Solution for ST516 HW2
2.11.
The breaking strength of a fiber is required to be at least 150 psi. Past experience has indicated
that the standard deviation of breaking strength is
σ
= 3 psi. A random sample of four specimens is
tested.
The results are
y
1
=145,
y
2
=153,
y
3
=150 and
y
4
=147.
(a)
State the hypotheses that you think should be tested in this experiment.
H
0
:
µ
= 150
H
1
:
µ
> 150
(b) Test these hypotheses using
α
= 0.05.
What are your conclusions?
n
= 4,
σ
= 3,
y
= 1/4
(145 + 153 + 150 + 147) = 148.75
148.75
150
1.25
0.8333
3
3
2
4
o
o
y
z
n
µ
σ
−
−
−
=
=
=
= −
Since
z
0.05
= 1.645, do not reject.
(c) Find the
P
-value for the test in part (b).
From the
z-
table:
(
)(
)
1
{1
0.7967
2 3
0.7995
0.7967
}
0.7986
P
≅
−
−
+
−
=
(d) Construct a 95 percent confidence interval on the mean breaking strength.
The 95% confidence interval is
(
)
(
)
(
)
(
)
2
3
96
.
1
75
.
148
2
3
96
.
1
75
.
148
2
2
+
≤
≤
−
+
≤
≤
−
µ
σ
µ
σ
α
α
n
z
y
n
z
y

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