Chapter 7
Inference for Distributions
Chapter 7
1
Introduction
•
Our study of Exploratory Data Analysis
proceeded in two steps:
•
Graphical techniques and numerical summaries for the
distribution of a single variable (Chapter 1)
•
Graphical techniques and numerical summaries for the
relationship between two variables (Chapter 2)
•
Our study of Statistical Inference will proceed in a
similar fashion.
•
Inference for parameters of a single distribution.
•
Inference for parameters describing the relationship
between two variables.
•
Inference for the comparison of parameters for two or
more distributions.
Chapter 7
2
Inference in Practice
•
In Chapter 6, we introduced confidence intervals
and tests of significance.
•
Our procedures used the onesample
z
statistic.
•
We made the somewhat unrealistic assumption that
σ
was known.
•
Chapter 7 emphasizes some of the most common
tools for statistical inference.
Chapter 7
3
Section 7.1
Inference for the Mean of a Population
Section 7.1
4
Introduction
•
Confidence intervals for the population mean
μ
are centered on the sample mean
¯
x
.
•
Test statistics for significance tests also use
¯
x
.
•
The sampling distribution of
¯
x
is known when the
population standard deviation
σ
is known.
•
In practice, we must also estimate
σ
, even though
we are primarily interested in
μ
.
•
We can estimate
σ
using the sample standard
deviation
s
.
Section 7.1
5
Sampling Distribution of
¯
x
•
Suppose we have a simple random sample (SRS)
from a population that has a Normal distribution
with mean
μ
and standard deviation
σ
.
•
The sample mean
¯
x
has distribution
N
μ
,
σ
√
n
Section 7.1
6
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Estimating
σ
•
When
σ
is unknown, we estimate it with the
sample standard deviation
s
.
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 Spring '08
 ABBEY
 Statistics, Normal Distribution, Standard Deviation, standard normal distribution

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