Constructing a Confidence Interval for a Population Proportion

AP Statistics· difficulty 3/5

Past studies show p ≈ 0.20. We want a 95% CI with margin of error ≤ 0.04.

0.04 ≥ 1.96·sqrt(0.2·0.8/n) n ≥ (1.96/0.04)² · 0.16

What minimum n is required?

  • A

    240

  • B

    1068

  • C

    385

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  • D

    97

Explanation

n ≥ (1.96/0.04)² · 0.16 = 2401·0.16 = 384.16, round up to 385.

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