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Hypothesis Testing  I
• Recall that we have an estimator,
Y
, of
μ
Y
.
• While this estimator is
unbiased
and
consistent
,
Y
will generally not be exactly
equal to
μ
Y
.
This is because we only used a
sample of size
n
.
Our sample may have
somewhat high
Y
i
’s (in which case
Y
will be
greater than
μ
Y
) or somewhat low
Y
i
’s (in
which case
Y
will be less than
μ
Y
)
Hypothesis Testing  II
• Suppose we want to formally "test” whether
μ
Y
equals a specific number, e.g. we want to test the
hypothesis that the mean wage in the US is 80
(thousand dollars), i.e. whether
μ
Y
=80.
• Suppose that you collect a random sample, and
suppose that
Y
= 84 (thousand dollars).
Should you
“reject” your hypothesis?
• The problem is that even if
μ
Y
does actually equal
80, it is possible that
Y
might equal 84 due to the
randomness in the sample.
Hypothesis Testing  III
• Hypothesis testing takes this possibility into
account and tells us whether, based on statistical
evidence, we should “reject” our hypothesis.
• Caveat: Hypothesis testing is still not 100%.
Due
to randomness in the sample, there is always the
possibility that we will come to the wrong
conclusion.
However, we can measure and
control this possibility and try to make it small.
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View Full DocumentHypothesis Testing  IV
• To formally do a hypothesis test, we set up
the test in terms of a “null hypothesis” (H
0
)
and an “alternative hypothesis” (H
A
)
• In our example, the test is:
H
0
:
μ
Y
= 80
vs.
H
A
:
μ
Y
≠
80
Hypothesis Testing  V
• There are two possible statistical conclusions of this
hypothesis test:
– 1) “Reject H
0
”
– 2) “Don’t reject H
0
”
• If we “Reject H
0
”, we are saying that there is statistical
evidence that H
0
is false and that H
A
is true.
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 Spring '07
 SandraBlack
 Econometrics

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