1. Homogeneity vs Goodness of Fit
In the Goodness of Fit test we are using:
One categorical variable with multiple categories from one population.
The test compares the distribution of sample counts with the hypothesized distribution of the population.

2. Homogeneity vs Goodness of Fit
In the X2 Test for Homogeneity we are comparing _______ _____________- proportions to each other and asking “_____________________” (___________________).
Used with a ________ ___________variable from two (or more) independent samples.
The z-test for two-proportions generalizes the X2 Test for Homogeneity, we use the X2 Test for Homogeneity to compare more.

3. Hypotheses These are written in words – be sure to write in context.
Ho:
Ha:

4. Assumptions/Conditions

5. Expected Counts and Degree of Freedom
Assuming Ho is true,
Expected counts =
df =

6. Example 1
A large city examined their records of twin births for several years and found the data summarized in the table below. Is there evidence that the way the hospital deals with pregnancies involving twins may have changed?
1990
1995
2000
Preterm w/procedure 11 13 19
Preterm w/o procedure 14 18
Term or postterm 27 26 32

7. Example 2
A certain brand of bite-sized candies comes in three varieties: creamy, crispy, and chewy. The manufacturer is interested if preferences for the types of candies differ between three school-age groups: elementary, middle, and high school. Random samples of students at three local schools, on of each age group, are taken and the sample data compiled in the table below. Is there evidence that the proportion of students that prefer each variety of candy differs among the various age groups?
Creamy
Crispy
Chewy
Elementary 33 14 19
Middle 21 16 17
High 12 32

8. Example 3
A university dean suspects that there is a difference between how tenured and nontenured professors view a proposed salary increase. She randomly selects 20 nontenured instructors and 25 tenured staff to see if there is a difference. She gets the results below. Do these data provided good statistical evidence that tenured and non tenured faculty differ in their attitudes towards the proposed salary increase?
Favor Plan
Do not favor plan
Tenured 15 10
Nontenured 8 12