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Examples for 11/17/2011
Fall 2011
1.
A new method of storing snap beans is believed to retain more ascorbic acid than
the old method.
In an experiment, snap beans were harvested under uniform
conditions and frozen in 250 equalsize packages. One hundred of those packages
were randomly selected and stored according to the new method, and the other 150
packages were stored by the old method.
Subsequently, ascorbic acid determinations
(in mg/kg) were made, and the following summary statistics were calculated.
New Method
Old Method
(sample) mean ascorbic acid
450
410
(sample) standard deviation
20
45
a)
Construct a 95% confidence interval for the difference in the mean amount
of ascorbic acid retained.
n
1
= 100 and
n
2
= 150 are large,
t
α
/
2
can be approximated by
z
α
/
2
.
( )
2
2
2
1
2
1
2
α
Y
X
n
s
n
s
z
+
±

⋅
( )
150
45
100
20
96
.
1
410
450
2
2
+
±

⋅
40
±
8.2
(
31.8
, 48.2
)
b)
Perform the appropriate test at a 1% level of significance.
Claim:
μ
New
>
μ
Old
H
0
:
μ
New
–
μ
Old
= 0
vs.
H
1
:
μ
New
–
μ
Old
> 0
Test Statistic:
Z =
( )
( )
150
45
100
20
0
410
450
Y
X
2
2
2
2
2
1
2
1
0
s
s
δ
+


=
+


n
n
=
9.562.
n
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 Spring '08
 Kim
 Statistics, Probability

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