Sampling Distributions for Sample Proportions

AP Statistics· difficulty 2/5

A pollster is comparing samples drawn at different sizes from a population with proportion p.

small n large n

If n is multiplied by 4, the standard deviation σ_p̂ is multiplied by what factor?

  • A

    1/2

    check_circle
  • B

    1/4

  • C

    2

  • D

    4

Explanation

σ_p̂ = √(p(1−p)/n). Multiplying n by 4 multiplies the SD by 1/√4 = 1/2.

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