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 (μ– *X**–*), gives the
number of samples as

7.7

where *s _{s}*2 and

This is not an uncommon
problem. For a target population with a relative
sampling variance of 50 and a desired relative
sampling error of ±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 ±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.

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