CEM
834
STATISTICS
FALL
2005
IV.
Statistical Examples
A.
Hypothesis Testing
(Ftest and ttest)
The formation constant (K
c
f
) for a complex was measured by spectrophotometry
(sp) and polarography (pol) with the following results:
Spectrophotometry
Polarography
Trial
K
c
f
Trial
K
c
f
1
98
1
104
2
109
2
101
3
105
3
95
4
120
sp
x
108
pol
x
100
2
sp
s
84.7
2
pol
s
21.0
We would like to determine if the results from these two methods are statistically
equivalent.
First, we need to establish whether the variances differ significantly.
For this Ftest, the null and alternative hypotheses are as follows:
H
0
:
2
pol
2
sp
s
s
=
H
a
:
2
pol
2
sp
s
s
(onetailed Ftest)
The Fstatistic is calculated as
03
.
4
0
.
21
7
.
84
s
s
F
2
pol
2
sp
=
=
=
From the tables of the Fstatistic,
F(
α
,
ν
1
,
ν
2
)
=
F(0.05, 3, 2)
=
19.16
Since the calculated Fstatistic of 4.03 is less than the critical value of 19.16, we
accept the null hypothesis at the 95% confidence level.
Because the variances do
not differ significantly, we can use the pooled variance:
2
.
59
2
n
n
s
)
1
n
(
s
)
1
n
(
s
pol
sp
2
pol
pol
2
sp
sp
2
pooled
=

+

+

=
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View Full DocumentNext, we need to establish whether the mean values differ significantly.
For this
ttest, the null and alternative hypotheses are as follows:
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 Fall '05
 MCGUFFIN
 Statistics, Normal Distribution, Standard Deviation, Null hypothesis, 90%

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