With the binary data, I was imagining that I would turn this into a percentage, and then use the binomial distribution to create a confidence interval. The quantitative data is already in percentage form, so with it, I'm able to create a normal distribution based on a t distribution. This has the classical confidence interval form, and I was wondering if it's possible to compare this normal distribution with the data generated from the binomial distribution. If this is possible, how do I do this, especially using something like R?

I was imagining that I would be able to do some sort of 2 sample t test with this data.