Transcript Section 10.3 Making Sense of Statistical Significance

Section 12.2
Comparing Two
Proportions
AP Statistics
Our inferential work so far…

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
x 
z
 n
x 
t
s n
x1  x2
t
s12 s22

n1 n2
x  
Has been about the
distribution of sample   
x
n
means
and the distribution of  x  x  1   2
the difference of
 12  22
 x x 

sample means.
n1 n2
and the distribution of
pˆ  p
 pˆ  p
z
sample proportions
pq
1
2
1
2
 pˆ 
pq
n
n
The sampling distribution of the
difference of proportions
 pˆ  pˆ   pˆ   pˆ  p1  p2
1

2
2
pˆ1  pˆ 2
1
  
 pˆ  pˆ 
1
2
2
pˆ1
2
2
pˆ 2
p1 1  p1  p2 1  p2 


n1
n2
p1 1  p1  p2 1  p2 

n1
n2
Formula for std dev true only if independence
condition is met: pop1 >10n1 & pop 2 >10n2
The shape of the sampling
distribution of difference of
proportions
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If these conditions are
met, the sampling
distribution of
difference of
proportions is
approximately normal
n1 pˆ 1  5
n1qˆ1  5
n2 pˆ 2  5
n2 qˆ 2  5
Two proportion confidence interval
SE 
pˆ1 1  pˆ1  pˆ 2 1  pˆ 2 

n1
n2
CI   pˆ1  pˆ 2   z  SE 
*
Example
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A study investigated the effect of pre-school on
use of social services.
What is the 95% confidence interval?
Population Description
1
Control
Sample
size
61
2
Preschool
62
Sample
proportion
.803
.613
Calculate the Confidence Interval
1: Populations & Parameter of Interest
2: Procedure Name & Conditions
3: Calculations
4: Interpret
1: Population, Parameter of Interest,
H0 and Ha
3: Calculations
H 0 : p1  p2
Ha :
where
p1  p2
n1 pˆ1  n2 pˆ 2
pˆ 
n1  n2
p1  p2
p1  p2
2: Procedure Name & Conditions
z
pˆ1  pˆ 2
1 1
pˆ 1  pˆ 

n1 n2
4: Interpret
1: Population, Parameter of Interest,
H0 and Ha
2: Procedure Name & Conditions
3: Calculations
4: Interpret
Assignment
Section 12.3: 12.23-12.33 odd
 Chapter Review: 12.35-12.45 odd
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