March 19th
Example
Bayport High was chosen to participate in a new curriculum program. A year later, 86 Bayport
sophomores who participated in this program was randomly selected to take a SATI math exam. The
national average on this exam was 494 with a standard deviation of 124. The 86 students averaged a score
of 528. Can it be claimed at the
0.05
α
=
level that the new curriculum is effective? (Another question
for later, if the true mean is 514, what is the power of the test at
0.05
α
=
?)
Solution
Test on one population mean
μ
86,
528,
124, large sample
n
x
σ
=
=
=
0
0
:
494
:
494
a
H
H
μ
μ
μ
=
←
f
Test statistic :
0
0
0
(0,1)
~
H
X
Z
N
n
μ
σ

=
&
0
528
494
2.54
124
86
z

=
=
At
0
0.05
0.05, z
2.54
1.645
Z
α
=
=
=
f
Therefore, we reject
0
H
and conclude the new curriculum is effective.
pvalue
It is the probability that we observe something at least as extreme as the sample
(or test statistic)
observed, given that the null hypothesis is true.
Example.
1.
Onesided to the right
1
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0
0
0
:
:
a
H
H
μ
μ
μ
μ
=
f
Test statistic :
0
2.54
z
=
0
0
0
0
0
0
0
pvalue
(

:
)
(
2.54 
:
) (
)
P Z
z
H
p
value
P Z
H
example
μ
μ
μ
μ
=
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 Spring '08
 Zhu,W
 Statistics, Normal Distribution, Statistical hypothesis testing, Z0, new curriculum, Bayport High

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