13.1 Test for Goodness of Fit
A. Chi-Squared Distribution
1. The Chi-Squared Distribution is skewed right.
2. Must use Degree’s of Freedom
3. As the sample size increases, the curve
B. The test is to verify whether or not a distribution
of a population is the same as the hypothesized
1. The Null Hypothesis
a. The actual proportions is equal to the
2. Alternative Hypothesis
a. The actual proportions is different from the
a. (see Chi-Squared Eqn)
a. All expected counts are at least 1 or above
b. No more than 20% of the expected counts
are less than five
13.2 Inference for Two-Way Tables
A. Two-Way Tables
1. Dimensions are r x c (row and column)
2. Expected counts are calculated by product of
row total and column total divided by the entire
3. Use the same equation as Test for Goodness of
4. Degree of Freedom is calculated by (r-1)(c-1).
B. Test for Homogeneity of Populations
1. Test is reveal if the proportions for each group
are the same.
C. Test for Independence.
1. Same test as Homogeneity, but the result is to
determine if one category influences another