Work out confidence level for survey instantly with clear inputs, formula shown and shareable results.
The margin of error for a proportion is z times sqrt(p(1-p)/n), maximised when p is 50%. At n = 400 and 95% confidence that gives 4.9 percentage points, so a 50% result means 45.1% to 54.9%. The finite population correction only matters when the sample exceeds about 5% of the population.
Margin of error
MOE = z x sqrt(p(1-p) / n)
Finite population correction
multiply by sqrt((N - n) / (N - 1))
Because p(1-p) peaks there at 0.25. A proportion near 5% or 95% has a much smaller standard error for the same sample size.
Quadruple the sample. Precision improves with the square root of n, which is why national polls stop around 1000-2000 respondents.