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THE COVER PAGE BUSINESS STATISTICS Subject Code ICON1193B Subject Name Business Statistics Campus Sai Gon South Campus Title of Assignment Individual Type of Assignment Individual case study Student Name Lam Thao Ngan Student ID Number S3863920 Lecturer Nga TT Assignment Due Date December 14th, 2020 Date of Submission December 14th, 2020 Number of page (including the cover page) pages I Introduction: The adolescent birth rate is the measurement of the number of births per years from 1000 women who aged 15-19 years (WHO 2010) Teenagers are more likely to face the danger during child-bearing period than mature women or even at risk of death and dis Besides, the newborns of teenage mothers are at higher risk of low born weight and mortality (Measure Evaluation) In addition, the adolescent fertility also leads to the poor socioeconomic outcomes, due to the school dropout, low productivity and poverty (Mcqueston, K & Silverman, R & Glassman, A 2012) Due to these reasons, raising the awareness as well as education in sex through sexual and reproductive medical care services is extremely essential (The United Nations) With the high GNI countries and the developing countries such as United States, China and Europe would possess a lower ratio of teenage pregnancy countries because they have taken advantaged from demographic dividend, so the reproduction have significantly decrease in the past few years In contrast, countries with lower GNI would possess a higher rate in reproduction, particularly Asia and Africa Based on these evidences, we can see that in terms of poor countries, young mothers usually receive low income from unstable works or even have not enough qualifications as well as experience to raise their children (Guillaume 2016) Meanwhile, the reduction in ratio of adolescent fertility in developed countries, which also illustrates that the environmental and well-being society are much better for children II Descriptive Statistics and Probability: Probability: Population Division (n.d) concluded that adolescent fertility rate is the annual number of births to per 1000 women who have ages from 15 to 19 Then, the measure which is more than 30 births per 1,000 women ages 15-19 is considered high adolescent fertility rate On the other hand, different GNI level will classify different income level of that country: ▪ 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 The studied countries in the provided data set would be divided into three categories based on their GNI condition and the level of adolescent fertility High Adolescent fertility rate (H) Low Adolescent fertility rate (L) Total Low-income countries (LI) Middle-income countries (MI) High-income countries (HI) 8 12 16 11 11 Total 20 15 35 Table 1.Contingency table for country categories in terms of income and the rate of adolescent fertility To determine if income level and mean annual adolescent fertility rate are statistically independent or not, conditional probability of related variables from two categories must be considered P(H) = 20 35 P(H\LI) = = P( H ∧LI ) P(LI ) = ≠ P (H ) =1 = 12 35 16 35 = = 35 11 35 =0 P( H ∧MI ) P(H\MI) = P(MI ) P( H ∧HI ) P(H\HI) = P( HI ) 35 35 ≠ P (H ) ≠ P (H ) ⇒ The categories countries above which are low, middle, and high income and high adolescent fertility rate are not statistically independent events 15 P(L) = = 35 P( L∧LI ) P(L\LI) = P( LI ) P( L∧MI) P(L\MI) = P(MI ) P(L\HI) = ⇒ P( L∧HI ) P(HI ) 35 35 = =0 = 35 16 35 = = 11 35 11 35 =1 ≠ P (L) ≠ P (L) ≠ P (L) The categories countries above which are low, middle, and high income and low adolescent fertility rate are also not statistically independent events a The probability of country categories are more likely to have high teenager fertility rate: P(H\LI) = P(H\MI) = P( H ∧LI ) P( LI ) = P( H ∧MI ) P(MI ) 35 35 = = 100% = 12 35 16 35 = = 35 11 35 = = 0% = 75% P(H\LI) > P(H\MI) > P(H\HI) P( H ∧HI ) P(H\HI) = P( HI ) ⇒ Countries with low income possess the highest in teenage birth rate Interpretation: As the independence between the country categories and low or high adolescent fertility rate, it shows that the countries with high income have the lower adolescent fertility rate whereas the low and middle income countries may face the risk of the higher level in teenager pregnancy Descriptive statistics: a Measures of Central Tendency: Low-income countries (births) 105.43 98.88 #N/A Middle-income countries (births) 47.19 47.34 #N/A High-income countries (births) Mean 10.21 Median 8.76 Mode #N/A Table2.Measures of Central Tendency for the adolescent fertility rate Key findings: - The average teenager pregnancy rate of low-income countries is the highest compared with that of middle-income countries and high-income countries (105.43 > 47.19 > 10.21) - Similarly, the median of middle-income countries and high-income countries is also lower than that os low-income countries ( 8.76 < 47.34 < 98.88) Analysis: In term of the Central Tendency of this case, the median is the most suitable compared with others The first reason is the distance between minimum values and maximum values is too far, which means the values of dataset have significant variation The major evident supporting the median measure is that all country categories have one outlier According to Jim, F (2019), mean is drastically impacted by outliers, specifically, outliers would pull mean away from the center towards the longer tail As a result, median is the better measurement to represent the central tendency for the distribution b Measures of Variation: Low-income countries (births) Middle-income countries (births) High-income countries (births) Range 104.05 98.69 17.13 IQR 31.3 28.36 5.34 Sample Variance 1071.67 658.5 25.87 Sample Deviation 32.74 25.66 5.09 CV (%) 31% 54% 50% Table3.Measures of Variation for the adolescent fertility rate Key findings: - All the measures of low-income countries is higher than these of middle-income countries and high-income countries Analysis: - In general, the standard deviation is considered as representative of the measurement of variation Standard deviation does not include the middle values, implying that it not takes into account the distribution of data Range measure is also affected by outliers With IQR, it does not observe all the values in the data set, it just simply calculates the distance between Q1 and Q3 Variance is a squared unit, then, it does not provide the clear interpretation The final measure is CV, CV is also regarded as a good measure, however, it is better when the difference distribution of values is drastically big In short, the best measure in this case is Standard deviation c Box and Whisker plot: Box Low-income countries (births) Middle-income countries (births) High-income countries (births) 12 < 19.3 17.74 > 10.62 1.86 < 3.52 Whisker 17.89 < 54.86 17.07 < 53.26 1.59 < 10.32 Median 29.89 < 74.16 34.81 < 63.88 3.45 < 13.68 Result Right skewed Right skewed Right skewed Table4.Box and Whisker plot III Confidence Intervals: Calculation: In this case, the confidence level would be randomly chosen at 95% in order to estimate the confidence interval In term of the sample size is 35 which is higher than 30, associating with the applying Central Limit Theorem (CLT) and the sampling distribution becomes normally distributed Because the population standard deviation ( σ ¿ is unknown, the sample standard deviation (S) is substituted, and the t-table would be used Population standard of deviation ( σ ¿ Unknown births Sample standard of deviation (S) 41.91 births Sample mean ( X ) 48.88 births Sample size (n) 35 countries Confidence level (1-α) 95 % Table5.Statistics Summary for the adolescent fertility rate Calculate confidence interval: α = 0,025 ⇒ t = ±2.0322 d.f = n-1 = 35-1 = 34 μ= X +t( S ) √n =48.88 ±14.4 ( 41.91 √35 ) ⇒μ=48.88 ± 2.0322 ⇒34.48 ≤ μ ≤ 63.28 Interpretation: Regarding with 95% of confidence, we can claim that the world average rate of adolescent fertility is between 34.48 births to 63.28 births per 1000 women Assumption: Regardless of the lack of the population standard deviation, there is no requirement for assumption As the sample size is 35 which is higher than 30, Central Limit Theorem (CLT) can be applied and the distribution would be normally distributed Supposing that the population standard deviation of adolescent fertility is known, indicating that all the values of the population is collected and population mean would be easier to calculate From the equations to calculate the interval confidence ( μ= X +Z ( σ ) and √n S ) ), the main difference of the population standard deviation existence √n is the application of the z-value instead of t-value Looking at the figure 1, we can see that the t-value is slightly bigger than z-value when the sample size is small Therefore, if the critical value is larger, confidence interval would become wider In other words, if we use population standard deviation to calculate, the confidence interval would decrease, however, the accuracy would be boosted μ= X +t( Figure Adapted from A Guide to Business Statistics (McEvoy 2018) IV Hypothesis testing According to The World Bank (2020), during the 18-year period, the mean of adolescent fertility rate saw a rapid decrease from 61.335 births per 1000 women (1996) to 48.36 births per 1000 women (2008), and the figure gradually go down to 46 births per 1000 women in 2014.In addition, based on the calculated confidence interval above (34.48 ≤ μ ≤ 63.28) , assuming that the average rate of adolescent pregnancy phenomenon would have tendency to decline in the future Therefore, Hypothesis Testing would be used to check whether this figure decrease or not Figure1.Measures of Variation for the adolescent fertility rate Hypothesis Testing (Critical Value approach) Step 1: Check for Central Limit Theorem (CLT) Since the sample size (n=35) is larger than 30, it is applicable to use CLT and the sampling distribution is normally distributed The null hypothesis H ; μ ≥ 46 Step 2: Determine hypothesis The alternativehypothesis H ; μ Trinh, T N 2020, ‘Inferential Statistics – Hypothesis Testing’, PowerPoint slides, ICON1193B, RMIT university, Vietnam United Nations 2014, Goal 3: Ensure healthy lives and promote well-being for all at all ages, United Nations, viewed 10 December 2020 World Health Organization 2018, Adolescent pregnancy, World Health Organization, viewed December 2020 ... with the larger one , namely, it would decrease the power of the study ⇒ Consequently, reducing the sample size reduces the confidence level of the study, which is related to the Z distribution The. .. however, the accuracy would be boosted μ= X +t( Figure Adapted from A Guide to Business Statistics (McEvoy 2018) IV Hypothesis testing According to The World Bank (2020), during the 18-year period, the. .. the population standard deviation existence √n is the application of the z-value instead of t-value Looking at the figure 1, we can see that the t-value is slightly bigger than z-value when the
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