Constructing a Confidence Interval for a Population Proportion

AP Statistics· difficulty 3/5

A researcher wants a 95% CI for a population proportion with margin of error at most 0.03. No prior estimate is available, so use p* = 0.5.

ME = z* · sqrt(p*(1-p*)/n) 0.03 = 1.96 · sqrt(0.25/n) Solve for n

What minimum sample size is required?

  • A

    1067

  • B

    1068

    check_circle
  • C

    267

  • D

    1500

Explanation

n ≥ (1.96/0.03)² · 0.25 = 1067.1, round up to 1068.

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