I am regularly use confidence intervals (CI) of the mean and more than comfortable with using them. However, in one particular analysis I am more interested in CI of the sum rather than the CI of the mean.
For example, let's say we have a dataset of elements between 1 and 9, where n=100. This gives a mean of 5.3 and a sum of 530. Is it possible to identify the CI for the sum?
The assumption in this question is that the sum is not fixed and, hence, has some degree of variance. So far my search has come up with nothing. The best approach seems to use a bootstrapping method.