comparing two independent binomial data sets, unequal size, Welchs t-test?

I would like to compare the pass rates of two different classes (say English 111 and English 113). The data is binomial (0= fail, 1=pass). The sets are unequal size. I think its safe to assume independent population means and unknown SD. I am inclined to use Welch's t - test. But I am not sure if it works for binomial data.

If Welch's can't be used with binomial data, can you provide a suggestion?

I did search the forums for information on Welch's t-test, but did not see this question come up.

Thank you in advance.
I don't have a good reason. I was concerned about the binomial data so I was searching with that being the key word, but I must have overcomplicated the issue. I just looked up the assumptions of the two-sample proportions test and they seem reasonable (see below, am I missing assumptions?). I know that any time I pick a certain test, I need to check that the assumptions are met, but with these assumptions I don't really need to check anything, right? Either the data meets these criteria or it doesn't. Also, is the correct R command prop.test? Why would one use Welch's t- test? Is it because the two sample proportions test is perfect for binomial data, so we really don't to go to Welch's (Which would be better suited for continuous data?)

Thank you again.

The sampling method for each population is simple random sampling.
The samples are independent.
Each sample includes at least 10 successes and 10 failures.
Each population is at least 20 times as big as its sample.


TS Contributor
this seems to fit the bill for the two samples proportion test perfectly and afaik prop.test is the right function. I would say that the argument against the Welch test is that it is simply not the right test for this situation:)