# how to present results for two group success rate with confidence interval

I have two groups A and B, and for each data point I have two possible outcomes, success and failures. For each group, I have calculated the success rate, and the confidence interval for a binomial proportion. For example:

A: success rate is 27% (interval +- 5) B: success rate is 42% (interval +- 4)

I have also used the Fisher exact t-test to calculate the p-value and make sure the results are significant. My question is the following, how do I present these results? Can I say that there is a 15% improvement in success rate? with what confidence interval? what is the p-value? what else can I tell about my experiment? Thank you.

When comparing the means of two independent populations with different variance, assuming the sample is big enough (so we can use central limit theorem), the confidence interval for $$u_X - u_Y$$ is given by: