Test a single population proportion

With x successes out of n independent Bernoulli observations, estimate p by phat=x/n. Under H0: p=p0, z=(phat-p0)/√[p0(1-p0)/n]. Use the null value p0 in the test SE. A normal approximation needs adequate expected success and failure counts; this pack uses np0≥10 and n(1-p0)≥10 as a conservative classroom check. Small counts call for an appropriate exact or other method.