  Confidence intervals for the population mean of normally distributed data are
some of the most standard statistical outputs one might want from a database.
In this work we give practical differentially private algorithms for this task.
We provide five algorithms and then compare them to each other and to prior
work. We give concrete, experimental analysis of their accuracy and find that
our algorithms provide much more accurate confidence intervals than prior work.
For example, in one setting (with {\epsilon} = 0.1 and n = 2782) our algorithm
yields an interval that is only 1/15th the size of the standard set by prior
work.
