1. Large Sample
Confidence Interval
for a Difference
Between two proportions

2. Difference Between Two Sample Proportions (p1 –p2)
Estimation Requirements:
The following conditions must be met in order to construct a CI for a difference
between sample means
1. both samples are simple random samples
2. samples are independent (one event doesn’t affect the probability of
another)
3. each sample includes at least 10 successes and 10 failures
( np > 10 AND nq > 10) where q=1-p
How to find CI for a proportion:
(method same as described before)
1. sample statistic (use sample proportion (p1- p2) to estimate population
proportion (P1- P2))
2. CL (90%, 95%, 99%)
3. ME= CV x SD or ME= CV x SE
4. Specify CI: sample statistic + ME
written as: (Sample Stat – ME, Sample Stat + ME)

3. Variability of the Difference Between Proportions
• Variability means that we must compute the SE of sampling distribution in order to
construct the CI
• When population parameters (P1- P2) are unknown, SD of sampling distribution cannot
be calculated. When this happens, calculate the Standard Error. When each population
size is at least 10 times greater than the samples size, then the SE can be approximated:
p1= sample proportion of sample 1
p2= sample proportion of sample 2
n1= sample size of sample 1
n2= sample size of sample 2
** this is found on the table under two-sample , difference between proportions