STT100 Statistics for Business: Hypothesis Testing and Analysis

This assignment, focusing on STT100 Statistics for Business, analyzes the median age of Andorra in comparison to the global average. The student begins by obtaining median age data from Wikipedia and using an online statistical tool to calculate the mean and standard deviation. The analysis then proceeds with hypothesis testing to determine if Andorra's median age is significantly different from the average, using a z-test due to known population standard deviation. The null hypothesis, that Andorra's median age is the same as the average, is rejected based on a calculated z-score of -23.14, which falls within the rejection region. The assignment further explores the demographic and economic implications of Andorra's aging population, including challenges related to social security, public services, and potential impacts on economic growth. It also discusses potential solutions, such as encouraging older individuals to remain in the workforce through phased retirement schemes and supporting increased birth rates. Visualizations, including a line graph and histogram, are used to represent the data. Finally, the assignment offers insights into the advantages and disadvantages of an aging population and suggests policy recommendations to mitigate potential negative impacts.

Running head: STT100 STATISTICS FOR BUSINESS
STT100 STATISTICS FOR BUSINESS
Name of the Student
Name of the University
Author Note

1STT100 STATISTICS FOR BUSINESS
Step 1:
The list of countries by median age data is obtained from the link.
https://en.wikipedia.org/wiki/List_of_countries_by_median_age
Now, the median years column is copied from the excel sheet and pasted to the online
statistical tool. The online statistical tool outputs the mean and standard deviation of median
ages of all the countries. The output is shown below.
Hence, from the online descriptive statistics calculator it is found that mean of the data is
approximately 30.74( μ0 ¿ and standard deviation is 8.89(σ).
Now, the country which is selected has much higher median (in years) than the computed
average or mean of 30.74. The selected country is Andorra and has the median (in years) of
44.3.
Step 2:

2STT100 STATISTICS FOR BUSINESS
Now, hypothesis testing is performed to check whether the median age of Andorra is
significantly different from the average.
Null hypothesis (H0): The median age of Andorra is same as the average of median ages of
all countries (x = μ0).
Alternative Hypothesis (H1): The median age of Andorra is significantly different from the
average of median ages of all countries ( x ≠ μ0).
The level of significance for the hypothesis testing is considered to be 5% or 0.05.
Now, as the standard deviation of the population i.e. the median ages of all countries is
known, hence, z test is applied here.
The sample size is the total number of countries in the world which are listed in excel file.
Sample size n = 230.
Now, from the ‘≠’ sign in alternative hypothesis the test is a two tailed test. Now, from
standard normal table the z score corresponding to 5% significance or 1- 0.05 = 95%
confidence level is 1.96 (Barrett 2017).
Hence, critical value is zcrit = 1.96.
Now, the test statistic of z test is given by,
z =
x−μ0
σ
√ n
=
30.74 – 44.3
8.89
√ 230
= 30.74 – 44.3
0.586 =¿-23.14
Step 3:

3STT100 STATISTICS FOR BUSINESS
Now, as normal distribution is symmetric hence, the z values over z = 1.96 and values below
z = -1.96 falls under the rejection region. If the test statistics falls in between [-1.96,1.96]
then the null hypothesis cannot be rejected.
Here, the z test statistics value is below critical z = -1.96 and hence null hypothesis is
rejected. Thus it can be concluded that as the test statistics falls in the rejection region, hence,
there is sufficient evidence to reject the null hypothesis and to accept the alternative
hypothesis.
Thus by statistical hypothesis testing it is found that alternative hypothesis is true or the
median age of Andorra is significantly different from the average of median ages of all
countries.
Step 4:
 The country Andorra has 11365 people under 15 years old of which 5837 are males
and 5529 are females and total of 52010 people inside age group 15 to 64 years of
which 27081 males and 24929 are females. Whereas most of countries like
Afghanistan, India, Bolivia and others have less percentage of people inside 15 to 64
years of age group resulting the average median age of all countries to be 30.74 years.
Hence, the median age of the country Andorra is higher than the average median age
of world. The special reason for having more older age people by Andorra than the
other countries could be slow death rate of 6.67 deaths per 1000 populations and low
birth rate of 8.88 births in 1000 populations as per the data of year 2013 (Travesset-
Baro et al. 2016). Older age people lives peacefully in Andorra and crime rate is also
low.
 There are more costs of having more aged people in a country than its benefits. As
there are more aged people in Andorra, hence, the country is likely to face challenges

4STT100 STATISTICS FOR BUSINESS
in providing social securities, public services while maintaining a good economic
growth. Now, if the aged population of Andorra rapidly increases in next few years
then it can be harmful to the economy of country in long run. The aging of average
population of the country can also lead to rise in government fund consumption for
the rise in demand of health care (Acemoglu and Restrepo 2017). This rise can lead to
a decrease in the total productivity which shifts away economic activity more to the
private sectors rather the public sectors. Ageing of population can also impact the
labour participation rate as decline of this magnifies the social security tax increase
and rapidly slows down the growth of productivity. There are a few advantages
having more old people in population, one of which is having more experienced
persons in the country in various fields like engineering, medical science, education
and others (Maestas, Mullen and Powell 2016). However, all the experienced persons
must be in a suitable physical state to use their experience in corresponding fields.
 The impact of population aging in a country cannot be reduced instantly but
government can take certain long term policies to visualize the impact in long term
such as 10 or 15 years. Now, a conventional policy for handling the situation by the
government is to motivate elder ones towards work. As we know for monetary and
non-monetary reasons work is the main pillar of well-being of any person. Now, when
work is paid then it also contributes towards the material and psychological well-
being via social interactions and provides enough opportunities for professional and
personal growth (Horioka and Niimi 2019). There are advantages of having older
people also as they have their most of time as leisure time they can do creative works
like volunteering younger people, care-taking works, artistic works and thus can
provide many psychological benefits to the society. If these positive works of elder
people are encourages and rewarded with payment or recognition then elders can also

5STT100 STATISTICS FOR BUSINESS
become partly a solution to the age related social and fiscal challenges. Thus
government can introduce a strategy in the country for elders allowing gradual
retirement scheme and some furnishing options with rewards for volunteering, care-
taking and artistic activities to the older age social members. Other countries like the
United States offers a phased-in retirement policies in which the workers can choose
to work for few hours and thus can remain in the workforce for a longer period of
time (Fuster 2017). The phased-in retirement scheme allows the continuity in the tax
revenues and the expenditures on the pensions can thus be reduced. This contributes
towards the macro-economic and monetary stability. Also, the older people can be of
much importance because of their experience and knowledge based skills.
 Now, the other changes that can be caused by having more amount of larger people in
the population is less participation in international sports by the countries or reduced
engagement in the extracurricular activities like soccer, baseball, tennis etc. This is
because the older people have less reflex than the younger ones and thus they are less
likely to participate in outdoor sports. This leads to decrease the ranking and
reputation of the country in the sport related international events like world cups,
Olympics etc. Now, there is a way of correcting this difference of having aged
population in the country than others by increasing the birth rates and nurturing the
younger people. The birth rates can be increased significantly by saving children from
poverty, increasing health care support for the poor children. Also, many young
females are killed in backward countries where people have the perceptions of males
as superior to the females and greater contributor to the country than the girls. Thus
awareness must be extended to all regions of the country to save girls and gender
equality must be established which can contribute towards increasing birth rate that
may be noticed in coming few years. Now, Andorra is not a very large country and

6STT100 STATISTICS FOR BUSINESS
the population of Andorra is quite low than other countries which is about 85
thousand as estimated in July 2018. The geographical area of Andorra is also very less
and the number of proper habitable places in Andorra is also lesser than other giant
countries like US, UK, India, China and Russia (Coale 2017). This geographical
disadvantage can restrict the growth of population in Andorra. There are other
disadvantages like the agriculture puts the country behind other countries from
growing. Only about 5% of area of Andorra is arable and thus the country mostly
relies on the imported food from its neighbours France and Spain. This also makes the
country’s economy vulnerable to the sudden increase in fuel and food price. Thus
these adverse conditions demotivates people of the country and affects the natural
birth rate of Andorra.
 Now, some graphs are used to display the median ages of different countries.
Line graph of Median ages by countries:

7STT100 STATISTICS FOR BUSINESS
Histogram of median ages of countries:
below 20 20 to 30 30 to 40 40 to 50 50 to 60
0
10
20
30
40
50
60
70
80
Histogram of median ages of countries
Age range
Frequency
It is evident from the line chart that the minimum median age of the countries in the
world is 15 years and maximum median age is close to 53 years. The histogram of
median ages shows that most countries have the median age in the range 20 to 40
years as the columns of 20 to 30 and 30 to 40 years are the two highest columns. This
makes the average median age close to 30 years as calculated in the descriptive
statistics. Now, this also supports the fact that Andorra has the median age of 44.3
years, which is higher the most of the countries which lies in the two highest columns
in the histogram.

8STT100 STATISTICS FOR BUSINESS

9STT100 STATISTICS FOR BUSINESS
References:
Acemoglu, D. and Restrepo, P., 2017. Secular stagnation? The effect of aging on economic
growth in the age of automation. American Economic Review, 107(5), pp.174-79.
Barrett, S., 2017. Applied Statistics.
Coale, A.J., 2017. How a population ages or grows younger. In Population Growth (pp. 47-
58). Routledge.
Fuster, V., 2017. Changing demographics: a new approach to global health care due to the
aging population.
Horioka, C.Y. and Niimi, Y., 2019. Financial Literacy, Incentives, and Innovation to Deal
with Population Aging.
Maestas, N., Mullen, K.J. and Powell, D., 2016. The effect of population aging on economic
growth, the labor force and productivity (No. w22452). National Bureau of Economic
Research.
Travesset-Baro, O., Gallachóir, B.P., Jover, E. and Rosas-Casals, M., 2016. Transport energy
demand in Andorra. Assessing private car futures through sensitivity and scenario
analysis. Energy Policy, 96, pp.78-92.