Cellphone companies often boast about how much of the country they cover. But with billions of federal dollars at stake to expand mobile broadband in rural America, state officials and other groups across 37 states say those claims aren’t always true.

The challenge is proving the carriers wrong. In Vermont, that meant sending out a guy in a gray Toyota Prius to imitate the ubiquitous “can you hear me now?” question as he motored among small towns and dairy farms in search of a signal. Other states took similar steps, and their concerns have caught the attention of the Federal Communications Commission, which has begun investigating the accuracy of the carriers’ claims.