The height n Telescope Conjecture for spectra

Let $T(n)$ denote the height-$n$ telescope and $K(n)$ the height-$n$ Morava $K$-theory, with $n\geq 0$. For a spectrum $E$, write $\langle E\rangle$ for its Bousfield class.

The height $n$ Telescope Conjecture. The Bousfield class of $T(n)$ agrees with the Bousfield class of $K(n)$:

$$\langle T(n)\rangle=\langle K(n)\rangle.$$

The conjecture compares the $T(n)$-localization and $K(n)$-localization of spectra and has equivalent formulations in chromatic homotopy theory. Its status is not resolved in the supplied source.