  We show that the $k$th order statistic from a heterogeneous sample of $n\geq
k$ exponential random variables is larger than that from a homogeneous
exponential sample in the sense of star ordering, as conjectured by Xu and
Balakrishnan (2012). As a consequence, we establish hazard rate ordering for
order statistics between heterogeneous and homogeneous exponential samples,
resolving an open problem of P\v{a}lt\v{a}nea (2008). Extensions to general
spacings are also presented.
