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Sampling Distributions for Sample Proportions

AP Statistics· difficulty 2/5

A simulation creates 10,000 random samples of size n = 40 from a population with p = 0.5 and computes p̂ each time.

Simulated p̂, n=40

What is the expected approximate SD of the simulated p̂ values?

  • A

    ≈ 0.079

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  • B

    ≈ 0.5

  • C

    ≈ 0.5/40 = 0.0125

  • D

    ≈ 0.25

Explanation

σ_p̂ = √(0.5·0.5/40) = √0.00625 ≈ 0.079.

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