SE shrinks as √n, not as n itself, because

Variance of x̄ scales as σ²/n; SD as σ/√n Var(x̄) = σ²/n; SD = √(σ²/n) = σ/√n.

Variance of x̄ scales as σ²/n; SD as σ/√n

Sampling Distributions for Sample Means

AP Statistics· difficulty 4/5

SE shrinks as \sqrtn, not as n itself, because

Explanation

Var(x̄) = σ²/n; SD = \sqrt(σ²/n) = σ/\sqrtn.

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