Hypothesis Tests for
μ
 Unknown
σ
In the last section, we learned how to perform hypothesis tests for the popu
lation mean when the population standard deviation is a known value. Now,
we show how to perform hypothesis tests when the population standard de
viation is not known.
•
We use the sample standard deviation
s
to estimate the population stan
dard deviation
σ
.
•
The test statistic is now
t
=
¯
x

μ
0
s/
√
n
•
The distribution of the test statistic now follows a
t
distribution with
(
n

1) degrees of freedom.
•
The procedure is the same as the procedure for the known
σ
case, but
p
values and critical values are computed using the
t
distribution with
(
n

1) degrees of freedom.
1
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OneTailed Test
Example
: The Employment and Training Administration reported the U.S.
mean unemployment insurance benefit of $238 per week.
A researcher in
the state of Virginia anticipated that sample data would show evidence that
the mean weekly unemployment insurance benefit in Virginia was below the
national level.
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 Fall '10
 Jager,AbigailL
 Statistics, Normal Distribution, Standard Deviation, unemployment insurance

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