The finite detection conjecture for the Brown–Comenetz dual of the sphere

Let $I$ be the Brown–Comenetz dual of the sphere, and let $F(n)$ denote a finite spectrum of type $n$.

Finite detection conjecture for I. If $E\wedge I\neq 0$, then

$$\langle E\rangle\geq\langle F(n)\rangle$$

for some $n$.

The source attributes this conjecture to Hovey and Strickland and notes that its converse is immediate from an earlier lemma. No resolution is given.