PRIMERA PRUEBA TEST

Statistics for Journalism
Examen final
La duración del examen es de 2 horas y media. Responder a todas las preguntas. La pregunta 1
vale 5 point (1 para cada apartado) y las preguntas 2 y 3 valoran 2,5 point cada una. Responder a la
pregunta 2 en una hoja y a la pregunta 3 en otra hoja. Recordar poner su nombre y grupo en todas
las hojas.
Student: ________________________________________
Group: _________
Date: ______________
Marcar con X la respuesta correcta de cada apartado de la pregunta 1 en la siguiente tabla.
Question
Correct answer
a
b
c
d
1 a)
1 b)
1 c)
1 d)
1 e)
1
PROBLEM 1.
a) The following table shows information about the daily sales of newspapers for each 1000 inhabitants of
8 Spanish Communities and the economic production of the community based on the PIB (Producto
Interiór Bruto) per resident.
PIB
8.3
9.7
10.7
Sales
57’4
106’8
104’4
Fuente: INE. Anuario Estadístico.
11.7
131’9
12.4
144’6
15.4
146’4
16.3
177’4
17.2
186’9
Supposing a linear relation between these variables, we obtain the following regression line which
explains the number of papers sold per 1000 inhabitants in terms of the PIB per resident in 1000’s of
euros:
y= −23.55 + 12.23x
What would be the predicted sales in a community with PIB per resident equal to 15.000 euros?
a.
b.
c.
d.
159.9 examples
159.9 examples for each 1000 inhabitants
183.430 examples
183.430 examples for each 1000 residents
b) In the UK, approximately 25% of all workers are Trades Union members. If two workers are randomly
sampled, the probability that exactly one of them is a Union member is
a.
b.
c.
d.
0.1875
0.3750
0.5625
0.0625
c) The table shows the ages and sex of different government ministers.
Name
Bibiana Aído
Carme Chacón
Ángeles GonzálezSinde
Cristina Garmendia
Trinidad Jiménez
José Blanco
Ángel Gabilondo
Elena Salgado
Sex
M
M
M
Ministry
Igualdad
Defensa
Cultura
Age
33
38
44
M
M
V
V
M
Ciencia e innovación
Sanidad y Política Social
Fomento
Educación
Economía y Hacienda
47
47
48
60
60
Which of the following affirmations is correct?
a.
b.
c.
d.
The range of ages is 33 and the absolute frequency of women is 6.
The mean age is 47 and the percentage of male ministers is 25%.
The first quartile of the ages is 41 and the third quartile is 54.
The modal age is 60 and the mean is 47.
2
d) The Interior Ministry released an informative note concerning the number of suicides per autonomous
community according to the latest data published by EUROSTAT. El País made a mistake in publishing
the news and affirmed that the yearly number of suicides was 1.41 suicides per 1000 residents instead
of the correct result of 1.41 suicides per 100000 residents. In the community of Madrid, there are 6.2
million residents. How many suicides in Madrid were there according to the story published in El País?:
a.
b.
c.
d.
8742
874.2
87420
87.42
e) The histograms show the times taken (in seconds) for 406 types of car to get from 0 to 100 km/h
(acceleration), when measured by two different workers, A and B.
WORKER A
WORKER B
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
1
5
9
13
17
21
Aceleración 0 a 100 km/h (segundos)
25
29
33
1
5
9
13
17
21
25
29
33
Aceleración 0 a 100 km/h (segundos)
Analyzing these histograms, which of the following affirmations is correct?
a. The mean acceleration measured by A is clearly different to the mean acceleration measured
by B.
b. The variance of the data measured by A is higher than the variance of the data measured by B.
c. The standard deviation of the data measured by A is lower than the standard deviation of the
data measured by B.
d. There median acceleration measured by A is clearly different to the median acceleration
measured by B.
3
PROBLEM 2.
The following table gives the cabinet ministers of the British coalition government, their
Political party, age and sex.
Name
David Cameron
Nick Clegg
William Hague
George Osborne
Liam Fox
Kenneth Clarke
Patrick McCoughlin
Theresa May
Andrew Lansley
Danny Alexander
Vince Cable
Michael Gove
Eric Pickles
Chris Huhne
Iain Duncan Smith
Dominic Grieve
Philip Hammond
Caroline Spelman
Andrew Mitchell
Owen Paterson
Michael Moore
Cheryl Gillan
Jeremy Hunt
Ministry
Prime Minister
Deputy Prime
Minister
Foreign Affairs
Exchequer
Defence
Justice
Chief Whip
Home Secretary
Health
Treasury
Business
Education
Local Government
Energy and Climate
Change
Work and Pensions
Attorney General
Transport
Environment
International Devel.
Northern Ireland
Scotland
Wales
Sport
Political Party
Conservative
Liberal Democrat
Age
43
43
Sex
Male
Male
Conservative
Conservative
Conservative
Conservative
Conservative
Conservative
Conservative
Liberal Democrat
Liberal Democrat
Conservative
Conservative
Liberal Democrat
49
38
48
69
52
53
53
38
67
42
58
55
Male
Male
Male
Male
Male
Female
Male
Male
Male
Male
Male
Male
Conservative
Conservative
Conservative
Conservative
Conservative
Conservative
Liberal Democrat
Conservative
Conservative
56
53
59
52
54
53
45
58
53
Male
Male
Male
Female
Male
Male
Male
Female
Male
Suppose that a cabinet member is selected at random.
a.
b.
c.
d.
What is the probability that they belong to the Liberal Democratic Party? (0,5 points)
What is the probability that they are under 50 or Liberal Democrat? (0,5 points)
Are the events “aged under 50” and “Liberal Democrat” independent? Why? (0,5 points)
Supposing that the selected cabinet minister is Conservative, calculate the probability that
they are female. (0,5 points)
e. Calculate the mean of the distribution of ages. (0,5 points)
4
PROBLEM 3.
In the Barómetro del CIS of April 2010, a sample of 2356 people awarded Mariano Rajoy
an average rating of 3.09 with a standard deviation of 2.5.
Answer the following questions.
a. Calculate a 95% confidence interval for the true rating of Mariano Rajoy at this time. (0,75 points)
b. The rating obtained by Mariano Rajoy in the Barómetro of April 2009 was 3.54. Is there any
evidence that the true rating of Mariano Rajoy in April 2010 is less than 3.54? Perform the test at a
5% significance level. (0,75 points)
c. In the April 2010 barómetro, 55% of a sample of 2479 Spanish adults said that they did not know
who Cayo Lara (the leader of IU) was. Is there any evidence from these data that more than half of
Spanish adults do not know Cayo Lara? Perform the test at a 5% significance level. (1 point)
5
CHULETARIO OFICIAL
i) Resultados básicos (basados en una muestra de tamaño n)
n
n
xi
X
i 1
n
S2x
n
x i2
i 1
n
x i yi
(x)
2
Cov(X, Y)
i 1
( x y) r ( X, Y )
n
Cov(X, Y)
Sx Sy
ii) Regresión
La recta de mínimos cuadrados es y = a + bx donde
b
Cov(X, Y)
S2x
r(X, Y)
Sy
Sx
a
y (b x )
iii) Intervalos de confianza de 95% (basada en una muestra de tamaño N) para
a) La media de una población normal (varianza conocida)
b) Una proporción
6
iv) Contrastes de hipótesis de nivel de significación .
Z representa el punto tal que P(Z <Z )=1- donde Z tiene una distribución normal estándar.
a) para la media de una población normal (varianza conocida)
Región de rechazo
H0
H1
= 0
< 0
= 0
> 0
= 0
≠
0
b) para una proporción
H0
H1
p = p0
p < p0
p = p0
p > p0
p = p0
p ≠ p0
Región de rechazo
v) Point críticos de la distribución normal estandár
P(Z ≤ 1,64) = 0,95
P(Z ≤ 1,96) = 0,975.
7
TABLAS DE LA DISTRIBUCIÓN NORMAL
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