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

Probability The adolescent birth rate statistics separate the 35 sample countries of the third sustainabledevelopment goal Table 1 into three distinct categories based on gross national

ECON1193 – BUSINESS STATISTICS 1

Assessment #2: Individual case study on Inferential Statistics

(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 primarygoal of ensuring human happiness by balancing social, economic and environmental factors,bringing prosperity to both present and future generations (UNDP, 2021) In consequence, theUnited 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 healthylives 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 beused to quantify the UN's goal; therefore, diminishing adolescent fertility and treatment ofunderlying issues are crucial to improving teens' sexual and reproductive health, as well astheir social and economic well-being (United Nation Statistical Division, 2021) Theadolescent 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 55births 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-oldgirls gave birth in evolving nations (WHO, 2021) The objective is to reduce the adolescentbirth 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 adolescentbirth rate, such as actual adolescent births, are not published precisely due to largepopulations and remote locations (WHO, 2021) Resultantly, despite the efforts of severalinternational organizations to reduce adolescent pregnancy rates, issues remain that must beaddressed in order to ensure that no female citizens are left behind

Adolescents understand and broaden their viewpoints and life skills during this vulnerablestage 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 1000girls When compared to non-teaching countries, Latin American countries have approvedlegislation requiring sex education in schools, and the AFR has dropped by a statisticallysignificant 6.73 points (Leung, 2019) Thence, education plays a key role in addressing thistroubling 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 inlow- and middle-income countries, for example, Yaya (2020) reported 110 births per 1000female teenagers compared to the global average of 47 births Hence, in addition toschooling, differences in AFR between nations are caused by differences in gross nationalincome (GNI) According to Schultz (2005); the average income index is inversely related tothe fertility rate, indicating that socioeconomic factors can increase or reduce this ratio Inactuality, the Africa region's teen fertility rate is the highest in the world in both 2000-2005and 2015-2020 (Figure 4) (UNICEF, 2021), which can be attributed to a lack of facilities aswell as investment in educational programs Figure 5, contrastly, illustrates that developedareas such as North America, Europe, and Asia have a lower AFR (24% of births per 1000female teenagers) than developing areas (53%) (United Nations, 2013) Due to this, thattestimony 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 andGNI in 35 countries in order to elucidate AFR trends in each country category

II Descriptive Statistics and Probability

1 Probability

The adolescent birth rate statistics separate the 35 sample countries of the third sustainabledevelopment goal (Table 1) into three distinct categories based on gross national incomeprovisions:

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 eachnation group, with low and high ratios demonstrating low and high dissimilarity A countrywith an AFR greater than 30 has a high adolescent birth rate (H), while a country with anAFR 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 eachcell, assisting in the calculation of the next probability

High Adolescent fertility rate (H) > 30

Low Adolescent fertility rate (L) 30 ≤

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 statisticallydependent or independent events in countries with low AFR(L) under conditions where theincome 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 AFRare statically dependent occurrences Therefore, adolescent fertility is directly affected bynational income level and vice versa

b) The clarification of three countries categorizes:

When using conditional probability, the probability of the common events of high adolescentbirth rates and each country's income divided by that country's income type, is the idealmetric for evaluating Which income category by country group has the greatest impact onAFR:

According to the statistics above, low-income countries have the highest rate of adolescentchildbearing, with an estimated 89 percent possibility This suggests that in 9 low-incomecountries, 89 percent of nations will attain a hegemonic AFR.

countries

13,31 > -16,9775 111,22 < 112,3625 No

outlier High-income

countries

3,19 > -2,485 58,68 > 16,795 1 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 descriptivestatistics According to the preceding test table, there is one existing upper outlier in the high-income category

a) Measure of central tendency

Mean Median Mode Low-income

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 circumstancebecause it is not inflated by the aforementioned outliners in this observation Low-incomecountries 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 ofmore than 90.15 per 1000 adolescent girls, according to the statement Middle-incomecountries ranked second, with 51.74 per 1000 women aged 15-19 years, half as low as thelow-income group but still outperforming the high-income group, with only 6.21 per 1000women aged 15-19 This segment is 14 times below average for low-income earners and 8times below average for middle-income earners As a result, the Median comparison showsthat the higher the economic level, the lower the fertility rate per 1000 adolescent girls.

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 dataseries to another, even when their means are considerably different (Frost, 2020) Thistechnique is very beneficial in this circumstance because the Mean values of the three groupsare so diverse Table 2.4 shows that the low-income countries with the lowest coefficient ofvariation (44%) show less frequent fluctuations in the adolescent fertility rate and are moreconcentrated on the average of 91,133 births births per 1000 female adolescents, whilemiddle-income countries have a coefficient of variation of 47% and high-income countrieshave a coefficient of variation of 144%, implying that both countries all have a higherdispersion 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 ofnoticeable outlier discrepancies In part because their Mean value is bigger than their Medianvalue, all three nations are right-skewed or positively skewed, as seen in Figure 6 However,

in high-income countries, the right box is longer than the left, whereas in low- and income countries, the right box is shorter It could be explained by the presence of an upper-bound outlier in the group of high-income countries, causing the Mean value to be higherthan it is The whiskers of the three types of countries, on the other hand, are longer to theright, meaning that more than half of the adolescent birth fertility ratio is concentrated more

middle-on the right sides of these three types

III Confidence Intervals

1 Calculation

For the purpose of determining a confidence interval for the worldwide mean fertility rate forwomen aged 15-19 years, the significance level ( ) is assumed to be 0.05, meaning that the�confidence level will be calculated as 1 - 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 beused, suggesting that the Student t distribution be employed instead of the normaldistribution:

 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

2 Assumption for calculation

Even if the population standard deviation is unknown, the sample size of all observations issufficiently large (n = 35) to meet a mandatory condition for applying the Central limittheorem (CLT) That is, regardless of the population's structure, this sampling distribution isalmost normal, hence no assumptions are required

3 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-valuetable 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 canvary significantly from one sample to the next, leading to many uncertainties in statisticalwork (Ranjan Rout, 2020) In principle, confidence intervals are used to assess the degree ofuncertainty or certainty in a sampling process; the smaller the confidence interval, the lowerthe 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 confidenceintervals Reduced confidence interval width, on the other hand, reduces the margin of error

(e), which is defined as a factor to assess the proportion of a collection of data that cangenerate errors, ensuring correct calculations results (KhanAcademy, 2017).

⟹ In a nutshell, when the population standard deviation is known, the width of theconfidence interval narrows for higher certainty, yielding in more precise confidenceintervals

IV Hypothesis Testing

1 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 samplemean 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 thisprediction will be confirmed through the hypothesis testing that follows

2 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

Sample Mean 52,06

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 normallydistributed because it meets the central limit theorem (CLT) criterion of n > 30

Step 2: Determine null and alternative hypothesis:

Null hypothesis: H : 0

Alternative hypothesis: H : 1

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, do not ruleout the null hypothesis (H ), but rather reject the alternative hypothesis (H ).0 1

Step 8: Generating a managerial decision:

Because H is not refuted, it may be concluded with 95 percent certainty that the global0

teenage fertility ratio would rise in the future

Step 9: Determining the possible errors:

If we do not reject Ho, we may have committed a Type II error ( ) P (Error Type II) = 1 – Test power β

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