Big Picture
          Hypothesis Tests that the Chi-Square Test 
          Statistic can Address:
          Goodness-of-Fit Test: Test a claim about the distribution of a categorical 
          variable in a population.
          •  The distribution of blood types for whites in the US is 45% type O, 41% 
             type A, 10% type B, and 4% type AB. Is the distribution of blood types 
             different for Asian Americans?
          Test of Independence: Test a claim about the relationship between two 
          categorical variables in a population.
          •  For young adults in the US, is gender related to body image?
          Test of Homogeneity: Test a claim about the distribution of a categorical 
          variable in several populations.
          •  Does the use of steroids in collegiate athletics differ across the three NCAA 
             divisions?
          Chi-Square Test
           •   
           The chi-square test statistic  measures how far the observed data are from 
           the null hypothesis by comparing observed counts and expected counts. 
           Expected counts are the counts we expect to see if the null hypothesis is 
           true.
          The Chi-Square Test Statistic and Distribution
           •
           Th e chi-square model is a family of curves that depend on degrees of 
           freedom. For a one-way table the degrees of freedom equals (). All chi-
           square curves are skewed to the right with a mean equal to the degrees of 
           freedom.
           A chi-square model is a good fit for the distribution of the chi-square test 
           statistic only if the following conditions are met:
           •  The sample is randomly selected.
           •  All expected counts are 5 or greater.
           If these conditions are met, we use the chi-square distribution to find the P-
           value. 
     The Chi-Square Test Statistic and Distribution 
     (cont.)
     •
     If t he P-value is at least as small as the 
     significance level, we reject the null 
     hypothesis and accept the alternative 
     hypothesis. 
     The P-value is the likelihood that results 
     from random samples have a  value equal 
     to or greater than that calculated from the 
     data if the null hypothesis is true. 
     For different degrees of freedom, the same 
      value gives different P-values.