  The comparison of multivariate population means is a central task of
statistical inference. While statistical theory provides a variety of analysis
tools, they usually do not protect individuals' privacy. This knowledge can
create incentives for participants in a study to conceal their true data
(especially for outliers), which might result in a distorted analysis. In this
paper we address this problem by developing a hypothesis test for multivariate
mean comparisons that guarantees differential privacy to users. The test
statistic is based on the popular Hotelling's $t^2$-statistic, which has a
natural interpretation in terms of the Mahalanobis distance. In order to
control the type-1-error, we present a bootstrap algorithm under differential
privacy that provably yields a reliable test decision. In an empirical study we
demonstrate the applicability of this approach.
