Andrea Szczepanski
Analytical Chemistry
Fall 2001
Chapter 7 Statistical Analysis: Evaluating the Data
I. Confidence Limits
A. Confidence limits define a numerical interval around x_ , experimental mean, that contains u, the mean
for a population, with a certain probability.
B. Confidence interval is the numerical magnitude of the confidence limit. It is computed from the
standard deviation and depends on how accurately we know s, the sample standard deviation,
compared to o, the population standard deviation.
In the absence of bias and assuming s, the sample standard deviation, is a good estimate of o, the
population standard deviation,
The confidence limit (CL) for a single measurement can be expressed by
CL = x+ zo
The confidence limit for N measurements can be expressed by
CL = x_ + zo
N square root
In determining the confidence levels, expressed as a percent, we can examine the normal bell curve.
INSERT 5 Bell CURVES from PAGE 150 HERE and EXPLAIN
Example 7-5 page 173
a) 90% Confidence Limit
8.53 ug Cu/mL + 1.64 X 0.32 ug Cu/mL / square root of 1 = 8.53 + 0.53ug Cu/mL
99% Confidence Limit
8.53 ug Cu/mL + 2.58 X 0.32 ug Cu/mL / square root of 1 = 8.53 + 0.80ug Cu/mL
b) 90% Confidence Limit
8.53 ug Cu/mL + 1.64 X 0.32 ug Cu/mL / square root of 4 = 8.53 + 0.26ug Cu/mL
99% Confidence Limit
8.53 ug Cu/mL + 2.58 X 0.32 ug Cu/mL / square root of 4 = 8.53 + 0.40ug Cu/mL
c) 90% Confidence Limit
8.53 ug Cu/mL + 1.64 X 0.32 ug Cu/mL / square root of 16 = 8.53 + 0.13ug Cu/mL
99% Confidence Limit
8.53 ug Cu/mL + 2.58 X 0.32 ug Cu/mL / square root of 16 = 8.53 + 0.21ug Cu/mL
