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STAT E50  Introduction to Statistics
Testing Hypotheses About Proportions
Hypotheses
±
The null hypothesis:
H
0
:
parameter = hypothesized value
±
The alternative hypothesis:
H
a
:
parameter = value we would accept if we reject the null hypothesis
Model
±
Specify the
model
you will use to test the null hypothesis
±
State the parameter of interest
±
List the assumptions and check the conditions
±
Name the statistical test you will use
Mechanics
±
Calculate a
test statistic
from the data
±
Obtain a
Pvalue
= the probability that the observed value of the test statistic (or
a more extreme value) could occur if the null model were correct
±
If the Pvalue is small enough, we will reject the null hypothesis
Conclusion
±
Statistical conclusion:
state whether you
reject
or
fail to reject
the null hypothesis
±
State your conclusion in context
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View Full Document Oneproportion ztest
H
0
: p = p
0
Test statistic is
0
ˆ
pp
z
ˆ
SD(p)
−
=
where
00
pq
ˆ
SD
(p)
n
=
When the conditions are met and the null hypothesis is true, this statistic
follows the standard Normal model.
Conditions:
Independence condition
Random sampling condition
10% condition
Success/failure condition
(using p
0
and q
0
)
Note:
p
0
is the value you are testing in H
0
;
q
0
= 1 
p
0
is the observed value of p
ˆ
p
Page
2
1. An
American Demographics
study conducted in 1980 found that 40% of new car
buyers were women.
Suppose that in a random sample of 120 new car buyers in 2000,
57 were women.
Does this indicate that the true proportion of new car buyers in 2000
who were women is significantly larger than the 1980 proportion?
Plan
What do we want to know?
What are the variables?
What are the W’s?
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This note was uploaded on 05/20/2008 for the course STAT 50 taught by Professor Weinstein during the Spring '08 term at Harvard.
 Spring '08
 WEINSTEIN
 Statistics

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