Posted On : 10.02.2018 03:32 pm

## Chapter: __Modern Analytical Chemistry: Obtaining and Preparing Samples for Analysis__

**How Many Samples to Collect**

In the previous section we considered the amount of sample needed to minimize the sampling variance.

**How Many Samples to Collect**

In the previous
section we considered the amount of sample needed
to minimize the sampling
variance. Another important
consideration is the number of samples
required to achieve a desired
maximum sampling error. If samples
drawn from the target population are normally
distributed, then the following equation describes the confidence interval for the sampling
error

where *n*_{s} is
the number of samples and *s*_{s}
is the sampling standard deviation. Rear- ranging and substituting *e *for
the quantity (Î¼â€“ *X**â€“*), gives the
number of samples as

7.7

where *s*_{s}2 and *e*2 are both expressed as absolute uncertainties or as relative uncertain- ties. Finding a solution to equation 7.7
is complicated by the fact
that the value
of *t *depends on *n*_{s}. As shown in Example 7.8, equation 7.7 is solved
iteratively.

This is not an uncommon
problem. For a target population with a relative
sampling variance of 50 and a desired relative
sampling error of Â±5%, equation
7.7 predicts that ten
samples are sufficient. In a simulation in which 1000
samples of size
10 were collected, however,
only 57% of the samples
resulted in sampling
errors of less than Â±5%. By increasing the
number of samples
to 17 it was possible to ensure that the desired sampling error
was achieved 95% of the time.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Modern Analytical Chemistry: Obtaining and Preparing Samples for Analysis : How Many Samples to Collect |