STATISTICS I

GROUP ASSIGNMENT

FALL 2021/2022

A. RULES

1. Groups must be of 3 or 4 elements, all from the same class
2. Deadline: Nov 14th 2021, 1159pm
3. The solution must be contained in one single PDF file, submitted for evaluation
4. GBi1 and GBi2 students must submit their assignments to Prof. Pedro Serrasqueiro
(pedro_serrasqueiro@iscte-iul.pt)
5. The filename must be of the kind: Assignment_80000_85000_90000_GBi1
6. Any evidence of plagiarism will result in a maximum grade of 10 points












B. ASSIGNMENT
Question 1:
The European Social Survey (ESS) is a transnational academic survey that measures attitudes, beliefs
and behavioral patterns in over 30 european countries (Portugal included). The survey consists of a
permanent module of measurements and additional rotational modules, dedicated to specific topics.
Among the permanent measures are: Well-being, Health, Trust in institutions, Human Values and
Demographics. For this survey, 1500 volunteers were invited from the population of Facebook users
with 15 years of age or older.
The data collection encompasses several continuous variables, namely: self-promotion [Aut_P; 1 to
7], conservation [Cons; 1 to 7], openness to change [OC; 0-6], and self-transcendence [Aut_T; 1 to
7]. Participants were also asked “how many times have you felt happy in the past week?” [Hap] (1 -
Never, 2 - Sometimes, 3 - Often, 4 - Always), Education level [Edu] (1 – Primary, 2 – Secondary, 3
– University) and Gender [Gender]
In the table below, the first 20 observations are shown:

Gender Edu Hap Aut_P Cons OC Aut_T
F Primary Sometimes 2.9 2.5 0.8 2.6
F Primary Sometimes 3.3 3.5 0.4 3.1
F Primary Always 3.7 3.2 2.7 3.2
F Primary Often 3.0 3.9 2.5 2.4
F Primary Sometimes 3.8 3.2 1.2 3.2
F Secondary Never 2.7 3.8 3.0 3.1
F University Often 3.5 3.8 1.1 3.4
F Secondary Sometimes 2.6 2.6 2.9 2.9
F Primary Sometimes 5.1 3.2 3.0 3.4
F University Sometimes 2.7 3.6 1.9 2.8
F University Always 3.6 3.1 3.2 3.2
F Secondary Often 4.0 4.0 1.5 2.7
F Primary Always 4.1 3.1 2.0 2.8
F Primary Never 3.9 3.4 8.0 2.7
Gender Edu Hap Aut_P Cons OC Aut_T
F University Never 2.9 2.6 3.9 3.1
F Secondary Sometimes 3.9 2.5 2.0 3.2
F Primary Always 3.4 3.9 2.7 4.0
F Primary Sometimes 3.7 2.9 2.3 2.8
F Primary Sometimes 3.2 4.2 0.8 3.0
F Primary Often 3.4 3.5 2.4 2.9

Analyse the data contained in BD_GBi1_GBi2.sav, using all measures and taking into account the
nature of the different variables. Provide an overall characterization of the sample, both globally and
by groups of interest, and interpret the results.

Question 2:
Consider the expression
VAR(X ± Y) = VAR(X) + VAR(Y) ± 2.COV(X,Y)

Explain, in a short text (max. 200 words), the rationale that underlies the expression. Refer to why
the variances of X and Y are still added when a new variable is generated by subtraction, e.g. Z =
(X-Y).

Question 3:
From the variables included in the dataset in Question 1, indicate (or create) a random variable that
may be well fitted by one of the discrete probability distributions covered in class. Justify your answer
thoroughly.



Question 4:
Research a practical application of two of the following four discrete distributions: uniform,
Bernoulli, binomial and Poisson. The selected application must not coincide with any
example/exercises covered in class. Cite your sources properly and provide a short summary of the
distributional properties in the application’s context.


































































































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