Page 33 - Quality control of pharmaceuticals (07-PA 704)

Note: The sample size n is assumed to be 30 or more.

We have seen that, in the absence of systematic errors, the mean of a
sample of measurements, , provides us with an estimate of the true
value, μ, of the quantity we are trying to measure. However, even in
the absence of systematic errors, the individual measurements vary
due to random errors and so it is most unlikely that the mean of the
sample will be exactly equal to the true value.

For this reason it is more useful to give a range of values which is likely
to include the true value. The width of this range depends on two
factors, the precision of the individual measurements, which in turn
depends on the standard deviation of the population; and the
number of measurements in the sample.

The term ‘confidence’ implies that we can assert with a given degree of
confidence, i.e. a certain probability, that the confidence interval does
include the true value. The size of the confidence interval will
obviously depend on how certain we want to be that it includes the
true value: the greater the certainty, the greater the interval required.