 8.96 6.21 58.68 Middle Income 63.26 13.31 63.76 62.55 GNI per capita, Atlas method (current US$) 93050 85780 57880 49030 47460 45790 40730 32970 14010 12300 10450 10100 9860 20 Romania Suriname Ecuador Thailand Samoa Philippines Indonesia Morocco Nigeria Lao PDR Vietnam India Kenya ROU SUR ECU THA WSM PHL IDN MAR NGA LAO VNM IND KEN Senegal Tanzania Zimbabwe Benin Comoros Mali Rwanda Togo Ethiopia SEN TZA ZWE BEN COM MLI RWA TGO ETH 34.38 47.33 75.28 51.74 25.63 59.21 48.61 32.26 111.22 63.96 30.79 26.00 83.09 Low Income 77.05 118.12 107.56 90.20 68.99 173.04 27.84 90.15 67.25 9530 8830 6000 5710 4070 3520 3430 3010 2850 2000 1950 1600 1310 980 910 890 870 790 790 710 610 600 Table The data set of 35 countries in 2015 (RMIT University Vietnam, Excel database, 2021) 21 ... Frost, J 20 20, “Coefficient of Variation in Statistics, ”... 47.33 75 .28 51.74 25 .63 59 .21 48.61 32. 26 111 .22 63.96 30.79 26 .00 83.09 Low Income 77.05 118. 12 107.56 90 .20 68.99 173.04 27 .84 90.15 67 .25 9530 8830 6000 5710 4070 3 520 3430 3010 28 50 20 00 1950... Standard Deviation Coefficient of Variation Low incomecountries 145 ,2 44, 72 1 621 ,27 3 40 ,27 1 44% Middle-income countries 97,91 32, 335 6 02, 156 24 ,539 47% High-income countries 55,49 4, 82 308,8382