# Section 9 3 23 Inference on 2 Percents 1 Inference On The Difference Of Two Percents Notation πi percent of successes in popula

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```					Section 9.3                           23-Inference on 2 Percents           1

Inference On The Difference Of Two Percents

Notation

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 =
 p -p
1    2



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)
 p p                           
1   2
n1                       n2

The estimator  p  p :
ˆ        1     2

p 1 (100  p 1 ) p 2 (100  p 2 )
 p p 
ˆ                            
1   2
n1               n2
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
females."
Section 9.3       23-Inference on 2 Percents   5