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Q3266698 Inglês

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    The disjunction between method as conceptualized by theorists and method as conducted by teachers is the direct consequence of the inherent limitations of the concept of method itself. First and foremost, methods are based on idealized concepts geared toward idealized contexts. Since language learning and teaching needs, wants, and situations are unpredictably numerous, no idealized method can visualize all the variables in advance in order to provide situation-specific suggestions that practicing teachers need to tackle the challenges they are confronted with every day of their professional lives.

    Not anchored in any specific learning and teaching context, and caught up in the whirlwind of fashion, methods tend to wildly drift from one theoretical extreme to the other. At one time, grammatical drills were considered the right way to teach; at another, they were given up in favor of communicative tasks. At one time, explicit error correction was not only favored but considered necessary; at another, it was frowned upon. These extreme swings create conditions where certain aspects of learning and teaching get overly emphasized while certain others are utterly ignored, depending on which way the pendulum swings.

    The limitations of the concept of method gradually led to statements such as “the term method is a label without substance” (Clarke, 1983, p. 109), and that it has “diminished rather than enhanced our understanding of language teaching” (Pennycook, 1989, p. 597). This realization has resulted in a widespread dissatisfaction with the concept of method.


(Kumaravadivelu, B. Beyond Methods: Macrostrategies for language teaching. Haven and London: Yale University Press. 2003. Adaptado)


In the text, the author 

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Q3266697 Inglês

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Text 1: Making a doctor’s appointment

(telephone rings)

Patient: Could I make an appointment to see the doctor, please?

Receptionist: Certainly, who do you usually see?

Patient: Dr Cullen.

Receptionist: I’m sorry but Dr Cullen has got patients all day.

Would Dr Maley do?

Patient: Sure.

Receptionist: OK then. When would you like to come?

Patient: Could I come at four o’clock?

Receptionist: Four o’clock? Fine. Could I have your name, please?

(Nunan and Lockwood 1991)


Text 2: Confirming an appointment with the doctor (telephone rings)

Receptionist: Doctor’s rooms, can you hold the line for a

moment?

Patient: Yes.

Receptionist: (pause) Thanks.

Receptionist: Hello.

Patient: Hello.

Patient: That’s all right … I’m just calling to confirm an appointment with Dr X for the first of October. Receptionist: Oh …

Patient: Because it was so far in advance I was told to.

Receptionist: I see what you mean, to see if she’s going to be

in that day.

Patient: That’s right.

Receptionist: Oh we may not know yet.

Patient: Oh I see.

Receptionist: First of October … Edith … yes.

Patient: Yes.

Receptionist: There she is. OK.. What’s your name?

Patient: At nine fift…

Receptionist: Got it got it.

(Burns, Joyce and Gollin 1996)


(Carter, Ronald et al. Telling tails: grammar, the spoken language and

materials development. In Tomlinson, B. (ed). Material Development in

Language Teaching. Cambridge: CUP. 1998/2011. Adaptado)

A teacher who believes firmly in language-centered approaches would state that

Alternativas
Q3266696 Inglês

Leia os diálogos, para responder à questão.


Text 1: Making a doctor’s appointment

(telephone rings)

Patient: Could I make an appointment to see the doctor, please?

Receptionist: Certainly, who do you usually see?

Patient: Dr Cullen.

Receptionist: I’m sorry but Dr Cullen has got patients all day.

Would Dr Maley do?

Patient: Sure.

Receptionist: OK then. When would you like to come?

Patient: Could I come at four o’clock?

Receptionist: Four o’clock? Fine. Could I have your name, please?

(Nunan and Lockwood 1991)


Text 2: Confirming an appointment with the doctor (telephone rings)

Receptionist: Doctor’s rooms, can you hold the line for a

moment?

Patient: Yes.

Receptionist: (pause) Thanks.

Receptionist: Hello.

Patient: Hello.

Patient: That’s all right … I’m just calling to confirm an appointment with Dr X for the first of October. Receptionist: Oh …

Patient: Because it was so far in advance I was told to.

Receptionist: I see what you mean, to see if she’s going to be

in that day.

Patient: That’s right.

Receptionist: Oh we may not know yet.

Patient: Oh I see.

Receptionist: First of October … Edith … yes.

Patient: Yes.

Receptionist: There she is. OK.. What’s your name?

Patient: At nine fift…

Receptionist: Got it got it.

(Burns, Joyce and Gollin 1996)


(Carter, Ronald et al. Telling tails: grammar, the spoken language and

materials development. In Tomlinson, B. (ed). Material Development in

Language Teaching. Cambridge: CUP. 1998/2011. Adaptado)

Compare the two dialogues. A feature that marks the second dialogue off as naturally occurring discourse is the presence of
Alternativas
Q3266695 Inglês

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The content of the answer provided by the internet could be an integral part of an English reading class to discuss issues directly related to the

Alternativas
Q3266694 Inglês

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AI tech products at schools and universities


    Every few years, an emerging technology shows up at the doorstep of schools and universities promising to transform education. The most recent? Technologies powered by generative artificial intelligence, also known as GenAI. These technologies are sold on the potential they hold for education. As optimistic as these visions of the future may be, the realities of educational technology over the past few decades have not lived up to their promises, as shown by rigorous investigations of technology after technology – from mechanical machines to computers, from mobile devices to massive open online courses.

    Yet, educational technology evangelists forget, remain unaware or simply do not care. Or they may be overly optimistic that the next new technology will be different than before.

    Here are four questions I believe should be answered before school officials purchase any technology that relies on AI.

    1. Is there evidence that a product works?

   Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist. Therefore, and unfortunately, it is the consumer who carries the onus of appraising products. My recommendation is: use multiple means for assessing product effectiveness.

    2. [...]

   Oftentimes, there is a divide between what entrepreneurs build and educators need. For example, one shortcoming of the One Laptop Per Child program – an ambitious program that sought to put small, cheap but sturdy laptops in the hands of children from families of lesser means – is that the laptops were designed for idealized younger versions of the developers themselves, not so much the children who were actually using them.

  Initiatives have been implemented in which entrepreneurs and educators work together to improve educational technology products. Some products are developed with input from students and educators. Questions to ask vendors might be: In what ways were educators and learners included? How did their input influence the final product?

    3. What educational beliefs shape this product?

   Educational technology is rarely neutral. It is designed by people, and people have beliefs, experiences, ideologies and biases that shape the technologies they develop.

   It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes. Questions to ask include: What pedagogical principles guide this product? What particular learning does it support or discourage?

    4. Does the product level the playing field?

   Finally, people ought to ask how a product addresses educational inequities. Is this technology going to help reduce the learning gaps between different groups of learners? Or is it one that aids some learners – often those who are already successful or privileged – but not others? Is it adopting an asset-based or a deficit-based approach to addressing inequities?

   Educational technology vendors and startups may not have answers to all of these questions. But they should still be asked and considered. Answers could lead to improved products.


(George Veletsianos. https://theconversation.com, 15.04.24. Adaptado)

 


 
 

Words ending in –ing may play a variety of roles in the English sentence. The word in bold is an adjective in alternative:

Alternativas
Q3266693 Inglês

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AI tech products at schools and universities


    Every few years, an emerging technology shows up at the doorstep of schools and universities promising to transform education. The most recent? Technologies powered by generative artificial intelligence, also known as GenAI. These technologies are sold on the potential they hold for education. As optimistic as these visions of the future may be, the realities of educational technology over the past few decades have not lived up to their promises, as shown by rigorous investigations of technology after technology – from mechanical machines to computers, from mobile devices to massive open online courses.

    Yet, educational technology evangelists forget, remain unaware or simply do not care. Or they may be overly optimistic that the next new technology will be different than before.

    Here are four questions I believe should be answered before school officials purchase any technology that relies on AI.

    1. Is there evidence that a product works?

   Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist. Therefore, and unfortunately, it is the consumer who carries the onus of appraising products. My recommendation is: use multiple means for assessing product effectiveness.

    2. [...]

   Oftentimes, there is a divide between what entrepreneurs build and educators need. For example, one shortcoming of the One Laptop Per Child program – an ambitious program that sought to put small, cheap but sturdy laptops in the hands of children from families of lesser means – is that the laptops were designed for idealized younger versions of the developers themselves, not so much the children who were actually using them.

  Initiatives have been implemented in which entrepreneurs and educators work together to improve educational technology products. Some products are developed with input from students and educators. Questions to ask vendors might be: In what ways were educators and learners included? How did their input influence the final product?

    3. What educational beliefs shape this product?

   Educational technology is rarely neutral. It is designed by people, and people have beliefs, experiences, ideologies and biases that shape the technologies they develop.

   It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes. Questions to ask include: What pedagogical principles guide this product? What particular learning does it support or discourage?

    4. Does the product level the playing field?

   Finally, people ought to ask how a product addresses educational inequities. Is this technology going to help reduce the learning gaps between different groups of learners? Or is it one that aids some learners – often those who are already successful or privileged – but not others? Is it adopting an asset-based or a deficit-based approach to addressing inequities?

   Educational technology vendors and startups may not have answers to all of these questions. But they should still be asked and considered. Answers could lead to improved products.


(George Veletsianos. https://theconversation.com, 15.04.24. Adaptado)

 


 
 

Leia as duas perguntas e a afirmação a seguir.



    – “In what ways were educators or learners included?” (parágrafo 6)


    – “How did their input influence the final product?” (parágrafo 6)


    – “It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes.” (parágrafo 7)



Em seu conjunto, as três citações refletem a preocupação do autor do texto em valorizar o professor no que concerne

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Q3266692 Inglês

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AI tech products at schools and universities


    Every few years, an emerging technology shows up at the doorstep of schools and universities promising to transform education. The most recent? Technologies powered by generative artificial intelligence, also known as GenAI. These technologies are sold on the potential they hold for education. As optimistic as these visions of the future may be, the realities of educational technology over the past few decades have not lived up to their promises, as shown by rigorous investigations of technology after technology – from mechanical machines to computers, from mobile devices to massive open online courses.

    Yet, educational technology evangelists forget, remain unaware or simply do not care. Or they may be overly optimistic that the next new technology will be different than before.

    Here are four questions I believe should be answered before school officials purchase any technology that relies on AI.

    1. Is there evidence that a product works?

   Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist. Therefore, and unfortunately, it is the consumer who carries the onus of appraising products. My recommendation is: use multiple means for assessing product effectiveness.

    2. [...]

   Oftentimes, there is a divide between what entrepreneurs build and educators need. For example, one shortcoming of the One Laptop Per Child program – an ambitious program that sought to put small, cheap but sturdy laptops in the hands of children from families of lesser means – is that the laptops were designed for idealized younger versions of the developers themselves, not so much the children who were actually using them.

  Initiatives have been implemented in which entrepreneurs and educators work together to improve educational technology products. Some products are developed with input from students and educators. Questions to ask vendors might be: In what ways were educators and learners included? How did their input influence the final product?

    3. What educational beliefs shape this product?

   Educational technology is rarely neutral. It is designed by people, and people have beliefs, experiences, ideologies and biases that shape the technologies they develop.

   It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes. Questions to ask include: What pedagogical principles guide this product? What particular learning does it support or discourage?

    4. Does the product level the playing field?

   Finally, people ought to ask how a product addresses educational inequities. Is this technology going to help reduce the learning gaps between different groups of learners? Or is it one that aids some learners – often those who are already successful or privileged – but not others? Is it adopting an asset-based or a deficit-based approach to addressing inequities?

   Educational technology vendors and startups may not have answers to all of these questions. But they should still be asked and considered. Answers could lead to improved products.


(George Veletsianos. https://theconversation.com, 15.04.24. Adaptado)

 


 
 

In a more formal register, the fragment “Therefore, and unfortunately”, in the answer to question 1, could be adequately replaced, without meaning change, by:
Alternativas
Q3266691 Inglês

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AI tech products at schools and universities


    Every few years, an emerging technology shows up at the doorstep of schools and universities promising to transform education. The most recent? Technologies powered by generative artificial intelligence, also known as GenAI. These technologies are sold on the potential they hold for education. As optimistic as these visions of the future may be, the realities of educational technology over the past few decades have not lived up to their promises, as shown by rigorous investigations of technology after technology – from mechanical machines to computers, from mobile devices to massive open online courses.

    Yet, educational technology evangelists forget, remain unaware or simply do not care. Or they may be overly optimistic that the next new technology will be different than before.

    Here are four questions I believe should be answered before school officials purchase any technology that relies on AI.

    1. Is there evidence that a product works?

   Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist. Therefore, and unfortunately, it is the consumer who carries the onus of appraising products. My recommendation is: use multiple means for assessing product effectiveness.

    2. [...]

   Oftentimes, there is a divide between what entrepreneurs build and educators need. For example, one shortcoming of the One Laptop Per Child program – an ambitious program that sought to put small, cheap but sturdy laptops in the hands of children from families of lesser means – is that the laptops were designed for idealized younger versions of the developers themselves, not so much the children who were actually using them.

  Initiatives have been implemented in which entrepreneurs and educators work together to improve educational technology products. Some products are developed with input from students and educators. Questions to ask vendors might be: In what ways were educators and learners included? How did their input influence the final product?

    3. What educational beliefs shape this product?

   Educational technology is rarely neutral. It is designed by people, and people have beliefs, experiences, ideologies and biases that shape the technologies they develop.

   It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes. Questions to ask include: What pedagogical principles guide this product? What particular learning does it support or discourage?

    4. Does the product level the playing field?

   Finally, people ought to ask how a product addresses educational inequities. Is this technology going to help reduce the learning gaps between different groups of learners? Or is it one that aids some learners – often those who are already successful or privileged – but not others? Is it adopting an asset-based or a deficit-based approach to addressing inequities?

   Educational technology vendors and startups may not have answers to all of these questions. But they should still be asked and considered. Answers could lead to improved products.


(George Veletsianos. https://theconversation.com, 15.04.24. Adaptado)

 


 
 

Observe a palavra destacada em negrito nas duas frases a seguir:



I. “Yet, educational technologist evangelists forget, remain unaware or simply do not care.” (parágrafo 2)


II. “Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist” (parágrafo 5).



O uso da palavra yet está corretamente explicado na alternativa:

Alternativas
Q3266690 Inglês

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AI tech products at schools and universities


    Every few years, an emerging technology shows up at the doorstep of schools and universities promising to transform education. The most recent? Technologies powered by generative artificial intelligence, also known as GenAI. These technologies are sold on the potential they hold for education. As optimistic as these visions of the future may be, the realities of educational technology over the past few decades have not lived up to their promises, as shown by rigorous investigations of technology after technology – from mechanical machines to computers, from mobile devices to massive open online courses.

    Yet, educational technology evangelists forget, remain unaware or simply do not care. Or they may be overly optimistic that the next new technology will be different than before.

    Here are four questions I believe should be answered before school officials purchase any technology that relies on AI.

    1. Is there evidence that a product works?

   Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist. Therefore, and unfortunately, it is the consumer who carries the onus of appraising products. My recommendation is: use multiple means for assessing product effectiveness.

    2. [...]

   Oftentimes, there is a divide between what entrepreneurs build and educators need. For example, one shortcoming of the One Laptop Per Child program – an ambitious program that sought to put small, cheap but sturdy laptops in the hands of children from families of lesser means – is that the laptops were designed for idealized younger versions of the developers themselves, not so much the children who were actually using them.

  Initiatives have been implemented in which entrepreneurs and educators work together to improve educational technology products. Some products are developed with input from students and educators. Questions to ask vendors might be: In what ways were educators and learners included? How did their input influence the final product?

    3. What educational beliefs shape this product?

   Educational technology is rarely neutral. It is designed by people, and people have beliefs, experiences, ideologies and biases that shape the technologies they develop.

   It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes. Questions to ask include: What pedagogical principles guide this product? What particular learning does it support or discourage?

    4. Does the product level the playing field?

   Finally, people ought to ask how a product addresses educational inequities. Is this technology going to help reduce the learning gaps between different groups of learners? Or is it one that aids some learners – often those who are already successful or privileged – but not others? Is it adopting an asset-based or a deficit-based approach to addressing inequities?

   Educational technology vendors and startups may not have answers to all of these questions. But they should still be asked and considered. Answers could lead to improved products.


(George Veletsianos. https://theconversation.com, 15.04.24. Adaptado)

 


 
 

In the first sentence of the second paragraph we find an example of ellipsis. Commonly found in oral or written texts, ellipsis can be described as
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Q3266689 Inglês

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AI tech products at schools and universities


    Every few years, an emerging technology shows up at the doorstep of schools and universities promising to transform education. The most recent? Technologies powered by generative artificial intelligence, also known as GenAI. These technologies are sold on the potential they hold for education. As optimistic as these visions of the future may be, the realities of educational technology over the past few decades have not lived up to their promises, as shown by rigorous investigations of technology after technology – from mechanical machines to computers, from mobile devices to massive open online courses.

    Yet, educational technology evangelists forget, remain unaware or simply do not care. Or they may be overly optimistic that the next new technology will be different than before.

    Here are four questions I believe should be answered before school officials purchase any technology that relies on AI.

    1. Is there evidence that a product works?

   Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist. Therefore, and unfortunately, it is the consumer who carries the onus of appraising products. My recommendation is: use multiple means for assessing product effectiveness.

    2. [...]

   Oftentimes, there is a divide between what entrepreneurs build and educators need. For example, one shortcoming of the One Laptop Per Child program – an ambitious program that sought to put small, cheap but sturdy laptops in the hands of children from families of lesser means – is that the laptops were designed for idealized younger versions of the developers themselves, not so much the children who were actually using them.

  Initiatives have been implemented in which entrepreneurs and educators work together to improve educational technology products. Some products are developed with input from students and educators. Questions to ask vendors might be: In what ways were educators and learners included? How did their input influence the final product?

    3. What educational beliefs shape this product?

   Educational technology is rarely neutral. It is designed by people, and people have beliefs, experiences, ideologies and biases that shape the technologies they develop.

   It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes. Questions to ask include: What pedagogical principles guide this product? What particular learning does it support or discourage?

    4. Does the product level the playing field?

   Finally, people ought to ask how a product addresses educational inequities. Is this technology going to help reduce the learning gaps between different groups of learners? Or is it one that aids some learners – often those who are already successful or privileged – but not others? Is it adopting an asset-based or a deficit-based approach to addressing inequities?

   Educational technology vendors and startups may not have answers to all of these questions. But they should still be asked and considered. Answers could lead to improved products.


(George Veletsianos. https://theconversation.com, 15.04.24. Adaptado)

 


 
 

Another very relevant reading ability to be developed in students is that of recognizing the gist of a text, or of a self-contained part of a text. A teacher’s instruction to help develop this ability would include asking the students to reread subitem 2 and provide a subtitle that both shows their understanding of the excerpt and corresponds to the way the text has been structured.


One correct subtitle would be: 

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Q3266688 Inglês

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AI tech products at schools and universities


    Every few years, an emerging technology shows up at the doorstep of schools and universities promising to transform education. The most recent? Technologies powered by generative artificial intelligence, also known as GenAI. These technologies are sold on the potential they hold for education. As optimistic as these visions of the future may be, the realities of educational technology over the past few decades have not lived up to their promises, as shown by rigorous investigations of technology after technology – from mechanical machines to computers, from mobile devices to massive open online courses.

    Yet, educational technology evangelists forget, remain unaware or simply do not care. Or they may be overly optimistic that the next new technology will be different than before.

    Here are four questions I believe should be answered before school officials purchase any technology that relies on AI.

    1. Is there evidence that a product works?

   Compelling evidence of the effect of GenAI products on educational outcomes does not yet exist. Therefore, and unfortunately, it is the consumer who carries the onus of appraising products. My recommendation is: use multiple means for assessing product effectiveness.

    2. [...]

   Oftentimes, there is a divide between what entrepreneurs build and educators need. For example, one shortcoming of the One Laptop Per Child program – an ambitious program that sought to put small, cheap but sturdy laptops in the hands of children from families of lesser means – is that the laptops were designed for idealized younger versions of the developers themselves, not so much the children who were actually using them.

  Initiatives have been implemented in which entrepreneurs and educators work together to improve educational technology products. Some products are developed with input from students and educators. Questions to ask vendors might be: In what ways were educators and learners included? How did their input influence the final product?

    3. What educational beliefs shape this product?

   Educational technology is rarely neutral. It is designed by people, and people have beliefs, experiences, ideologies and biases that shape the technologies they develop.

   It is important for educational technology products to rely on what educators have experienced as relevant to the students they meet in their real-life classes. Questions to ask include: What pedagogical principles guide this product? What particular learning does it support or discourage?

    4. Does the product level the playing field?

   Finally, people ought to ask how a product addresses educational inequities. Is this technology going to help reduce the learning gaps between different groups of learners? Or is it one that aids some learners – often those who are already successful or privileged – but not others? Is it adopting an asset-based or a deficit-based approach to addressing inequities?

   Educational technology vendors and startups may not have answers to all of these questions. But they should still be asked and considered. Answers could lead to improved products.


(George Veletsianos. https://theconversation.com, 15.04.24. Adaptado)

 


 
 

The teaching of reading in English implies helping students foster reading skills and abilities, among them critical reading skills. A teacher willing to deal with critical reading in their classes would tell students to go over the article “AI tech products at schools and universities” in order to identify the author’s opinion on the topic, which is summarized in alternative:
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Q3266674 História

Uma peculiaridade da Carta de 1824 foi incluir um artigo reproduzindo quase palavra por palavra a Declaração dos Direitos do Homem emitida na França em 1789. Comparado ao original havia, no entanto, algumas omissões bastante significativas e curiosas. Não foi incluído na Carta outorgada o artigo que, na versão original francesa, dizia: “O princípio de toda soberania reside essencialmente na nação. Nenhum corpo nem indivíduo podem exercer autoridade que não emane expressamente dela”. Também faltava o artigo VI: “A lei é expressão da vontade geral”. Finalmente, o artigo II: “O objetivo de toda associação política é a preservação dos direitos naturais e inalienáveis do homem. Estes direitos são a liberdade, a propriedade, a segurança e a resistência perante a opressão” foi reproduzido omitindo-se as seis últimas palavras.


(Emília Viotti da Costa, Da monarquia à república:

momentos decisivos, p. 141-142. Adaptado)


Para Emília Viotti da Costa, tais omissões podem revelar

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Q3266537 Estatística
Sobre o teste qui-quadrado, é correto afirmar:
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Q3266536 Estatística
Um pesquisador em educação infantil deseja verificar se existe (ou não) associação entre desenvolvimento da fala e o engatinhar (se engatinhou ou não engatinhou) de bebês de uma determinada região. Para isso, ele observou uma amostra de 70 bebês de uma mesma faixa etária e sexo. Na tabela a seguir é apresentado um resumo (frequências absolutas) obtido desse estudo.

Captura_de tela 2025-03-28 081306.png (246×114)

Considerando um nível de significância de 10%, o valor aproximado calculado do teste (utilize para os cálculos os valores inteiros aproximados das frequências esperadas), juntamente com a sua conclusão, são, respectivamente: 
Alternativas
Q3266535 Estatística
Um modelo de regressão linear simples (Yi = a + b Xi + ei, sendo i = 1, 2, ...,33) foi ajustado a uma amostra aleatória de uma determinada população, onde se obteve as seguintes informações referentes à análise de variância desse modelo: (i) a soma de quadrados referente a regressão foi igual a 3390; e (ii) a soma de quadrados totais foi igual a 3713. A estimativa não viciada para a variância populacional e a interpretação do coeficiente de determinação desse modelo são, respectivamente: 
Alternativas
Q3266534 Estatística
No ajuste de qualquer modelo estatístico, uma das principais tarefas do analista é avaliar se as pressuposições assumidas por determinada metodologia são satisfeitas, bem como a qualidade desse ajuste aos dados. Para isso, fazer uma análise de resíduos se torna imprescindível. Há três tipos de violações das suposições que são prontamente detectados por meio do uso de gráficos residuais; são elas: (i) presença de valores discrepantes; (ii) variância do erro heterogênea; e (iii) especificação do modelo inadequada.

Diante disso, o gráfico de valores preditos Captura_de tela 2025-03-28 081156.png (27×26) versus resíduos padronizados (ei), que indica uma especificação do modelo inadequada para a situação em estudo, é:
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Q3266533 Estatística
Em relação ao coeficiente de correlação de Pearson populacional e amostral (ρ e r, respectivamente), é correto afirmar:
Alternativas
Q3266532 Estatística
São vários os procedimentos para a busca do “subconjunto ótimo” de variáveis, na ausência da ortogonalidade, para obter uma equação de estimação adequada que relaciona uma variável Y a todas ou a um subconjunto de variáveis independentes. Considere o seguinte procedimento: 

PASSO 1: Escolha a variável que fornece a maior soma de quadrados da regressão em regressão linear simples com Y ou, de maneira equivalente, que forneça o maior valor de R2. Chamaremos essa variável inicial de X1.

PASSO 2: Escolha a variável que, quando inserida no modelo, fornece o maior aumento em R2, na presença de X1, sobre o valor de R2 encontrado no passo 1, isto é, a variável Xj para a qual:
Rj1) = R1, βj) – R1)
é maior. Vamos chamá-la de variável X2. O modelo de regressão com X1 e X2 é, então, ajustado e R2 é observado. 

PASSO 3: Escolha a variável Xj que fornece o maior valor de:
Rj1, β2) = R1, β2, βj) – R1, β2),
resultando novamente em um aumento em R2 sobre aquele dado no PASSO 2. Ao chamar essa variável de X3, agora temos um modelo de regressão que envolve X1, X2 e X3. Esse processo é continuado até que a variável inserida mais recentemente falhe ao produzir um aumento significativo na regressão explicada. Tal aumento pode ser determinado em cada passo, devendo-se usar o teste F (ou t) apropriado.

Por exemplo, no PASSO 2, o valor: Captura_de tela 2025-03-28 081059.png (142×33) pode ser determinado para testar a adequação de X2 no modelo. De maneira similar, no PASSO 3 a razão: Captura_de tela 2025-03-28 081107.png (173×38) testa a adequação de X3 no modelo.

Se f < f(1, n-3; α) no PASSO 2, para um nível de significância preestabelecido, X2 não é incluído e o processo é encerrado, resultando em uma equação linear simples que relaciona Y e X1.

Contudo, se f >f(1, n-3; α) deve-se seguir para o PASSO 3. Novamente, se f < f(1, n-4; α) no PASSO 3, X3 não é incluído e o processo é encerrado com a equação de regressão apropriada que contém as variáveis X1 e X2.

Notações utilizadas: 
R2 é o coeficiente de determinação do modelo de regressão;
R(.) é a soma dos quadrados do modelo de regressão em questão;
βj é o coeficiente do modelo de regressão que acompanha a variável Xj;
A notação ‘|’ indica a probabilidade condicional; 
Captura_de tela 2025-03-28 081130.png (39×31) é o quadrado do erro médio para o modelo que contém as variáveis X1 e X2;
Captura_de tela 2025-03-28 081141.png (47×32) é o quadrado do erro médio para o modelo que contém as variáveis X1, X2 e X3.

Essa descrição se refere ao método de seleção de variáveis:
Alternativas
Q3266531 Estatística
Considere a população de crianças, do sexo masculino, de faixa etária de 6 a 7 anos de uma determinada região. É de desejo realizar o seguinte teste de hipóteses para a proporção (p) de crianças com o índice de massa corpórea (IMC) maior que 30 dessa população (que é normalmente distribuída para essa variável): p = 0,6 contra p > 0,6. Fixando um nível de significância de 5%; considerando pc o um ponto crítico para a tomada de decisão e o estimador Captura_de tela 2025-03-28 081023.png (19×30) da verdadeira proporção de crianças com o índice de massa corpórea (IMC) maior que 30, p, é correto afirmar que:
Alternativas
Q3266530 Estatística
A abordagem do teste de hipóteses para a inferência estatística é muito próxima à abordagem do intervalo de confiança. Essa equivalência se estende às diferenças entre duas médias, variâncias, razão de variâncias e assim por diante. Para o caso de uma única média populacional µ com variância σ2 conhecida, considerando um nível de significância α e uma amostra aleatória de tamanho n dessa população, é correto afirmar:
Alternativas
Respostas
1681: D
1682: A
1683: C
1684: B
1685: B
1686: A
1687: E
1688: D
1689: C
1690: D
1691: A
1692: A
1693: E
1694: B
1695: B
1696: C
1697: E
1698: A
1699: D
1700: A