Section 9.3 23-Inference on 2 Percents 1
Inference On The Difference Of Two Percents
πi = percent of successes in population i
pi = percent of successes in sample i
1. The two samples are taken from two independent populations.
2. The samples taken from each population are large. For each
sample np > 500 and n(100-p) > 500. This reduces to having a
minimum of five successes and five failures in each sample.
( p1 - p 2 )
Test statistic: z =
Confidence interval (1 - 2): (p1 - p2) ± z/2 p p 1 2
The standard error of the difference between percentages:
1(100 1) 2(100 2)
The estimator p p :
ˆ 1 2
p 1 (100 p 1 ) p 2 (100 p 2 )
Section 9.3 23-Inference on 2 Percents 2
Ex: Grady Gallagher was "interested in the difference in the
percent of deaths of chicks. I am interested in the difference of the
death rate for the chicks on a feed called Cage Crumbles compared
to the death rate of chicks that are on a feed called Chick Starter."
In a sample of 50 chicks feed Cage Crumbles, 15 died; of 50
chicks feed Chick Starter, 6 perished.
Stat>Basic Statistics>2 Proportions
Section 9.3 23-Inference on 2 Percents 3
Section 9.3 23-Inference on 2 Percents 4
Ex Danny Lessley "obtained my data from asking 60 people on
campus between the ages of eighteen and twenty-two if they were
a smoker of cigarettes or not. When I say regular smoker I mean at
least three cigarettes a day. I sampled thirty males and thirty
Section 9.3 23-Inference on 2 Percents 5
Read pp.412-416, STR 9.3 #5,8,9,16,17,22,23