1
STAT 2000
Chapter 7
C
fid
I t
l
Confidence Intervals
Agresti-Franklin
Identify
Objective
Question(s)
about a
population
Design Study
and
Collect Data
Select a sample
from a population
Make Inferences
The Process of a Statistical Study
Describe
Data
Organize and
present
sampledata
about a
population
Make predictions
and draw
conclusions
Principles of
Probability
As we begin to talk about Inference, let’s look back
at what we have done before, and why.
•
Gathering Data – Statistical inference methods
assume that data was collected with some type of
randomization.
•
Sampling Distributions – Probability calculations
Sampling Distributions
Probability calculations
used in inference refer to sampling distributions.
Two types of Inference
•
Estimation – Chapter 7
•
Hypothesis Testing – Chapters 8-9
A
point estimate
of a population parameter is an
estimate given by a single value.
Sample Statistics are point estimates of
Population Parameters.
Sample
Population
Statistic
Parameter
Mean
μ
Standard Deviation
s
σ
Proportion
p
x
ˆ
p
An
interval estimate
of a population parameter is
given by two values between which we expect to
have the population parameter.
(Why would we want an interval estimate instead of
a point estimate?)
Our
interval estimate
is given by
point estimate
±
margin of error
The
margin of error
is how much we expect to be
*off*.
SAMPLE: Interviews with 706
likely voters, conducted by
telephone on July 9-11, 2004.
MARGIN
OF
ERROR: ± 4%
The point estimate of the proportion that would vote
for Bush was 0.46.
The interval estimate would be 0.46 ± 0.04, and we
would write this as (0.42, 0.50).
The lower limit is 0.42, and the upper limit is 0.50.

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