Statistics for Journalism
Test 3A
PROBLEM 1. A statistical institute has carried out a survey to predict the voting
habits of first time voters, currently of ages 18 to 20 in the next elections in
the UK. The number of people sampled was 3000. It is wished to study the
relationship between the intention to vote and age. Let X = Political party
and Y = age of the respondent:
Conservative
Labour
Liberal
Nationalist
groups
Independents
18
450
250
145
19
300
270
170
20
210
330
200
95
50
150
115
180
85
Which one of the following options is correct?
a)
b)
c)
d)
Solution
a)
33.5% of the people sampled are under 20 years old.
5.67% of the people sampled are 19 year old Liberal voters.
10% of the people sampled are Independents.
10% of 19 year olds are Conservative voters.
b)
c)
d)
PROBLEM 2. Following from the previous question, signal the correct answer.
a)
b)
c)
d)
Solution
a)
31.76% of the people who intend to vote Labour are 20 years old.
29.41% of the prospective Labour voters are 19 years old.
29.41% of the prospective Labour voters are 18 years old.
38.82% of the people who intend to vote Labour are 19 years old.
b)
c)
d)
PROBLEM 3. The table shows the Gross National Product per head in US
dollars in 2008 and 2009 for the G8 countries.
Country
Canada
France
Germany
Italy
Japan
Russia
UK
USA
GNP 2008
x
42030
45981
44471
38309
38443
11339
43088
46716
GNP 2009
y
39217
42091
39442
34955
39573
8874
35728
46443
The covariance between the two variables is 116000000 and the correlation is 0,974.
The Libyans prefer to measure GNP in Libyan dinars. The dollar dinar Exchange rate
is (approximately) 1 dollar = 2 dinars.
Measuring the GNP per head in Libyan dinars, which of the following options is
correct?
a)
b)
c)
d)
Solution
a)
Both the covariance and the correlation do not change.
The correlation is 0.2475 and the covariance does not change.
The covariance is 464000000 and the correlation doesn’t change.
Both the covariance and the correlation change to a quarter of their previous
values.
b)
c)
d)
PROBLEM 4. 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
Solution
a)
b)
c)
d)
PROBLEM 5. A US newspaper is carrying out a study on racism in the US
army. They have calculated the following scatterplot shows the percentages
of coloured military recruits (y) against the general population size (x) for
various US states.
Which of the following regression lines is correct?
a)
b)
c)
d)
Solution
a)
y = 1.08x
y=9.55-1,08x
y=9.55+1,08x
y=-9.55-1,08x
b)
c)
d)
CHULETARIO OFICIAL
n
X
 xi
i 1
n
 n 2
 xi 
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 n 




 n

x
y

i
i

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  ( x  y)
Cov(X, Y)   i1
 n 




Cov(X, Y)
r (X, Y) 
Sx  S y
b
Sy
Cov(X, Y)

r
(
X
,
Y
)

Sx
S2x
a  y  (b  x )
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