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O gráfico abaixo ilustra o comportamento da temperatura média mensal em uma determinada região do estado de São Paulo.
A partir da análise do gráfico, conclui-se que a série
Análise fatorial é uma técnica multivariada que tem como um de seus objetivos a redução da dimensão do conjunto de dados. Para essa técnica, as quantidades que podem substituir as variáveis originais com fins de redução de dimensão são as denominadas
Considere um intervalo de confiança de 90%, simétrico, para a média μ de uma população com distribuição normal [5; 15].
No teste de hipótese H0: μ = 0 x H1: μ ≠ 0, tem-se que a hipótese nula de H0
Duas variáveis x e y apresentam covariância amostral sxy = 100 e desvios padrões amostrais sx = 10 e sy = 20. Considere um modelo de regressão linear simples para explicar o comportamento de y a partir de x : y = β0 + β1x + ε, sendo ε um ruído branco Gaussiano. Se estimarmos esse modelo, utilizando o método de mínimos quadrados ordinários, a estimativa do coeficiente de inclinação β1 será
Um bairro possui 100 quarteirões, sendo que cada quarteirão possui 121 domicílios. Em uma pesquisa por amostragem domiciliar, foram selecionados aleatoriamente 15 quarteirões, sendo entrevistados os moradores de todos os domicílios dos quarteirões selecionados. Se o coeficiente de correlação intraclasse é 0,8, o efeito de conglomeração é, aproximadamente,
Uma pesquisa por amostragem domiciliar foi realizada em uma localidade que possui 30 domicílios. A amostra de 5 domicílios foi obtida de acordo com os seguintes passos:
Passo 1 - organização dos 30 domicílios em uma lista, numerando-os de 1 a 30.
Passo 2 - seleção aleatória de um domicílio, dentre aqueles numerados de 1 a 6 (o domicílio selecionado no passo 2 foi o de número 4).
Passo 3 - inclui-se na amostra os seguintes domicílios (além do 4, selecionado no passo 2): 10, 16, 22 e 28 (ou seja, a partir do domicílio 4, seleciona-se de 6 em 6 domicílios).
A amostragem adotada foi
O salário médio dos 7 funcionários de um departamento de uma empresa era de R$ 1.000,00. Em determinado momento, o salário desses funcionários foi reajustado em 10%. Além disso, uma outra pessoa foi contratada, com o salário de R$ 3.000,00. O salário médio do departamento passou a ser, em reais, de
Um município contém 200 escolas, totalizando 2.000 turmas e 45.000 alunos de ensino médio (as escolas têm diferentes números de turmas, e as turmas têm diferentes números de alunos). Uma pesquisa por amostragem foi feita para avaliar a qualidade do ensino médio no município, utilizando um plano amostral em dois estágios. No primeiro estágio foram selecionadas 40 escolas por amostragem com probabilidades proporcionais ao tamanho (PPT) sem reposição, tendo sido adotado, como medida de tamanho, o número de turmas das escolas. No segundo estágio foram selecionadas, por amostragem aleatória simples sem reposição, 5 turmas dentro de cada escola selecionada no primeiro estágio. Foram entrevistados todos os alunos das turmas selecionadas no segundo estágio.
A probabilidade de inclusão de cada aluno do município na amostra final é
O Teorema Espectral para matrizes simétricas elenca diversas propriedades importantes dessas matrizes, no que se refere às características dos seus autovalores e à estrutura dos respectivos autoespaços.
Uma dessas propriedades é aquela que afirma que se λ1 e λ2 são dois autovalores distintos de uma matriz simétrica Anxn, então dois respectivos
Sejam X e Y duas variáveis aleatórias contínuas, com funções de densidade marginais fX(x) e fY(y), respectivamente, e função de densidade conjunta fX,Y(x,y).
As variáveis X e Y são independentes se
A altura das mulheres de uma população segue uma distribuição normal de probabilidade, com média 1,60 e variância 0,0036.
Na população considerada, cerca de 95% das mulheres têm altura entre
Um carteiro decide registrar o número de cartas enviadas a um endereço nos últimos 7 dias. No entanto, ele se esquece do número de cartas do primeiro dia, lembrando-se apenas daqueles correspondentes aos 6 dias restantes: 3, 5, 4, 5, 4 e 3, e de que, nos 7 dias considerados, a média, a mediana e a moda foram iguais.
O número de cartas enviadas no primeiro dia foi
A função de densidade de uma variável aleatória X é dada por f(x) = x/4, para 1 ≤ x ≤ 3, com f(x) = 0 para os demais valores de x. A probabilidade de que X assuma um valor menor que 2 é
Um supermercado recebe fruta tropical proveniente de dois fornecedores, A e B. Enquanto A fornece caixas de 20 frutos, B fornece caixas maiores com 100 frutos cada uma. Alguns dos frutos, sem qualidade, têm peso inferior ao peso estabelecido para que seja considerado aceitável pelo supermercado.
Com vistas a comparar a qualidade dos frutos fornecidos por A e B foi feito um estudo, obtendo-se os seguintes dados:
Fornecedor A
|
Número de frutos sem qualidade |
Número de caixas |
0 |
25 |
1 |
36 |
2 |
19 |
3 |
11 |
4 |
5 |
5 |
4 |
Fornecedor B
|
Número de frutos sem qualidade |
Número de caixas |
0 - 4 |
17 |
5 - 9 |
49 |
10 - 14 |
22 |
15 - 19 |
8 |
20 - 24 |
3 |
25 - 29 |
1 |
A média de frutos sem qualidade, por caixa, para os fornecedores A e B é, respectivamente,
Estatísticas do Departamento de Trânsito sobre o envolvimento de motoristas em acidentes com até 2 anos de habilitação indicam que o seguinte modelo pode ser adotado, ou seja, a variável aleatória X representa o número de acidentes e assume valores 0, 1, 2, 3 e 4:
Número de Acidentes (X) |
0 |
1 |
2 |
3 |
4 |
P(X = x) |
0,3 |
0,2 |
0,1 |
0,1 |
0,3 |
O valor esperado e o desvio padrão da variável aleatória X são, respectivamente,
Text II
Off the Deep End in Brazil
Gerald Herbert
With crude still hemorrhaging into the Gulf of
Mexico, deep-water drilling might seem taboo just
now. In fact, extreme oil will likely be the new normal.
Despite the gulf tragedy, the quest for oil and gas in
5 the most difficult places on the planet is just getting
underway. Prospecting proceeds apace in the ultra-
deepwater reserves off the coasts of Ghana and
Nigeria, the sulfur-laden depths of the Black Sea, and
the tar sands of Venezuela’s Orinoco Basin. Brazil’s
10 Petrobras, which already controls a quarter of global
deepwater operations, is just starting to plumb its 9 to
15 billion barrels of proven reserves buried some four
miles below the Atlantic.
The reason is simple: after a century and a
15 half of breakneck oil prospecting, the easy stuff is
history. Blistering growth in emerging nations has
turned the power grid upside down. India and China
will consume 28 percent of global energy by 2030,
triple the juice they required in 1990. China is set to
20 overtake the U.S. in energy consumption by 2014.
And now that the Great Recession is easing, the
earth’s hoard of conventional oil is waning even
faster. The International Energy Agency reckons the
world will need to find 65 million additional barrels a
25 day by 2030. If the U.S. offshore-drilling moratorium
drags on, look for idled rigs heading to other shores.
Available in:
<http://www.newsweek.com/2010/06/13/off-the-deep-end-in-brazil.html>
Retrieved on: June 19, 2011.
In Text II, Herbert illustrates the possibility of “...idled rigs heading to other shores.” (line 26) EXCEPT when he mentions
Text II
Off the Deep End in Brazil
Gerald Herbert
With crude still hemorrhaging into the Gulf of
Mexico, deep-water drilling might seem taboo just
now. In fact, extreme oil will likely be the new normal.
Despite the gulf tragedy, the quest for oil and gas in
5 the most difficult places on the planet is just getting
underway. Prospecting proceeds apace in the ultra-
deepwater reserves off the coasts of Ghana and
Nigeria, the sulfur-laden depths of the Black Sea, and
the tar sands of Venezuela’s Orinoco Basin. Brazil’s
10 Petrobras, which already controls a quarter of global
deepwater operations, is just starting to plumb its 9 to
15 billion barrels of proven reserves buried some four
miles below the Atlantic.
The reason is simple: after a century and a
15 half of breakneck oil prospecting, the easy stuff is
history. Blistering growth in emerging nations has
turned the power grid upside down. India and China
will consume 28 percent of global energy by 2030,
triple the juice they required in 1990. China is set to
20 overtake the U.S. in energy consumption by 2014.
And now that the Great Recession is easing, the
earth’s hoard of conventional oil is waning even
faster. The International Energy Agency reckons the
world will need to find 65 million additional barrels a
25 day by 2030. If the U.S. offshore-drilling moratorium
drags on, look for idled rigs heading to other shores.
Available in:
<http://www.newsweek.com/2010/06/13/off-the-deep-end-in-brazil.html>
Retrieved on: June 19, 2011.
According to Text II, in spite of the oil spill disaster in the Gulf of Mexico,
Text I
Brazil: Platform for growth
By Joe Leahy
On the Cidade de Angra dos Reis oil platform,
surrounded by the deep blue South Atlantic, a
Petrobras engineer turns on a tap and watches black
liquid flow into a beaker.
5____It looks and smells like ordinary crude oil.
Nevertheless, for Brazil, this represents something
much more spectacular. Pumped by the national oil
company from “pre-salt” deposits – so-called because
they lie beneath 2,000m of salt – 300km off the coast
10 of Rio de Janeiro, it is some of the first commercial
oil to flow from the country’s giant new deepwater
discoveries.
Already estimated to contain 50bn barrels, and
with much of the area still to be fully explored, the
15 fields contain the world’s largest known offshore oil
deposits. In one step, Brazil could jump up the world
rankings of national oil reserves and production, from
15th to fifth. So great are the discoveries, and the
investment required to exploit them, that they have
20 the potential to transform the country – for good or for ill.
Having seen out booms and busts before,
Brazilians are hoping that this time “the country
of the future” will at last realise its full economic
potential. The hope is that the discoveries will provide
25 a nation already rich in renewable energy with an
embarrassment of resources with which to pursue the
goal of becoming a US of the south.
The danger for Brazil, if it fails to manage this
windfall wisely, is of falling victim to “Dutch disease”.
30 The economic malaise is named after the Netherlands
in the 1970s, where the manufacturing sector withered
after its currency strengthened on the back of a large
gas field discovery combined with rising energy prices.
Even worse, Brazil could suffer a more severe
35 form of the disease, the “oil curse”, whereby nations
rich in natural resources – Nigeria and Venezuela, for
example – grow addicted to the money that flows from
them.
Petrobras chief executive says neither the
40 company nor the country’s oil industry has so far
been big enough to become a government cash cow.
But with the new discoveries, which stretch across an
800km belt off the coast of south-eastern Brazil, this is
going to change. The oil industry could grow from about
45 10 per cent of GDP to up to 25 per cent in the coming
decades, analysts say. To curb any negative effects,
Brazil is trying to support domestic manufacturing
by increasing “local content” requirements in the oil
industry.
50____Without a “firm local content policy”, says
Petrobras CEO, Dutch disease and the oil curse will
take hold. However, “if we have a firm and successful
local content policy, no – because other sectors in the
economy are going to grow as fast as Petrobras”.
55___The other long-term dividend Brazil is seeking
from the discoveries is in research and development
(R&D). Extracting oil from beneath a layer of salt at
great depth, hundreds of kilometres from the coast, is
so challenging that Brazilian engineers see it as a new
60 frontier. If they can perfect this, they can lead the way
in other markets with similar geology, such as Africa.
For its part, Petrobras is spending $800m-$900m
a year over the next five years on R&D, and has
invested $700m in the expansion of its research
65 centre.
Ultimately, Brazil’s ability to avoid Dutch disease
will depend not just on how the money from the oil
is spent. The country is the world’s second biggest
exporter of iron ore. It is the largest exporter of beef.
70 It is also the biggest producer of sugar, coffee and
orange juice, and the second-largest producer of soya
beans.
Exports of these commodities are already driving
up the exchange rate before the new oil fields have
75 fully come on stream, making it harder for Brazilian
exporters of manufactured goods. Industrial production
has faltered in recent months, with manufacturers
blaming the trend on a flood of cheap Chinese-made
imports.
80____“Brazil has everything that China doesn’t and it’s
natural that, as China continues to grow, it’s just going
to be starved for those resources,” says Harvard’s
Prof Rogoff. “At some level Brazil doesn’t just want
to be exporting natural resources – it wants a more
85 diversified economy. There are going to be some
rising tensions over that.”
Adapted from Financial Times - March 15 2011 22:54. Available in:
<http://www.ft.com/cms/s/0/fa11320c-4f48-11e0-9038-00144feab49a,_i_email=y.html>
Retrieved on: June 17, 2011.
Text II
Off the Deep End in Brazil
Gerald Herbert
With crude still hemorrhaging into the Gulf of
Mexico, deep-water drilling might seem taboo just
now. In fact, extreme oil will likely be the new normal.
Despite the gulf tragedy, the quest for oil and gas in
5 the most difficult places on the planet is just getting
underway. Prospecting proceeds apace in the ultra-
deepwater reserves off the coasts of Ghana and
Nigeria, the sulfur-laden depths of the Black Sea, and
the tar sands of Venezuela’s Orinoco Basin. Brazil’s
10 Petrobras, which already controls a quarter of global
deepwater operations, is just starting to plumb its 9 to
15 billion barrels of proven reserves buried some four
miles below the Atlantic.
The reason is simple: after a century and a
15 half of breakneck oil prospecting, the easy stuff is
history. Blistering growth in emerging nations has
turned the power grid upside down. India and China
will consume 28 percent of global energy by 2030,
triple the juice they required in 1990. China is set to
20 overtake the U.S. in energy consumption by 2014.
And now that the Great Recession is easing, the
earth’s hoard of conventional oil is waning even
faster. The International Energy Agency reckons the
world will need to find 65 million additional barrels a
25 day by 2030. If the U.S. offshore-drilling moratorium
drags on, look for idled rigs heading to other shores.
Available in:
<http://www.newsweek.com/2010/06/13/off-the-deep-end-in-brazil.html>
Retrieved on: June 19, 2011.
Comparing Texts I and II,
Text I
Brazil: Platform for growth
By Joe Leahy
On the Cidade de Angra dos Reis oil platform,
surrounded by the deep blue South Atlantic, a
Petrobras engineer turns on a tap and watches black
liquid flow into a beaker.
5____It looks and smells like ordinary crude oil.
Nevertheless, for Brazil, this represents something
much more spectacular. Pumped by the national oil
company from “pre-salt” deposits – so-called because
they lie beneath 2,000m of salt – 300km off the coast
10 of Rio de Janeiro, it is some of the first commercial
oil to flow from the country’s giant new deepwater
discoveries.
Already estimated to contain 50bn barrels, and
with much of the area still to be fully explored, the
15 fields contain the world’s largest known offshore oil
deposits. In one step, Brazil could jump up the world
rankings of national oil reserves and production, from
15th to fifth. So great are the discoveries, and the
investment required to exploit them, that they have
20 the potential to transform the country – for good or for ill.
Having seen out booms and busts before,
Brazilians are hoping that this time “the country
of the future” will at last realise its full economic
potential. The hope is that the discoveries will provide
25 a nation already rich in renewable energy with an
embarrassment of resources with which to pursue the
goal of becoming a US of the south.
The danger for Brazil, if it fails to manage this
windfall wisely, is of falling victim to “Dutch disease”.
30 The economic malaise is named after the Netherlands
in the 1970s, where the manufacturing sector withered
after its currency strengthened on the back of a large
gas field discovery combined with rising energy prices.
Even worse, Brazil could suffer a more severe
35 form of the disease, the “oil curse”, whereby nations
rich in natural resources – Nigeria and Venezuela, for
example – grow addicted to the money that flows from
them.
Petrobras chief executive says neither the
40 company nor the country’s oil industry has so far
been big enough to become a government cash cow.
But with the new discoveries, which stretch across an
800km belt off the coast of south-eastern Brazil, this is
going to change. The oil industry could grow from about
45 10 per cent of GDP to up to 25 per cent in the coming
decades, analysts say. To curb any negative effects,
Brazil is trying to support domestic manufacturing
by increasing “local content” requirements in the oil
industry.
50____Without a “firm local content policy”, says
Petrobras CEO, Dutch disease and the oil curse will
take hold. However, “if we have a firm and successful
local content policy, no – because other sectors in the
economy are going to grow as fast as Petrobras”.
55___The other long-term dividend Brazil is seeking
from the discoveries is in research and development
(R&D). Extracting oil from beneath a layer of salt at
great depth, hundreds of kilometres from the coast, is
so challenging that Brazilian engineers see it as a new
60 frontier. If they can perfect this, they can lead the way
in other markets with similar geology, such as Africa.
For its part, Petrobras is spending $800m-$900m
a year over the next five years on R&D, and has
invested $700m in the expansion of its research
65 centre.
Ultimately, Brazil’s ability to avoid Dutch disease
will depend not just on how the money from the oil
is spent. The country is the world’s second biggest
exporter of iron ore. It is the largest exporter of beef.
70 It is also the biggest producer of sugar, coffee and
orange juice, and the second-largest producer of soya
beans.
Exports of these commodities are already driving
up the exchange rate before the new oil fields have
75 fully come on stream, making it harder for Brazilian
exporters of manufactured goods. Industrial production
has faltered in recent months, with manufacturers
blaming the trend on a flood of cheap Chinese-made
imports.
80____“Brazil has everything that China doesn’t and it’s
natural that, as China continues to grow, it’s just going
to be starved for those resources,” says Harvard’s
Prof Rogoff. “At some level Brazil doesn’t just want
to be exporting natural resources – it wants a more
85 diversified economy. There are going to be some
rising tensions over that.”
Adapted from Financial Times - March 15 2011 22:54. Available in:
<http://www.ft.com/cms/s/0/fa11320c-4f48-11e0-9038-00144feab49a,_i_email=y.html>
Retrieved on: June 17, 2011.
The boldfaced item is synonymous with the expression in parentheses in
Text I
Brazil: Platform for growth
By Joe Leahy
On the Cidade de Angra dos Reis oil platform,
surrounded by the deep blue South Atlantic, a
Petrobras engineer turns on a tap and watches black
liquid flow into a beaker.
5____It looks and smells like ordinary crude oil.
Nevertheless, for Brazil, this represents something
much more spectacular. Pumped by the national oil
company from “pre-salt” deposits – so-called because
they lie beneath 2,000m of salt – 300km off the coast
10 of Rio de Janeiro, it is some of the first commercial
oil to flow from the country’s giant new deepwater
discoveries.
Already estimated to contain 50bn barrels, and
with much of the area still to be fully explored, the
15 fields contain the world’s largest known offshore oil
deposits. In one step, Brazil could jump up the world
rankings of national oil reserves and production, from
15th to fifth. So great are the discoveries, and the
investment required to exploit them, that they have
20 the potential to transform the country – for good or for ill.
Having seen out booms and busts before,
Brazilians are hoping that this time “the country
of the future” will at last realise its full economic
potential. The hope is that the discoveries will provide
25 a nation already rich in renewable energy with an
embarrassment of resources with which to pursue the
goal of becoming a US of the south.
The danger for Brazil, if it fails to manage this
windfall wisely, is of falling victim to “Dutch disease”.
30 The economic malaise is named after the Netherlands
in the 1970s, where the manufacturing sector withered
after its currency strengthened on the back of a large
gas field discovery combined with rising energy prices.
Even worse, Brazil could suffer a more severe
35 form of the disease, the “oil curse”, whereby nations
rich in natural resources – Nigeria and Venezuela, for
example – grow addicted to the money that flows from
them.
Petrobras chief executive says neither the
40 company nor the country’s oil industry has so far
been big enough to become a government cash cow.
But with the new discoveries, which stretch across an
800km belt off the coast of south-eastern Brazil, this is
going to change. The oil industry could grow from about
45 10 per cent of GDP to up to 25 per cent in the coming
decades, analysts say. To curb any negative effects,
Brazil is trying to support domestic manufacturing
by increasing “local content” requirements in the oil
industry.
50____Without a “firm local content policy”, says
Petrobras CEO, Dutch disease and the oil curse will
take hold. However, “if we have a firm and successful
local content policy, no – because other sectors in the
economy are going to grow as fast as Petrobras”.
55___The other long-term dividend Brazil is seeking
from the discoveries is in research and development
(R&D). Extracting oil from beneath a layer of salt at
great depth, hundreds of kilometres from the coast, is
so challenging that Brazilian engineers see it as a new
60 frontier. If they can perfect this, they can lead the way
in other markets with similar geology, such as Africa.
For its part, Petrobras is spending $800m-$900m
a year over the next five years on R&D, and has
invested $700m in the expansion of its research
65 centre.
Ultimately, Brazil’s ability to avoid Dutch disease
will depend not just on how the money from the oil
is spent. The country is the world’s second biggest
exporter of iron ore. It is the largest exporter of beef.
70 It is also the biggest producer of sugar, coffee and
orange juice, and the second-largest producer of soya
beans.
Exports of these commodities are already driving
up the exchange rate before the new oil fields have
75 fully come on stream, making it harder for Brazilian
exporters of manufactured goods. Industrial production
has faltered in recent months, with manufacturers
blaming the trend on a flood of cheap Chinese-made
imports.
80____“Brazil has everything that China doesn’t and it’s
natural that, as China continues to grow, it’s just going
to be starved for those resources,” says Harvard’s
Prof Rogoff. “At some level Brazil doesn’t just want
to be exporting natural resources – it wants a more
85 diversified economy. There are going to be some
rising tensions over that.”
Adapted from Financial Times - March 15 2011 22:54. Available in:
<http://www.ft.com/cms/s/0/fa11320c-4f48-11e0-9038-00144feab49a,_i_email=y.html>
Retrieved on: June 17, 2011.
In “Without a ‘firm local content policy’, says Petrobras CEO, Dutch disease and the oil curse will take hold.” (lines 50-52), “take hold” means to
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