SECTION 9.2 Summary

• The chi-square goodness-of-fit test examines the null hypothesis that the probabilities of the possible outcomes for a categorical variable are equal to a particular set of values, . The data for the test are the observed counts in the cells, .
• Expected cell counts under the null hypothesis are
  
  
  where is the total number of observations.
• The chi-square statistic measures how much the observed cell counts differ from the expected cell counts. The formula for the statistic is
  The degrees of freedom are , and P-values are computed from the chi-square distribution. Use this procedure when the expected counts are all 5 or more.