Math 2311
Class Notes for Section 8.1
8.1  Inference for the Mean of a Population
In chapter 7, we discussed one type of inference about a population – the confidence interval.
In this
chapter we will begin discussion the
significance test
.
H
0
:
is the
null hypothesis.
The
null hypothesis
states that there is no effect or change in the
population.
It is the statement being tested in a test of significance.
H
a
:
is the
alternate hypothesis
.
The
alternative hypothesis
describes the effect we suspect is true, in
other words, it is the alternative to the “no effect” of the null hypothesis.
Since there are only two hypotheses, there are only two possible decisions:
reject the null hypothesis in
favor of the alternative
or
don’t reject the null hypothesis
.
We will never say that we accept the null
hypothesis.
For inference about a population mean:
0
0
:
H
μ
μ
=
where
0
μ
represents the given population mean.
Alternate Hypothesis
Rejection Region
0
:
a
H
μ
μ
<
0
:
a
H
μ
μ
>
0
:
a
H
μ
μ
≠
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The probability, computed assuming that the null hypothesis is true, that the test statistic would take a
value as extreme or more extreme than that actually observed is called the
p
value
of the test.
A result
with a small
p
value is called
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 Statistics, Null hypothesis, Statistical hypothesis testing, $76.42, $312.34, $325.16

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