I'm hoping someone can give me a push in the right direction here. I think I have answered the first part of this question, but now I am stuck on the last part.

53 percent adults call themselves middle class. sample size n=2413. How confident am I that between 51 and 55 percent of Americans call themselves middle class? How likely is it that more than 55 percent call themselves middle class?

I calculated plus four estimate of confidence interval and estimated with 90% confidence that between 51 and 55 percent of Americans call themselves middle class. I also calculated the sample size needed for the margin of error (1.67 percent), which turned out to be larger than the given sample size.

I am now at the question of the likelihood that more than 55 percent call themselves middle class. How would I solve this? I thought perhaps by testing hypotheses: Ho: p = 55, Ha: p > 55, but I don't know how to begin.

Thank you.