Making sense of confidence intervals

It is important that you can construct confidence intervals accurately and quickly, but it is also important that you know exactly what they are telling you - and what the 'confidence' really is.

In practical terms there are situations in which the variation in the population is known even though the mean is not. Although this seems curious or even perverse, it happens for instance in production lines where the quality of the tools and materials determine how consistent the output is.

In such cases i.e. in which you already know the standard deviation, then you can use the Normal distribution directly. This also applies when the sample size is large enough to assume that your estimate of the standard deviation is good. This is the case you meet first in A-level Statistics, and is the only one covered in some specifications.

However, if the standard deviation is not known then you have to take account of the extra uncertainty introduced by having to estimate it from the sample data. This requires the use of the Student's t distribution, and is typical of examples arising in applied statistics contexts.

	Normal distribution only: run simulation worksheet
	t distribution as well as Normal: run simulation worksheet