x = (m/n-P) / SqRt[P(1-P)/n]
m= "yes" response n = random sample size p = proportion P = populationThis formula is used to test three hypotheses:
p ≤ P p ≥ P p = PThe p-test statistic typically follows a standard normal distribution when large sample sizes are used, and researchers use Z-tests to determine whether a hypothesis passes based on a specific significance level will be rejected. The larger the p-value in the p-test, the more likely the hypothesis is true.
For example, a polling group contacted a group of investors and asked if they felt that the economy would fall into a recession. Of the 1000 people contacted, 700 said that they thought that the economy was heading toward recession. The researchers then applied the P-Test to determine if p ≤ 0.60, p ≥ 0.60, or p = 0.60; basically, what percentage of the population believe that the economy will fall into a recession.