Houjun Liu


A z-test is a hypothesis test for statistical significance between two sample proportions. Before it can be conducted, it must meet the conditions for inference for a z-test.

conditions for inference (z-test)

  • has to be random
  • has to be reasonably normal (vis a vi test for normality)
  • each sample has to be independent (or 10% rule)

use a z-statistic to find p-value

  1. Given a sample proportion, calculate the sample proportion standard deviation (given on the formula sheet)
  2. Then, divide the difference between measured and null proportions to figure \(z\)

that is,

\begin{equation} z = \frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \end{equation}

Look up the probability of \(z\) taking place on a \(z\) table. Then, \(1-z\) would yield the \(p\) vaule.