STAT 400
Homework #9
Fall 2011
( due Friday, November 4, by 3:00 p.m. )
1.
A store sells "16ounce" boxes of
Captain Crisp
cereal.
A random sample of 9 boxes
was taken and weighed.
The results were the following (in ounces):
15.5
16.2
16.1
15.8
15.6
16.0
15.8
15.9
16.2
Assume the weight of cereal in a box is normally distributed.
a)
Compute the sample mean
x
and
the sample standard deviation
s
.
9
1
.
143
=
=
∑
n
x
x
i
=
15.9
.
( )
( )
8
5
.
0
8
9
1
.
143
79
.
2275
1
2
2
2
2
=
=
=



∑
∑
n
n
x
x
s
i
i
=
0.0625.
OR
1
)
(
2
2


∑
=
n
x
x
s
i
=
8
5
.
0
=
0.0625.
0625
.
0
2
=
=
s
s
=
0.25
.
b)
Construct a 95% confidence interval for the overall average weight of boxes of
Captain Crisp
cereal.
σ
is unknown.
n
= 9  small.
The confidence interval :
X
t
s
±
α
2
n
.
α
= 0.05
α
2
=
0.025
.
number of degrees of freedom =
n

1 = 9

1 =
8.
t
α
2
=
2.306.
9
25
.
0
306
.
2
9
.
15
⋅
±
15.9
±
0.192
( 15.708 , 16.092 )
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Construct a 95% confidence upper bound for the overall average weight of boxes of
Captain Crisp
cereal.
+
n
s
t
X
,
0
α
8 degrees of freedom
t
0.05
=
1.860.
+
⋅
9
25
.
0
1.860
15.9
,
0
( 0 , 16.055 )
d)
Construct a 90% confidence lower bound for the overall average weight of boxes of
Captain Crisp
cereal.

∞
,
X
s
t
n
8 degrees of freedom
t
0.10
=
1.397.

∞
⋅
,
9
25
.
0
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 Spring '08
 Kim
 Statistics, Probability

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