(TIỂU LUẬN) ASIGNMENT 2 individual case study on inferential statistics in term of relationship between the age dependency ratio and GNI

ASIGNMENT 2: Individual Case Study on Inferential Statistics Course Code: ECON1193B Course Name: Business Statistic Lecturer: Huy Doan Bao Campus: Saigon South Student Name: Le Cong Minh Student ID: S3824313 World count: 2785 Numbers of pages: Table of content I Introduction .3 II Descriptive statistics and probability 2.1 Probability 2.2 Descriptive statistics III Confidence intervals a Calculation b Assumption IV V Hypothesis Testing .7 Conclusion VI Reference 11 VII Appendices 12 I Introduction In recent years, population aging has been recognized as a global phenomenon Beside the concern of population explosion, another inextricable issue is the imbalance in age dependency, which is considered as the main reason why measures of age dependency ratio are extremely integral According World Bank (2020), age dependency ratio is defined as the ratio between dependents people (younger than 15 or older than 64) and the working age population (range from 15 to 64) More tellingly, the meaning of dependency ratio is supporting economists by providing them clearly an overall change of population growth Additionally, it also shows the impacts of population ageing on society in several fields including productivity, disability and dependence, social security sustainability and innovation due to the different characteristics of old and young individuals (BMJ Global Health 2019) For a typical example, if the dependency ratio is high, it means the number of retirement population will go up substantially, which leads to the decrease of saving rates With the lower saving rates, economic growth will be facing to the prevention of investment rate since there will be less funding for investment projects Therefore, it will cause long-term economic changes After conducting several academic researches, WHO (2011) stated that we will have more older people sooner or later and more people at extreme old age than ever before It means the fewer people of working age; the fewer people can support the society Last year, the total number of people over 65 was estimated around 700 million In addition, this global number is predicted to reach over 1.5 billion people, which means will double the present number in over next decades (Appendix 1) (United Nations 2019) It happens due to a remarkable improvement in life expectancy (WHO 2011) For instance, the rise of risk diseases such as: heart disease, cancer and diabetes lead to the changes in healthier lifestyle and diet as well as the rapid development of healthcare industry The dominant mission of SDG3 is ensure healthy lives and promote well-being for all at all ages (United Nations 2015) so monitoring the ratio of age dependency certainly plays a crucial role For example, by observing the ratio, it is obvious that the number of older people keeps rising well while the proportion of children under years old surviving decreases moderately each year since 1970s (Appendix 2) In order to reach one of SDG3 targets that ending all preventable deaths under years of age, WHO and UNICEF has cooperated together worldwide to overcome this difficulty by providing nutrition, immunization, high-impact health, HIV and early child development interventions, as well as safe water and sanitation services in every region of the world, including in fragile and conflict settings (WHO 2020) They are taking attempt to ensure the chance of children survival, growth, and benefit from a safe and clean environment In term of relationship between the age dependency ratio and GNI, United Nations (2015) measured that 22% of the population in high-income countries was older people while it occupies about 13% for upper-middle-income countries and 5% for low-income countries (Appendix and 4) Due to the enormous growth of economy in developed countries, older people have a higher level of consumption (Appendix 5) as well as better government support and treatment such as transfer payments, saving rates, coverage pension, inactive labour force than their peers in developing countries Consequently, it jumps to the conclusion that highincome countries tend to be the most aged (United Nations 2015) Overall, this paper purpose is illustrating the clear relation between the age dependency ratio and GNI by applying descriptive statistics, inferential statistics, and probability to analyze the data set of 35 countries II Descriptive statistics and probability 2.1 Probability United Nations (2020) concluded that the proportion of age dependency in a country, which is greater than 20%, is regarded as the high level of age dependency ratio On the other hand, the income levels of each country will be divided into groups based totally on the GNI level    Considering as a low-income country (LI), the GNI must be less than $1,000 per capita, Considering as a middle-income country (MI), the GNI must be in the range between $1,00 and $12,500 per capita Considering as a high-income country (HI), the GNI must be greater than $12,500 per capita According to the provided data (Appendix 6), the contingency table was drawn and characterized by the combination between GNI condition and the level of age dependency ratio Low-income countries (LI) Middle-income countries (MI) High-income countries (HI) Total High age dependency ratio (H) Not high age dependency ratio (N) Total 16 16 14 14 14 21 35 Figure Contingency table for country categories in terms of income level and age dependency ratio a To illustrate whether the income level and the age dependency ratio are statistically independent or not, we must find out exactly the conditional probability of two relevant events from both two categories by academic accounting In this case, it is obviously recognized that two integral events will be high-income countries (HI) and high age dependency ratio (H) P ( H )= 14 35 14 P(H∧HI ) 35 = =1 P ( H|HI )= 14 P (HI ) 35 14 ≠ ), high age dependency ratio 35 and high income is not considered as the independent events so one event will be surely affected by the probability of another one Thus, we can sum up that income and age dependency ratio are statistically dependent Due to the difference between P ( H ) and P ( H|HI ) ( b The ability of a country category does not have a high age dependency ratio can be compared more clearly and informatively by accounting the probabilities of not high age dependency ratio with each income level P (N∧LI ) 35 =1 =100 % = P ( N ∨LI ) = P(LI ) 35 16 P ( N ∧MI ) 35 P ( N |MI )= = =1=100 % 16 P(MI ) 35 P(N∧HI ) 35 = =0=0 % P ( N |HI )= 14 P(HI ) 35  P ( N ∨LI ) =P ( N| MI )> P (N |HI ) Accordingly, the above calculations stated that all of countries with middle-income and lowincome tend to have a low age dependency ratio with the same probabilities of 100% whereas thanks to the improvement in life expectancy as well as modern healthcare system, country with high-income has become a safe home for elders and infants 2.2 Descriptive statistics Low-income Middle-income High-income countries (LI) countries (MI) countries (HI) Mean 4.93 9.52 27.66 Median 5.05 9.1 28.35 Mode No mode No mode No mode Figure Measurement of central tendency table of age dependency ratio of three country categories (%) Minimum LI Low outlier >,, 5.55 MI 17.77 > Figure comparison tables between extreme value and maximum, minimum value of age dependency ratio (%) 15.75 As the results in Figure show that outliers exist in this data set, Mean cannot be the most suitable HI 37.8 > 34.99 measure due to its sensitization to outliers Furthermore, this data set contains only numerical data as well as Mode cannot be identified clearly so it will be rejected to be an ideal approach at all In short, among all tendency methods, Median seems to be the most effective measure in this case The high-income category accounted for the highest median (28.35%) with all of units higher than the standard level of high age dependency ratio (20%) Incidentally, this properly 14 35 appropriate to the probability calculation: P ( H|HI ) = =1 =100 % , which means 100% 14 35 of high-income countries will have the age dependency ratio more than 20% and is possibly considered as a high ratio On the contrary, the median of both medium-income and lowincome countries’ age dependency ratio (9.1% and 5.05%) are the same lower than the figure for high-income countries (28.35%) As this result, high age dependency ratio is likely to occur in high-income countries rather than the rest III Confidence intervals a Calculation In case of estimating the confidence intervals, the confidence level must be selected Due to no requirement, I randomly choose 95% in this case Unknown % Population standard of deviation (σ ) Sample standard of deviation (S) 10.28 % Sample mean ( X ) 16.12 % Sample size (n) 35 countries Confidence level (1-α) 95 % t-critical value (using online calculator) ± 2.03 Figure Statistics summary table for the age dependency ratio As the data set includes 35 countries, it means the sample size will be equal to 35 (n=35), which is greater than 30 Therefore, we will apply Central Limit Theorem (CLT) for accounting as well as the sampling distribution is normally distributed Beside that, by missing the population standard of deviation ( σ ), it results in the substitution of sample standard of deviation (S) and the use of T-table  Confidence interval formula: μ= X +t( S ) √n  =16.12 ±3.53 ( 10.28 √ 35 )  μ=16.12 ± 2.03 => 12.59 ≤ μ ≤ 19.65 Statement: we are 95% confident to jump to the conclusion that the world average of age dependency ratio will fluctuate from 12.59% to 19.65% b Assumption Despite of the lack of population standard of deviation, any requirement for assumption is not integral and become excessive as the sample size (n=35) is obviously greater than 30 Hence, Central Limit Theorem (CLT) should be made use of accounting in case of this normal sampling distribution c Because the world standard deviation of age dependency ratio is supposed to be known, it means calculating the population mean as well as collecting all the values in the entire population can be conducted more easily Therefore, infernal statistics are not essential for the population mean estimation Additionally, there is a lack of major difference between sample to sample, which leads to no commitment for the standard error of the mean (Levine et al 2016) σ S ) and μ= X +t( ) , it obviously shows √n √n that instead of calculating t-value, z-value will be applied As the t-distribution shape seems to be flatter than the z-distribution (Figure 5), the t-value is marginally greater than the z-value in case of the small sample size (McEvoy 2013) The greater critical value is, the larger confidence interval width will be so violating in the inverse relationship: the narrower confidence interval width, the higher accuracy According to the equations: μ= X +Z ( Figure Image captured from A Guide to Business Statistics (McEvoy 2018) In short, if the world mean standard deviation of age dependency ratio is given, the confidence interval will be decreased Otherwise, the result will become more exact IV Hypothesis Testing a According to the World Bank (2020), during the time period time from 1990 to 2013, the world average of age dependency ratio only continuously went up and reached the peak at 12.062% in 2013 (Appendix 7) Then, in the next year, WHO (2014) reported that this total number was up to 12.9% Based on the above result of confidence interval ( 12.59 ≤ μ ≤ 19.65 ), it is predicted that the global mean ratio of age dependency will have an upward tendency in the future Unknown % Population standard of deviation (σ ) Sample standard of deviation (S) 10.28 % Sample mean ( X ) 16.12 % Sample size (n) 35 countries Confidence level (1-α) 95 % Figure Statistics summary table for world average of age dependency ratio Hypothesis Testing Calculation (Critical Value approach) Step 1: Verify the Central Limit Theorem (CLT) As the sample size (n=35) is higher than 30, it leads to the normal sampling distribution and application of CLT Step 2: State hypothesis { The null hypothesis H :μ ≤ 12.9 The alternative hypothesis H : μ>12.9(claim) Step 3: Based on the above alternative hypothesis ( H ), they contain ‘ ¿ ’ Therefore, upper-tailed test would be applied in this case Step 4: Due to missing the population of standard deviation as well as the conclusion of a normal sampling distribution, T-table will be applicable for this calculation Step 5: Define critical value } Level of significance α=0.05 Degrees of freedom d f =34 ⇒ Upper−tailed test t cv =1.69 Step 6: Calculate test statistic t stat ¿ X−μ 16.12−12.9 = =1.85 10.28 S √n √ 35 Step 7: Make statistical decision In case of the fall of test statistic into Rejection Region (t stat > t cv (1.85>1.69)) and the calculated confidence interval in part III, H will consequently be rejected while H is acceptable at all Step 8: Interpretation Because of the result of confidence interval and support evidence from the rejection of H by Hypothesis Testing, we could infer that the increase in mean of age dependency ratio will continuously boost in the future with 95% level of confidence Step 9: As H is rejected, it means we would commit Type I error to our analysis With P (Type I) = α = 0.05 = 5%, which is regarded as the percentage of the chance that the mean of age dependency ratio could stop increasing in the future In order to minimize the Type I error, decrease the significance level is the most common way Thus, in this case, the level of significance should be determined at 1% (0,01), which means only 1% probability of incorrectly rejecting the null hypothesis b Double sample size Even though the supposition of a double number of countries is carried out, there is still no any effects on the conclusion of the aforementioned hypothesis testing, apart from being more precise Certainly, the rise in sample size (n) as well as degrees of freedom (df) are directly resulted from the double number of countries Hence, it leads to the change in t-distribution by moving gradually nearer to standardize normal distribution Figure shows that the more sample size increase, the more homogeneous these distribution shapes will be Then, if the sample size seems to be large enough, t and Z distribution are likely to have no variance Consequently, the accuracy of estimating the standard of deviation will be improved sharply (Berenson 2015) Figure Standardized normal distribution and t distribution for degrees of freedom, adopted from Basic Business Statistics eBook (Berenson 2015) So as to gain a better evaluation, we should widen our knowledge about studied population dramatically by increasing the sample size based on the theory that the greater sample size is, the more margin of error in the confidence interval can be decreased (Bowerman, Froelich and Duckworth 2018) Moreover, the reduction of uncertainty and inaccuracy will be enhanced as the narrower confidence interval is, which caused by the increase in sample size, the more statistical power and greater precision can be achieved (Littler 2015) V Conclusion After illustrating the relationship between GNI and the age dependency ratio by calculation and analysis on the summarized descriptive analysis, probability, confidence intervals and hypothesis testing, we gain some key findings from the above inferential statistics First of all, by drawing the contingency table and calculating the probability, it shows that the level of income and the age dependency ratio are both dependent events, which leads to the GNI impact on the ratio of age dependency when some changes happen Due to the strong association between the income level and age dependency ratio, developed countries with high-income (GNI over $12500) level will trend in the growth rate of high age dependency steadily whereas in developing countries with low-income or medium-income level (GNI less or equal to $12500), the welfare of older and infant population needs to be concerned in order to lengthen the life expectancy as well as strengthen the survival rate Next, it is reckoned that 100% of high-income countries will have the age dependency ratio higher than 20% On the other hand, the probabilities of medium-income and low-income countries having a high age dependency ratio are the same and equal to 0% Furthermore, the median of high-income category (28.35%) can be seen obviously the highest one from descriptive analysis, meanwhile the lowest median (5.05%) belongs to the low-income countries Beside that, the median of medium-income countries (9.1%) is extremely less than the critical value of age dependency level (20%) As this result, it is inferred that the higher income level, the higher age dependency will be Last but not least, with the support evidence from confidence intervals as well as hypothesis testing, we are 95% confident to estimate that the world average age dependency ratio will continuously keep the upward trend in growing in the future Based on the above calculation, the mean age dependency ratio in 2015 (16.12%) is enormously greater than the 2014 (12.9%) Hence with 95% level of confidence, we can conclude that the world mean age dependency ratio will be volatile in the range from 12.59% to 19.65% Fortunately, the hypothesis testing also supports our conclusion 10 As I mentioned above, monitoring age dependency ratio certainly plays a vital role in achieving the Sustainable Development Goal In this case report, our analysis depends on the relevance of GNI and the age dependency ratio with the data from the 2015 World Bank to make a conclusion that the age dependency ratio can be affected by various factors, especially GNI level VI Reference Berenson, M et al 2015, Basic Business Statistics EBook, Pearson Education Australia, ProQuest database BMJ Global Health 2020, ‘Dependency Ratios In Healthy Ageing’, viewed December, Littler, S 2015, ‘The Importance and Effect of Sample Size’, Select Statistical Services, viewed 13 December 2019, McEvoy, DM 2018, A guide to business statistics, John Wiley & Sons, Inc., Hoboken, New Jersey The World Bank 2020, ‘Age Dependency Ratio (% Of Working-Age Population) | Data’, viewed December 2020, United Nations 2015, ‘World Population Ageing’, viewed December 2020, United Nations 2019, ‘World Population Ageing 2019 Highlights’, viewed December 2020, WHO 2011, ‘Global Health And Aging’, viewed December 2020, WHO 2020, ‘WHO And UNICEF Recommit To Accelerating Health And Well-Being At All Ages’, viewed 10 December 2020, 11 VII Appendices Appendix 1: Image captured from United Nations World Population Ageing Report 2015 12 Appendix 2: Image captured from Global Health Ageing Report (WHO 2011) Appendix 3: Image captured from United Nations World Population Ageing Report 2015 13 Appendix 4: Image captured from United Nations World Population Ageing Report 2015 Appendix 5: Image captured from United Nations World Population Ageing Report 2015 14 Appendix 6: Division of countries based on GNI and the age dependency ratio 15 Appendix 7: Image captured from The World Bank (2020) 16 ... Testing a According to the World Bank (20 20), during the time period time from 1990 to 20 13, the world average of age dependency ratio only continuously went up and reached the peak at 12. 0 62% in. .. estimate that the world average age dependency ratio will continuously keep the upward trend in growing in the future Based on the above calculation, the mean age dependency ratio in 20 15 (16. 12% ) is... 8: Interpretation Because of the result of confidence interval and support evidence from the rejection of H by Hypothesis Testing, we could infer that the increase in mean of age dependency ratio