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The Sampling Distribution for a Proportion Has a Formula for That

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The sampling distribution for a proportion has a formula for that standard error that involves using p. Yet when a confidence interval is calculated for a proportion, the standard error formula uses the sample proportion. Why do they differ?

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Definitions:

Hot Spots

Areas of the Earth's mantle that are exceptionally hot, which can lead to volcanic activity on the surface.

Shelled Arthropod

Arthropods that have an external skeleton or shell, such as crustaceans and certain insects, providing protection and support.

Fossil

Physical evidence of an organism that lived in the ancient past.

Cambrian Period

A geological era around 541 million years ago, marked by a rapid diversification of life forms and the appearance of most major groups of animals in the fossil record.

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