Hypothesis Testing about a Populatiin Proportion,
p
Just as we conducted hypothesis tests for a
population mean,
µ
, we can conduct hypothesis tests
for a population proportion,
p
.
The three possible setups for a test of hypothesis
about p are as follows:
0
0
1
0
:
:
H
p
p
H
p
p
≥
<
0
0
1
0
:
:
H
p
p
H
p
p
≤
0
0
1
0
:
:
H
p
p
H
p
p
=
≠
Lowertailed test
uppertailed test
twotailed test
Where
0
p
denotes a hypothesized value for the
population proportion (such as 0.10, or 0.64, etc.)
When the null hypothesis is true, the distribution of
the point estimate for p is:
(
29
(
29
0
0
0
1
p
p
p
p
N
with E p
p
and
n
σ

=
=
:
.
We should, of course, check to see if
p
is
approximately normal.
To do this, we use the same
test that we used in Chapter 7.
That is, check to see
if:
0
5
np
≥
and also that
(
29
0
1
5
n
p

≥
.
If the conditions for normality are met, then the
following quantity is a standard normal, or “zscore”.
0
p
p
p
z
σ

=
.
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We can conduct our hypothesis tests for
p
using
either the pvalue approach or the critical value
approach.
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 Fall '09
 Rollins
 Statistical hypothesis testing, zcalc, brand ketchup

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