Chapter 22: Comparing Two
Proportions
AP Statistics
In this chapter, we take what we have
learned and apply it to comparing two
proportions and determining if there is a
difference between the two proportions
(obtained from two samples).
Assumptions and Conditions for
Two-Proportion z-interval and TwoProportion z-test
Independent Trials (Individuals
Assumption:
Random Condition
10% Condition
Independent Group Assumption:
Can be assumed by looking at the way
data was
collected
Normal Distribution Assumption:
Success/Failure Condition
Sampling Distribution Model for a
Difference Between TwoIndependent Proportions
Only, if we know population proportion
(very unlikely)
How we make our sampling
model (Normal Model)—may
need to use SE
How To Determine a TwoProportion z-Interval
When we don’t know population
proportions (likely)
Example
A magazine article surveyed 12,460 males
and 12,678 females to see if they had
finished high school (all aged 24). 84.9%
of males and 88.1 females reported “yes”.
Create a 95% confidence interval for the
difference in graduation rates between
males and females and interpret it in
context.
Example
Two-Proportion z-Test
Typically, we start off with our null
hypothesis stating that there is NO
difference between the two groups.
Remember, the null hypothesis basically
says that nothing is going on.
Two-Proportion z-Test
Our Null Hypothesis, typically looks like (but in
context for subscripts):
Pooled Data
• Since we assume that the difference in
proportions is zero, we are therefore saying that
the two proportions are assumed to be EQUAL.
• If the two proportions are assumed to be equal,
then we also assume that their standard errors
are also EQUAL.
Pooled Data
In order to calculate what that equal proportion is, we
combine the data (pool the data) to get one overall
proportion.
That pooled proportion is then used to find the
standard error,
Make sure “successes” are whole numbers.
Two-Proportion z-Test
Other Things
• When checking “Success/Failure Condition” you
should be checking four different situations.
• CHECK assumptions/conditions and NEVER
use two-proportion method if they are not
satisfied.
• Same method as with one-proportion z-test.
• Use the calculator (STAT TESTS)
• Be careful with the alternative hypothesis.
Example
Is there a difference between the proportion
of males and females who have graduated
from high school? Perform a 2-proportion
z-test. (Remember, you have already
satisfied the conditions necessary to
proceed).
Try pg 510, #20