AMS 315
Data Analysis
Chapter Five Study Guide
Inferences about Population Central Values
Fall 2010
Context
The one sample tests discussed here are a basic tool of statistical analysis.
Student’s work developing a practical onesample test is the foundation of applied
statistics. The material of this chapter should be familiar to you from your prerequisite
class.
Chapter Five
5.1. Introduction
This section is introductory. You should review the discussion of the vocabulary of
testing a hypothesis.
5.2. Estimation of
μ
This section specifies the one sample confidence interval for
. The formula on page
229 is fundamental, and the values in Table 5.2 are commonly called for in statistics
examinations.
5.3. Choosing the sample size for estimating
This section gives the solution to the problem of how large the sample size n should be so
that the width of the confidence interval for
meets a specification. Note the formulaa
on page 231. This has great application in opinion sampling. A Bernoulli trail is the
correct random variable to use for an opinion survey. The random variable
i
Y
takes the
value 1 if respondent
i
meets a criterion (for example, supports candidate A in an
upcoming election) and is 0 otherwise. Then,
p
Y
E
i
=
)
(
, where
p
is the fraction in the
population meeting the criterion, and
25
.
0
)
1
(
)
var(
≤

=
p
p
Y
i
. The estimate of
p
based
on a random sample of size
n
is
n
n
i
i
Y
n
Y
p
=
=
∑
=
1
ˆ
. Now,
.
25
.
0
)
1
(
)
var(
n
n
p
p
Y
n
≤

=
Then, a
random sample of size
2
2
2
/
)
(
25
.
0
E
z
n
α
≥
will have a confidence interval of halfwidth
E
or
less.
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View Full Document5.4. A statistical test for
μ
This section contains the specification of the one sample test of the null hypothesis
=
)
(
:
0
Y
E
H
when the
)
var(
Y
is explicitly stated in an examination problem. It also
contains further basic vocabulary about testing hypotheses. There will be examination
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 Fall '08
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 Normal Distribution, Discrete probability distribution, binomial Review

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