Hypothesis Testing
Hypothesis Testing
Whenever we have a decision to make about a population characteristic, we make a hypothesis. Some
examples are:
μ
> 3
or
μ
5.
Suppose that we want to test the hypothesis that
μ
5
. Then we can think of our opponent suggesting
that
μ
= 5
. We call the opponent's hypothesis the
null hypothesis
and write:
H
0
:
μ
= 5
and our hypothesis the
alternative hypothesis
and write
H
1
:
μ
5
For the null hypothesis we always use equality
, since we are comparing
μ
with a previously determined
mean.
For the alternative hypothesis, we have the choices:
<
,
>
, or
.
Procedures in Hypothesis Testing
When we test a hypothesis we proceed as follows:
1.
Formulate the null and alternative hypothesis.
2.
Choose a level of significance.
3.
Determine the sample size. (Same as confidence intervals)
4.
Collect data.
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5.
Calculate
z
(or
t
) score.
6.
Utilize the table to determine if the
z
score falls within the acceptance region.
7.
Decide to
a.
Reject the null hypothesis and therefore accept the alternative hypothesis or
b.
Fail to reject the null hypothesis and therefore state that there is not enough
evidence to suggest the truth of the alternative hypothesis.
Errors in Hypothesis Tests
We define a
type I error
as the event of
rejecting the null hypothesis when the null hypothesis was true
.
The probability of a type I error (
α
) is called the significance level.
We define a
type II error
(with probability
β
) as the event of
failing to reject the null hypothesis when the
null hypothesis was false
.
Example
Suppose that you are a lawyer that is trying to establish that a company has been unfair to minorities with
regard to salary increases. Suppose the mean salary increase per year is
8%
.
You set the null hypothesis to be
H
0
:
μ
= .08
H
1
:
μ
< .08
Q.
What is a type I error?
A.
We put sanctions on the company, when they were not being discriminatory.
Q.
What is a type II error?
A.
We allow the company to go about its discriminatory ways.
Note:
Larger
α
results in a smaller
β
, and smaller
α
results in a larger
β
.
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 Spring '10
 Driscoll
 Statistics, Null hypothesis, Statistical hypothesis testing

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