1. Test for Equality of Several Proportions
Chi-Square Tests
Goodness-of-Fit Test
Test for Independence
Test for Equality of Several Proportions

2. Chi-square Test Statistic
Reject Ho if
The degrees of freedom depends on the application
Chi-square Tests : PLBautista

3. Goodness-of-fit Tests
We wish to test if the data follows a specified distribution.
Ho: The data follows the specified distribution.
H1: The data does not follow the specified distribution.
df=k-1, where k is the number of cells
Chi-square Tests : PLBautista

4. Chi-square Tests : PLBautista
Example
Consider the experiment of tossing a six-sided die. We wish to test if the die is balanced (that is, that the distribution of our data is uniform). We then toss the coin 120 times and obtain the following data:
Test if the die is balanced using a 0.05 level of significance.
Chi-square Tests : PLBautista

5. Chi-square Tests : PLBautista
Test for Independence
We wish to test if two variables are independent of one another
Ho: Variable A and Variable B are independent.
H1: Variable A and Variable B are not independent.
df = (r-1)(c-1), where r is the number of rows and c is the number of columns
Chi-square Tests : PLBautista

6. Chi-square Tests : PLBautista
Example
Suppose we wish to test if the presence or absence of hypertension is independent of one’s smoking habits. We obtain the following data from a sample of 180 individuals:
Test if the presence or absence of hypertension is independent of a person’s smoking habits using a 0.05 level of significance.
Chi-square Tests : PLBautista

7. Test for Equality of Several Proportions
We wish to test if the proportion of success is equal for more than two populations
Ho: p1=p2=…=pk
H1: at least one pair is not equal
Like the test for independence with r=2
df = k-1, where k is the number of populations
Chi-square Tests : PLBautista

8. Chi-square Tests : PLBautista
Example
In a shop study, a set of data was collected to determine whether or not the proportion of defectives produced by workers was the same for the day, evening, or night shift worked. The following data were collected:
Use a level of significance to determine if the proportion of defectives is the same for all three shifts.
Chi-square Tests : PLBautista

9. Chi-square Tests : PLBautista
Exercise
In a study to estimate the proportion of wives who regularly watch soap operas, it is found that 48 of 200 wives in Denver, 29 of 150 wives in Phoenix, and 35 out of 150 wives in Rochester watch at least one soap opera. Use a 0.05 level of significance to test the hypothesis that there is no difference between the true proportions of wives who watch soap operas in these three cities.
Chi-square Tests : PLBautista