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Using OC Curve to Determine
Sample Size
Example 4.51, p 255
. Standard pro
duction setup. Average time
μ
= 30
minutes to complete task. Assume
X
∼
N
(30
,
1)
.
Change suggested. New
X
∼
N
(
μ,
1) where hoped
μ <
30
.
Sample
size
n
workers to test
H
0
:
μ
= 30
H
1
:
μ <
30
1
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. The rejection (or critical
region) CR is the set of data values for
which
H
0
is rejected.
Natural choice for this problem is the
region:
If
c
too small, then tend not to reject
and have
large
Type II error probability.
If
c
too large, then tend to reject and
have
large
Type I error probability.
2
. CR =
{
¯
x
≤
29
.
5
}
,n
= 4
.
OC
(
μ
) =
P
(accept
H
0

μ
)
=
P
(
¯
X >
29
.
5

μ
)
=
P
(
¯
X

μ
1
/
√
n
>
29
.
5

μ
1
/
2

μ
)
=
P
(
Z >
29
.
5

μ
1
/
2
)
= 1

Φ(
29
.
5

μ
1
/
2
)
Selected values:
μ
28.5
29
29.5
30
OC
(
μ
)
0.0228
0.1587
0.500
0.8413
Read oﬀ table:
Type I error probability is 10.8413 = 0.1587.
Type II error probability at
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This note was uploaded on 01/03/2012 for the course EE 1244 taught by Professor Drera during the Fall '10 term at Conestoga.
 Fall '10
 drera

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