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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?

A posteriori, after observing the data Signup and view all the answers

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

2var(xi) > 0 Signup and view all the answers

What does the term 'IID sample' refer to?

A sample of independent and identically distributed observations Signup and view all the answers

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

To account for uncertainty in the estimation of parameters Signup and view all the answers

How are the unknown parameters β0 and β1 estimated?

By replacing the unknown expected value with an appropriate estimator Signup and view all the answers

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

The expectation of the sample average estimates being equal to the population parameter β Signup and view all the answers

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

yi = β0 + β1 xi + ei Signup and view all the answers

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

To examine the unbiasedness of the sample average estimates Signup and view all the answers

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

The expected value of a bias variable given observed mean and standard deviation Signup and view all the answers