margin of error (proportion)

± 0.031

As a percentage: about ± 3.1 points. To halve the margin of error you need roughly four times the sample size.

Steps

  1. 1.z* for 95% confidence = 1.96
  2. 2.SE = sqrt(p-hat(1 - p-hat)/n) = sqrt(0.5 x 0.5 / 1000) = 0.01581
  3. 3.ME = z* x SE = 1.96 x 0.01581 = 0.031

Margin of error calculator: formula and worked example · free from StatsLearn