1
Example 1
.Suppose that a pharmaceutical company
is concerned that the mean potency
µ
of an
antibiotic does not meet the minimum government
potency standards. They need to decide between
two possibilities:
–
The mean potency
µ
does not exceed the mean
allowable potency.
–
The mean potency
µ
exceeds the mean
allowable potency.
Chapter 8.4: Testing hypotheses about a population
mean
m
(large samples).
Example 2
. In trying a person for a crime, the jury
needs to decide between one of two possibilities:
–
The person is guilty.
–
The person is innocent.
• To begin with, the person is assumed innocent.
• The prosecutor presents evidence, trying to
convince the jury to reject the original
assumption of innocence, and conclude that the
person is guilty.
Main steps in testing statistical
hypotheses.
1.Formulate the null hypothesis
and the research (alternative)
hypothesis.
The null hypothesis,
H
0
:status quo,
present state. Assumed to be true until
we can prove otherwise.
The alternative hypothesis, H
1
:
it is called
research, because it implies that some
action is to be performed. We do not
prove H
0
rather look for evidence to support
H
1.
Court trial:
Pharmaceuticals:
H
0
: innocent
H
0
:
µ
does not exceed allowed amount
H
1
: guilty
H
1
:
µ
exceeds allowed amount
Types of Hypotheses: TwoTailed Tests
•
Example 3: Is it true that the average hourly wage of construction
workers in California is different from $14, which is the national
average?
– Answering this question is equivalent to testing the hypothesis :
H
0
:
µ
=14
against H
1
:
µ≠
14
where
µ
is the average hourly wage of construction workers in
the USA.
•
This is an example of a
twotailed
test of hypotheses.
directions of H
1
µ
=14
µ>
14
µ<
14
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Types of Hypotheses: The
onetailed
test
•
Example 4:
The average duration of Alzheimer’s disease from the
onset of symptoms until death
is 8 years. A pharmaceutical
company claims to have developed a new drug which increases the
expected lifetime.
– Verifying the company’s claim would be equivalent to testing:
H
0
:
µ
=8
against H
1
:
µ
>8
where
µ
is the average duration of the disease (i.e. average time
before death).
This is an example of the
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 Spring '08
 palmero
 Null hypothesis, Statistical hypothesis testing, Type I and type II errors, pharmaceutical company, rejection region

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