1. COMPARING TWO PROPORTIONS
AP STATISTICS LESSON
COMPARING TWO PROPORTIONS

2. Confidence intervals for Comparing Two Proportions
Draw an SRS of size n from a population having proportion p of successes and draw an independent SRS of size n from another population having proportion p of successes. When n and n are large, an approximate level C confidence interval for
p1 – p2 is (p1 – p2) ± z* SE
In this formula the standard error (SE) of
p1 – p2 is
SE = √p 1(1 – p1)/n1 + p 2(1 – p2)/n2 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

3. Confidence Interval (continued…)
And z* is the upper (1 – C)/2 standard normal critical value.
Conditions: In practice, use this confidence interval when the populations are at least 10 times as large as the samples and
n 1p1, n 1(1 – p1), n2 p2 and n 2(1 – p2) are all 5 or more. ^ ^ ^ ^

4. Example 12.11 Page 704 How Much Does Preschool Help?
Population
Population Description
Sample Size
Sample Proportion 1
Control
N1 = 61
P1 = 0.803 2
Preschool
N2 = 62
P2 = 0.613 ^ ^
We are 95% confident that the percent needing social services is somewhere between 3.3% and 34.7% lower among people who attended preschool. The confidence interval is wide because the samples are quite small.