Work out confidence interval for proportion instantly with clear inputs, formula shown and shareable results.
The Wald interval for a proportion is p̂ ± z√(p̂(1 − p̂)/n). It relies on a normal approximation, so it needs both np̂ and n(1 − p̂) to be at least about 10.
Proportion interval
p̂ ± z(α/2)·√(p̂(1 − p̂)/n)
p̂ = 0.42, the standard error 0.0403, so the margin is 0.079 and the interval runs 0.341 to 0.499.
The Wald interval performs badly. Use the Wilson score or Agresti-Coull interval instead.