Assuming that all conditions for inference have been met, which of the following equations gives the appropriate chi-square test statistic and the correct number of degrees of freedom to determine if there is an association between grade level and whether a student approves of the food choices in the cafeteria? A) χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 4 degrees of freedom B) χ2=(50−35)250+(20−35)220+(30−45)230+(60−45)260 with 4 degrees of freedom C) χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 4 degrees of freedom D) χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 1 degree of freedom E) χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 1 degree of freedom
Assuming that all conditions for inference have been met, which of the following equations gives the appropriate chi-square test statistic and the correct number of degrees of freedom to determine if there is an association between grade level and whether a student approves of the food choices in the cafeteria?
A) χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 4 degrees of freedom
B) χ2=(50−35)250+(20−35)220+(30−45)230+(60−45)260 with 4 degrees of freedom
C) χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 4 degrees of freedom
D) χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 1 degree of freedom
E) χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 1 degree of freedom
Answer
Answer: E) χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 1 degree of freedom
Explanation: The chi-square test statistic is calculated as the sum of squared differences between observed and expected counts divided by the expected counts. The degrees of freedom for the test depend on the number of categories (rows) minus 1 multiplied by the number of groups (columns) minus 1.
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