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error α
n
n
1
2 p( −p) p( −p)
interval
11
1
21
2
d±z 2
+
α
estimate
n
n
1
2 Example Given these samples, what is the
interval estimate for the difference in
awareness of the product? Hypothesis Tests Market Research(1  p1 ) p2 (1  p2 )
p1
Difference Between 2
d is conducting +
Associates ± za 2
n1
n2
Population Proportions
research to evaluate the
effectiveness pBeforeclient’s new pAfter (1  pAfter )
of a (1  pBefore )
D = p1 – p2
parameter
= d ± za
+
advertising2campaign. A
n Before
n After
survey conducted
point
d = pAfter  pBefore = 0.08
immediately after the.4 (1  .4 ) .48(1  .48)stimator
new
e
=  0 08 ± 1.96
campaign .showed 120 150 of +
out
250 standard
p( −p) p ( −p )
11
1
21
2
250 households “aware” of
σ=
+
=  0.08 ± 0.0999
error d
n
n
1
2
the client’s product.
0.1799 £ D £ 0
Before the new campaign.0199
p( −p) p ( −p )
margin of
11
1
21
2
began, a telephone survey 0.02
 0.18 £ D £ of
z2
+
error α
n
n
1
2
150Hence, the 95% confidence interval for
households in the test
market difference in before and after
p( −p) p( −p)
interval...
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 Spring '13

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