Wald interval (aka one proportion z-interval): + z*

Score interval (aka Wilson) inverts

The midpoint of the Score interval can be rewritten as: (n /(n + z²)) + .5(z²/(n+z²)), a weighted average of and 0.50.

Adjusted Wald interval: + z* where = (X+.5z*²)/(n+z*²), ñ= n+z*²

For 95% confidence this is approximately: = (X+2)/(n+4) and ñ = n+4 which adds two successes and two failures to the sample (“plus four” method)

Finite Population Correction Factor (N = population size)

+ z*