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76 Modern Analytical Chemistry

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EXAMPLE .12
What is the 95% confidence interval for the amount of aspirin in a single
2
analgesic tablet drawn from a population where mis 250 mg and s is 25?
SOLUTION
According to Table 4.11, the 95% confidence interval for a single member of a
normally distributed population is
X i = m±1.96s= 250 mg ± (1.96)(5) = 250 mg ± 10 mg
Thus, we expect that 95% of the tablets in the population contain between 240
and 260 mg of aspirin.

Alternatively, a confidence interval can be expressed in terms of the popula-
tion’s standard deviation and the value of a single member drawn from the popu-
lation. Thus, equation 4.9 can be rewritten as a confidence interval for the popula-
tion mean

m= X i ± zs 4.10

4 3
EXAMPLE .1
The population standard deviation for the amount of aspirin in a batch of
analgesic tablets is known to be 7 mg of aspirin. A single tablet is randomly
selected, analyzed, and found to contain 245 mg of aspirin. What is the 95%
confidence interval for the population mean?
SOLUTION
The 95% confidence interval for the population mean is given as
m= X i ± zs= 245 ± (1.96)(7) = 245 mg ± 14 mg

There is, therefore, a 95% probability that the population’s mean, m, lies within
the range of 231–259 mg of aspirin.

Confidence intervals also can be reported using the mean for a sample of size n,
drawn from a population of known s. The standard deviation for the mean value,
–
s X, which also is known as the standard error of the mean, is
s
s X =
n

The confidence interval for the population’s mean, therefore, is
z s
m = X ± 4.11
n