Is a sea urchin a arthropod?

No. Sea urchins are echinoderms, meaning, appropriately enough, "spiny skin". Some of the characteristics of arthropods are jointed appendages, an exoskeleton, and a segmented body. While the hard test, or shell, of sea urchins could be thought of as an exoskeleton, sea urchins have no jointed appendages and do not have a segmented body.

Some examples of arthropods are shrimps, crabs, lobsters, and insects.