Test of a hypothesis
I
A sewer pipe manufacturer claim that, on average their
pipes have breaking strength beyond 2,400 pounds.
Suppose you have a dataset consisting 50 measurements,
namely the breaking strength measured on 50 sections of
a sewer pipe the company produced. Can you test the
claim in a ‘convincing’ way?
I
Null hypothesis:
H
0
:
μ
≤
2
,
400, where
μ
is the mean
breaking strength of the sewer pipe the company can
produce.
I
Alternative hypothesis:
H
a
:
μ >
2
,
400.
I
Does the data show convincing evidence to reject
H
0
in
favor of
H
a
.
I
From the actual data
y
, ¯
y
= 2
,
460 pounds per linear
foot, and
s
= 200 pounds per linear foot.
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I
For the zvalue of that particular dataset, if we are
comparing it with the value 1.645, and decide to reject
H
0
whenever the sample
z
value exceeding 1.645. This is
called a level
α
test, and the
α
is given by .05. Another
interpretation for this value is the type I error probability.
Why? remember we are using the rejection region
(1
.
645
,
+
∞
); if the null is indeed true, we may still have
α
probability of seeing
z
values in that region. Since we
have decided that’s the rejection region, then can you
ﬁgure out the implication?
I
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 Spring '10
 Zhao
 Null hypothesis, Statistical hypothesis testing, Type I and type II errors, Virginia elementary school

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