Suppose you are conducting a two-way ANOVA with factors $E$ ($3$ levels) and $F$ ($2$ levels). Which of the following is NOT a correct null hypothesis for this test?

$H_0^E:$ The means for all levels of factor $E$ are equal.

$H_0^F:$ The means for all levels of factor $F$ are equal.

$H_0^{EF}:$ There is an interaction effect between $E$ and $F$.

$H_0^{EF}:$ There is no interaction effect between $E$ and $F$.