GLM mixed model with quasibinomial family

Dear R-users,

I am using the 'lmer' function from package 'lme4', looking for a
regression model which takes into account the grouped nature of my
data. I am using frequencies as the dependent variable and percentages
as the independent one. After some reading I think I should use the
'quasibinomial' family because there is 'overdispersion' in my data
set (greater residual deviance than residual degrees of freedom). So,
I test this regression model but I do not get a significance p-value
for the regression! I have to test many different regressions with
different data, so how can I assess the significance of each of of
them?

Thank you very much for your help!

Javier