Analysing proportions from replicated experiments

In molecular biology experiments, we often apply a treatment or placebo to plates of cells then measure some sort of proportional variable (e.g. the number of dead cells). In the literature, I usually see this sort of proportional data analysed using a t-test to determine whether the difference in the means of the treatment and control proportions is equal to zero. Is this approach suitable? What about when the proportions lie close to zero or one? I assumed methods such as the Chi-squared or Fisher’s exact test would be more appropriate, but I’m not sure how would you incorporate information about the variability between replicates?