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)