Chemistry 5
January 30, 2008
Lecture 3
Reading Assignment:
Chapters 9-11
Statistical Analysis of Data II
a)
Confidence interval: the idea and examples
•
with 95% confidence:
1.96
i
x
μ
σ
=
±
1.96
(
)
x N
N
σ
μ
=
±
•
if the population standard deviation
σ
is not known:
(
)
t s
x N
N
μ
=
±
where Student's
t
parameter depends on the selection of
the confidence level and degrees of freedom (N-1)
b)
To assess accuracy of a technique, we can compare an experimental
mean with a known
μ:
if
μ
lies outside the confidence interval of the
mean
(
)
ts
x N
N
±
, or
1.96
(
)
x N
N
σ
±
, we can say with the chosen
certainty that the mean is significantly different than the true value.
If
μ
lies inside the confidence interval of the mean
we cannot say that
the technique is inaccurate
.
(Clearly in the latter case it would be
wrong to say with that level of certainty that the technique is accurate.
These statements can only refer to the difference between μ and

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