Sampling Distributions for Sample Means

AP Statistics· difficulty 2/5

Two simulated sampling distributions of x̄ are overlaid on the same axes.

Two sampling distributions of x̄ have the same mean μ but different SDs. Which has a smaller σ?

  • A

    Cannot tell.

  • B

    The taller, narrower one (larger n).

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  • C

    Both have the same SD.

  • D

    The wider one (smaller n).

Explanation

A narrower sampling distribution corresponds to a smaller σ_x̄ = σ/√n, which occurs with larger n.

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