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Hypothesis Testing
•
basic ingredients of a hypothesis test are
1. the
null hypothesis
, denoted
H
o
2. the
alternative hypothesis
, denoted
H
a
3. the
test statistic
4. the
the data
5. the
conclusion
•
the hypotheses are usually statements about the values of one or more
unknown parameters, denoted
θ
here
•
the null hypothesis is usually a more restrictive statement than the alter
native hypothesis,
e.g.
H
o
:
θ
=
θ
o
,
H
a
:
θ
6
=
θ
o
•
the burden of proof is on the alternative hypothesis
•
we will continue to believe in the null hypothesis unless there is very strong
evidence in the data to refute it
•
the test statistic measures agreement of the data with the null hypothesis
–
a reasonable combination of the data and the hypothesized value of
the parameter
–
gets bigger when the data agrees less with the null hypothesis
•
when
ˆ
θ
is an estimator for
θ
with standard error
s
ˆ
θ
, a common test statistic
has the form
z
=
ˆ
θ

θ
o
s
ˆ
θ
•
when the data agrees perfectly with the null hypothesis,
z
= 0
•
when the estimated and hypothesized values for
θ
become farther apart,
z
increases in magnitude
•
there are two closely related approaches to testing
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 Spring '12
 daniel

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