Asymptotic tests for interval-valued means

•Asymptotic tests are developed for the means of interval-valued populations.•The limiting null distributions are derived in analytical form.•Large sample tests can be performed by numerical integration of Bessel function.

We develop asymptotic tests for the means of interval-valued population. The problem is formulated and studied in the framework of random compact convex sets. Under both one-sample and two-sample settings, we derive analytical forms of the probability density functions for the limiting null distributions. Large sample testing rules are given based on numerical integration of the Bessel function.