What is the difference between confidence intervals and precision?

Question

I'm studying to be an auditor (CIA exam), but I do not have a statistics background and I'm very confused regarding the difference between confidence intervals and precision, then how they relate to confidence level. I know that as a confidence level is increased (eg: 90% to 95%), the confidence interval widens. In my exam material, it states, "in terms of a stated confidence level, precision is the range into which an estimate of population characteristic is expected to fall. Based on a random sample, it is estimated that 4%, plus or minus 2%, of a firm's invoices contain errors. The plus or minus 2% is the estimate's precision". This sounds almost exactly like what a confidence interval is to me, yet the terms are used separately and seem to have different relationships with the confidence level, "when a confidence level is changed from 95% to 99% and no change in sample standard deviation takes place, the sample size would be larger but achieved precision would not change".

Thank you so much!

Answer 1

Precision is usually referred to as the reciprocal of variance. There is another definition which treats it as the standard error of an estimate. Confidence intervals are different. They provide a statistical interval that in repeated sampling the true parameter will fall in the interval !-$\alpha$% of the time where 1-$\alpha$ is the confidence level.

Answer 2

I was struggling with that notion also because from the many resources I read, it seems that there are different interpretations of:

• the precision (i.e. the width of a CI or, in other words, the degree of random error associated with it) and
• the accuracy (i.e. whether the CI includes the population parameter that is determined by the selected level of confidence)