Let $f:X\rightarrow Y $ be a fibration (with fiber $F$) between simply connected spaces such that 
$H_{\ast}(f):H_{\ast}(X,\mathbb{Z})\rightarrow H_{\ast}(Y,\mathbb{Z})$ is an isomorphism for $\ast\leq n$, is it true that the reduced homology of the fiber is $\tilde{H}_{\ast}(F,\mathbb{Z})=0$ for $\ast\leq n$ ?