6.2.3 One Sample z-test of Proportions and Confidence Interval

Assumptions are that data are from a Binomial distribution and that nπ > 15 and n(1 - π) > 15. This is an approximation, for small sample size one should use the exact distribution, the Binomial distribution.

H0  : π = π0

         ˆp - π0
z =  ∘--------------
       π0(1 - π0)∕n

A (1 - α)100% confidence interval for π is,

(        ∘ -----------         ∘ -----------)
 ˆp - zα∕2  ˆp(1 - ˆp)∕n ,pˆ+ zα∕2  pˆ(1 - ˆp)∕n  .