Problem

A fixed-size simple random sample is drawn without replacement from a roster. Explain what is randomized, what repetition creates, and what inference the design supports and does not support.

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Treatment labels are randomly assigned to roster members with fixed group sizes. Repetition gives a random-assignment distribution that supports causation rather than inference to roster-covered units.

Which roster names enter the sample is randomized, with sample size fixed. Repetition gives a sampling distribution that reduces selection bias and supports inference to roster-covered units, not causation.

Which roster names enter the fixed-size sample is randomized. Repetition guarantees a perfectly representative sample with no uncertainty and also establishes causal effects.

Each roster member's outcome is randomized while sample size varies. Repetition creates new outcomes, eliminates selection uncertainty, and supports both causation and population generalization.

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A fixed-size simple random sample is drawn without replacement from a roster. Explain what is randomized, what repetition creates, and what inference the design supports and does not support.

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