Assignment 2 individual case study inferential statistics

ECON1193 – BUSINESS STATISTICS Assignment – Individual Case Study - Inferential Statistics Subject Name Business Statistics Subject Code ECON1193 Campus SGS Campus Student Name Tran Bao Chau Student ID S3818482 Lecturer’s Name Park, S Word count Part Introduction Sustainability is the development that fulfills present needs without undermining future generations' potential, maintaining a balance between economic growth, concern for the environment and social well-being (Acciona n.d.) In today world, the term 'sustainable development' is gradually becoming popular not only in businesses but also in our society Initially, this term was originated from the Brundtland report in 1987, defined sustainable development as ‘the human ability to make development sustainable-to ensure that it meets the needs of the present without compromising the ability of future generations to meet their own needs’ (Robert, Parris & Leiserowitz 2005, p.10) In 2015, the United Nations adopted the 2030 Agenda, which includes the Sustainable Development Goals (SDG) – a plan developed to protect the planet and ensure the well-being of people around the world SDGs consist of 17 goals which are planned to achieve in 15 years, from 2015 to 2030 (Appendix A) One of the goals is SDG Goal specifies Decent work and Economic growth To make this goal more coherent, there is a factor we can consider using: Individuals using Internet As defined, Internet users are individuals who have spent the last three months using the Internet from any area worldwide The Internet can be accessed through a mobile phone, a computer, personal digital assistant, games machine, digital TV and so on (Roser, Ritchie & Ortiz-Ospina 2015) The individuals using internet indicator refers to the percentage of internet users in the global population According to the International Telecommunication Union n.d (ITU), the number of internet users increased sharply after 10 years due to the rapid growth of technology and the popularity of social media, from only 1.5 billion people in 2008 to 4.1 billion people by the end of 2019 which accounts for 53.6% of global population (Appendix B) In some regions such as Europe, Americas, there has been higher number of individuals using the Internet per 100 inhabitants than other areas (Appendix C), in which ‘the Internet will produce significant cost savings in many sectors of the economy, resulting in faster productivity growth It will also produce lower prices for consumers, resulting in faster growth in living standards’ (Rivlin & Litan 2001) Hence, the use of the internet and technology for administrative, social affairs and economic development should be highly encouraged to achieve the SDG Goal In addition, the relationship between Individuals using internet and gross nation income (GNI) has been noticeable The income classification is determined using the Atlas process, based on a calculation of national income per person, or GNI per capita Prydz & Wadhwa (2019) defined the low-income economies with the GNI per capita of $1,025 or less in 2018; middle-income countries with GNI per capita between $1,026 and $12,375; lastly, high-income nations achieved GNI per capita of $12,376 and above Three income groups expressed an upward trend in the percentage of individuals using internet, recorded by World Bank Low-income countries have the lowest percentage of internet users, at 15.8% of population; followed by is middle-income with 45.8% of population who went online On the contrary, countries with high GNI per capita showed a large gap with the two first groups, account for 84.6% of population, which is also higher than the world’s individuals using internet in 2017 (Appendix D) Nevertheless, GNI is not the only factor that affect the proportion of individuals using the Internet, it can be driven by other factors Part Descriptive Statistics and Probability Probability 1.1 Consider whether income and Individuals using internet are statistically independent events 38 chosen countries in the data set #9 are divided into groups of income: • Low-Income countries (LI): countries with a GNI less than $1,000 per capita • Middle- Income countries (MI): countries with a GNI between $1,000 and $12,500 per capita • High-Income countries (HI): countries with a GNI greater than $12,500 per capita These countries are also sorted based on the Internet usage: • • Low usage of internet (A): individual using the Internet less than 40% of population High usage of internet (A’): individual using the Internet more than 40% of population We create a contingency table (unit: Number of countries): High usage of Low usage of internet Internet (A) (A’) Total Low-income countries (LI) 5 Middle-income countries (MI) 11 20 High-income countries (HI) 13 13 Total 14 24 38 Next, we will compare two probabilities to check if individuals using internet and income are statistically independent or not The two probabilities are: the marginal probability that a random chosen country has low internet usage, which is P(A); and the conditional probability that a random chosen country has low internet usage, regarding low income, denoted P(A|LI) 14 = 0.37 (1) = 19 38P(A ∩ LI) P(A|LI) = = = (2) P(LI) P(A) = From (1) and (2) → P(A) ≠ P(A|LI) The outcome presents that the marginal probability that a random chosen country has low internet usage is different from the conditional probability that a random chosen country has low internet usage, given that low income As a result, the number of individuals using internet and income are statistically dependent In other words, individuals using internet and income are related to each other 1.2 Which country categories are more likely to have high usage of internet? Based on the Contingency table above, to identify which country categories are likely to have high usage of Internet (above 40% of population), we calculate the conditional probability of countries have high usage of Internet regarding each category: Low-income, Middle-income and High-income P (A′ ∩ HI) P (A’|HI) = P (A’|MI) = P (A’|LI) = = 13 = = 100% P(HI) 13 P (A′ ∩ MI) 11 P(MI) P (A′ ∩ LI) P(LI) P (A’|HI) > P (A’|MI) > P (A’|LI) = 20 = 0.55 = 55% = = = 0% In conclusion, high income countries are the most likely to have high usage of internet with 100% of population using the internet – the highest usage among three categories Follow by is middle income countries still recorded high internet usage with 55% Except for low income countries, it is recorded with 0% individual using the Internet Descriptive Statistics Measures of Central Tendency Low-income Middle-income High-income Mean 18.41 42.15 82.92 Median 21.96 43.62 84.45 Mode #N/A #N/A #N/A Table The measures of Central Tendency of Individuals using the Internet (% of population) 3.5 2.5 1.5 0.5 Histogram of MI countries' individuals using Internet Number of MI countries 17 More Histogram of HI countries' individuals using Internet 1 58.77 71.02 5 11.92 26.53 41.13 55.73 Figure Histogram of MI countries Figure Histogram of LI countries 7 More Individuals using Internet (% of population) Individuals using Internet (% of population) Number of HI countries Number of LI countries Histogram of LI countries' individuals using Internet 83.26 More We have created histograms of three country categories to decide whether any outliers are apparent or not Based on the observation from the chart, there is no outlier showing in the three country categories Therefore, since no outlier is found, Mean is the best measure of central tendency Indivuduals using the Internet (% of population) Figure Histogram of HI countries According to Table 1, the average of individuals using Internet in selected HI countries is the highest with 82.92%, come after is MI countries and LI countries with 42.15% and 18.41% respectively In conclusion, HI countries tend to have a higher average of individuals using Internet in population than MI and LI countries Part Confidence Intervals a We suppose a 95% confidence interval for the world average individuals using Internet in 2017 Sample Mean X 52.98 Sample size n 38 26.92 Sample Standard Deviation S Population Standard Deviation 𝛔 Unknown 95% Confidence level (1-α) *100% We have 1- α = 0.95 → significance level α = 0.05 As population standard deviation σ is unknown, we have to use T-table instead of Z-table Significance level α = 0.05; 𝛼 ⁄2 = 0.025 According to T-table Degree of Freedom d.f = n – = 38 - = 37 ➔ t(n-1, S Confidence interval estimates: X ± t × √n → 𝛼 ) = t(50,0.025) = 52.98 + 2.0262 × = 52.98 - 2.0262 × 44.13 ≤ 𝜇 ≤ 61.83 2.0262 26.92 √38 = 61.83 26.92 √38 = 44.13 → We are 95% confident that the true world average of individuals using the internet is between 44.13% and 61.83% of population in 2017 b Although the population standard deviation σ is unknown, the sample size of the assigned dataset is 38, greater than 30, which is large enough to apply for Central Limit Theorem (CLT) CLT is applicable so the distribution of the sample mean will become approximate normal distribution, regardless of the shape of the population Therefore, no assumption is needed to calculate these confidence intervals c In case the population standard deviation σ is known, the confidence interval will show a decrease (the gap becomes smaller) Since the sample standard deviation S varies from sample to sample, it induces some confusion and the results may not convincing enough Instead, the population standard deviation 𝜎 can increase a more accurate and precise result McLeod (2019) stated that ‘The narrower the confidence interval (upper and lower values), the more precise is our estimate’ Besides, the width of confidence interval values will become narrow as the sample size increases, which means the bigger the sample size n, the more accurate the outcomes show Part Hypothesis Testing a According to a report published by the World Health Organization (WHO), in 2016, the world average individual using the Internet (% of population) is 44.7% In part 3a, we are 95% confident that the true world average of individuals using the internet ranged from 44.13% to 61.83% in 2017 However, it is uncertain to assert the global average of individuals using the internet will remain constant, increase, or decrease in coming years Still, the sample mean (the point estimate of confidence interval) is 52.98% in 2017, which is seen to be higher than 44.7% in 2016 Hence, the world’s individuals using the Internet is predicted to rise in the future A hypothesis test we conduct below will reinforce our statement Sample Mean  𝐗 52.98 Sample size n 38 Sample Standard Deviation S 26.92 Population Standard Deviation 𝛔 Unknown Population Mean μ 44.7 Confidence level (1 – α) *100% 95% Significance level α 0.05 Step 1: Check the CLT As the sample size n = 38, is greater than 30, CLT can be applied And the sampling distribution of all possible mean becomes normally distributed since sample size n increases Step 2: State the Null Hypothesis, H0 and the Alternative Hypothesis, H H0; μ ≤ 44.7 H1; μ > 44.7 Step 3: Choose level of significance α = 0.05; sample size n = 38 Since H1 shows the sign “>”, we use an upper-tail test Step 4: Determine which table to use Since the population standard deviation is unknown, and the sampling distribution of all sample mean is normally distributed, we will use the T-table Step 5: Determine Critical value (CV) Because it is upper tail test, the t critical value (tCV) is 1.6871 Level of significance α = 0.05 Degree of freedom d.f = n -1 = 38 – = 37 Step 6: Calculate test statistic t ttest = − μ X S √n = 52.98 − 44.7 26.92 √38 = 1.896 Step 7: Make statistical decision The ttest > tCV (1.896 > 1.6871), so the test statistic belongs to rejection region → Reject the Null Hypothesis H0 1.6871 1.896 Step 8: Make a managerial decision in the context of the problem As we reject H0, hence with 95% level of confidence we can conclude that the world average individual using the Internet will not increase Step 9: Discuss the possible errors As we reject H0, we might have committed Type I error (α) We are concluding that the world average individual using the Internet will not increase in the future, but there are still opportunities that it may increase The probability of Type I error can be reduced by minimizing the significance level α Because level of significance is picked by researchers, it can be changed easily The significance level, for instance, can be reduced to 0.01 (1%), which means there is a chance of 1% that the null hypothesis is mistakenly rejected (Corporate Finance Institute n.d.) b Suppose the number of countries in the assigned data set triples, the result will be more precise To be more specific, we will inspect the two formulas which are the sample standard deviation (S) and the test statistic t S=√ ∑ ni=1(Xi−X ) ttest = n−1 X− μ S √n Firstly, considering the sample standard deviation formula, S and degree of freedom (n – 1) have an inverse relationship, when sample size n increases, S will decrease Then, considering t test with the sample standard deviation formula, S and t test are inversely related; plus, sample size n and t test show a direct relationship As a result, when n increases and decreases, t test will increase, shift to the right but remains in the rejection region area From the Figure above, we can observe that t test and t value will be quite far from each other Hence, the statistical decision could be said to remain unchanged The triple in the sample size n will increase the accuracy of the results Determining Standard error’s formula SE = SD/√n, the standard error falls when we increase the sample size n as they are inversely related, and in contrast, the standard deviation will likely not to change due to the increase of the sample size (Altman & Bland 2005) Thus, in our case, the three times increase in the sample size will certainly decrease the standard error of the test by 1.7 times The smaller the error we get, the more reliable the results turn out, the more appropriate of the sample value of the whole population (Kenton 2020) Part Conclusion In brief, the sustainable development goals established by United Nations has been positively responded by many countries around the world They analyze the global problems we are facing today related to hunger, poverty, climate change, environmental degradation, peace and justice (United Nations n.d.) The 17 goals are set to eliminate the challenges above and are committed to accomplish within a 15-year period One of the goals related to this analysis is Goal economic growth and decent work Through this goal, the number of individuals using the internet - the main topic of this article, partly reflects the development of the economy Some significant findings can be derived from the calculation and analysis of individuals using the Internet in 38 selected countries Firstly, we concluded that income and individuals using the Internet are statistically dependent in the first part From the calculation and conclusion, it is noticeable that high income countries (GNI above $12,500) recorded the highest usage of internet with 100% individuals using the Internet, follow by is middle income countries with 55%, and low income at 0% Next, with the descriptive statistics, after calculating the Mean of three categories, one more time we conclude that HI countries observed the highest average of individuals using the Internet Besides, we are 95% confident that the true world average of individuals using the internet is between 44.13% and 61.83% of population in 2017 Besides, according to WHO’s report, the world average individual using the Internet (% of population) is 44.7% in 2016, and in 2017 our data set recorded 52.98%, which is predicted to rise in the future However, after conducting the hypothesis test, there are still chances of this number to decrease which is type II error Moreover, an increase in the sample size by three times is proven to have no impact on the statistical decision of the true world average number of individuals using the Internet Also, it can improve the accuracy of the test Finally, from all findings above, it is recommended that government should innovate and highlight the use of the Internet and technology not only for our daily life, but also for economic and social purposes By applying the Internet and modern technology, census and administrative tasks are quicker and easier for both citizens and government to achieve Therefore, improving the quality of life as well as the income REFERENCES Acciona n.d, 'What is sustainable development and how to achieve it?', Acciona, viewed 15 August 2020, Altman GD & Bland JM 2005, ‘Standard deviations and standard errors’, PMC, viewed 23 August 2020,