It is well known the following result:

**Lemma:** Let $F\rightarrow E\rightarrow B$ be a fibration with $B$ connected and
simply connected. Suppose that $F$ is $n$-acyclic, i.e. $H^{p}\left( F;%
%TCIMACRO{\U{211a} }
%BeginExpansion
\mathbb{Q}
%EndExpansion
\right) =H^{p}\left( pt;%
%TCIMACRO{\U{211a} }
%BeginExpansion
\mathbb{Q}
%EndExpansion
\right) $ for $p\leq n$. Then
$$
H^{p}\left( B;
\mathbb{Q}
\right) \rightarrow H^{p}\left( E;%
%TCIMACRO{\U{211a} }
%BeginExpansion
\mathbb{Q}
%EndExpansion
\right)
$$
is an isomorphism for $p\leq n$ and a monomorphism for $q=n+1$.

The converse of this lemma is true? That is, if $$ H^{p}\left( B;% %TCIMACRO{\U{211a} }% %BeginExpansion \mathbb{Q} %EndExpansion \right) \rightarrow H^{p}\left( E;% %TCIMACRO{\U{211a} } %BeginExpansion \mathbb{Q} %EndExpansion \right) $$ is an isomorphism for $p\leq n$ and a monomorphism for $q=n+1$, then $F$ is $% n$-acyclic?