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Lecture Notes
Chapter Seven: Inferences Based on a Single Sample: Estimation with Confidence Intervals
Randall Miller
1 
Page
1.
Identifying the Target Parameter
Definition 7.1
The unknown population parameter (e.g., mean or proportion) that we are interested in estimating
is called the
target parameter
.
Determining the Target Parameter
Parameter
Key Words or Phrases
Type of Data
µ
Mean; average
Quantitative
p
Proportion; percentage; fraction; rate
Qualitative
2.
LargeSample Confidence Interval for a Population Mean
Definition 7.2
An
interval estimator
(or
confidence interval
) is a formula that tells us how to use sample data
to calculate an interval that estimates a population parameter.
Definition 7.3
The
confidence interval
is the probability that an interval estimator encloses the population
parameter – that is, the relative frequency with which the interval estimator encloses the
population parameter when the estimator is used repeatedly a very large number of times.
The
confidence level
is the confidence coefficient expressed as a percentage.
Definition 7.4
The value
z
α
is defined as the value of the standard normal random variable
z
such that the area
will lie to its right.
In other words,
( )
Pz z
>=
.
Commonly Used Values of
/2
z
Confidence Level
( )
100 1
−
z
90%
0.10
0.05
1.645
95%
0.05 0.025
1.96
99%
0.01 0.005
2.575
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View Full DocumentLecture Notes
Chapter Seven: Inferences Based on a Single Sample: Estimation with Confidence Intervals
Randall Miller
2 
Page
LargeSample
( )
α
100 1
%
Confidence Interval for
µ
The largesample
( )
100 1
%
α
−
confidence interval for
is
/2
x
xz
n
αα
σ
±=
±
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 Fall '08
 STAFF
 Statistics

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