I have two samples of documents where one sample contains documents of a certain category and another sample contains documents of another category. I am analysing the occurrence of a certain word in the documents.
I want to do an hypothesis test to check if the proportions of this word is the same in both populations or not. I know the sample sizes (200,40) and I know the proportions but I do not know the variances of the population.
The basic method is to assume that the difference of proportions is normal and to calculate a z-score for the difference of proportions. Is it correct even if I do not know the variances?
The reason why I am asking this question is that if I am comparing the means of two different samples with different means and I do not know the variances, I should use t-test and take into consideration that I do not know the variances.
Is there a corresponding t-test for significance in the proportions in the population?