Bivariate Population Sampling Quiz

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Questions and Answers

What is the goal of statistical inference?

  • To analyze the distribution of one random variable in isolation
  • To learn about features of a bivariate population
  • To learn about features of a population from a sample (correct)
  • To draw random samples from a population

Why are observations of a sample considered random a priori?

  • Because the sample does not accurately represent the population
  • Because the sample is selected without any knowledge of their values (correct)
  • Because the observations are numerical values
  • Because the sample is not representative until observations are made

What conditions need to hold for the sample to be representative?

  • The sample must be infinitely large
  • The sampling scheme must satisfy certain assumptions (correct)
  • The sample must have a complex object to learn about
  • The sample must consist of random numerical values

In statistical inference, when do observations of the sample become no longer random?

<p>A posteriori, after observing the data (B)</p> Signup and view all the answers

What condition must be satisfied for the solution to be a unique minimum?

<p>2var(xi) &gt; 0 (C)</p> Signup and view all the answers

What does the term 'IID sample' refer to?

<p>A sample of independent and identically distributed observations (C)</p> Signup and view all the answers

What is the purpose of view the observations as random for statistical analysis?

<p>To account for uncertainty in the estimation of parameters (D)</p> Signup and view all the answers

How are the unknown parameters β0 and β1 estimated?

<p>By replacing the unknown expected value with an appropriate estimator (B)</p> Signup and view all the answers

What does E[β] {z i=1} | =β represent in the context of the given text?

<p>The expectation of the sample average estimates being equal to the population parameter β (C)</p> Signup and view all the answers

In the practical example provided, what is the population model for generating the samples?

<p>yi = β0 + β1 xi + ei (A)</p> Signup and view all the answers

What is the purpose of simulating 2,000 samples of size n = 50 in the given context?

<p>To examine the unbiasedness of the sample average estimates (C)</p> Signup and view all the answers

What does E[.su bias Variable | Obs Mean Std.Dev.] represent in the given text?

<p>The expected value of a bias variable given observed mean and standard deviation (A)</p> Signup and view all the answers

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