Problem

Compare a random sample of \(1,000\) people from a full roster with a voluntary online poll of \(5,000\) people. State the plan that gives better population inference and explain why.

Big Picture

What this problem is really about

Judge inference quality by how participants enter the study before comparing sample sizes. Chance-based selection from a covering frame addresses systematic selection bias, while voluntary participation can overrepresent people with stronger opinions or greater interest. A very large self-enrolled sample may be precise for its respondents yet still be systematically unrepresentative of the target population.

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The voluntary online poll of 5000 gives better inference because more people can choose to participate, so it has better coverage of the population.

Both plans give about the same inference quality because each uses a large sample, so the way the sample is chosen matters less.

The voluntary online poll of 5000 gives better inference because the larger sample size makes its results automatically more accurate.

The random sample of 1000 from the full roster gives better inference because random selection makes the sample more representative and reduces bias.

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Compare a random sample of \(1,000\) people from a full roster with a voluntary online poll of \(5,000\) people. State the plan that gives better population inference and explain why.

What this problem is really about

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