Fixed effects vs Random Effects Panel data

[vad1234]

Having conducted both fixed and random effects regressions, I get significant p values at the 5% level for my coefficients under fe, but very insignificant p values under re. Is that possible or have I conducted one/both of the tests incorrectly? For the record conducting a Hausman test led to it saying the fe model was more appropriate to my data set.
Therefore can I just ignore the insignificant outcomes from the re model?
I am using Eviews 7 if that helps.