Is the $15 to $30 the price for the #1 spot? Adsense uses smart pricing which is a method of determining how relevant and important your site is in the eyes of google. A new site for such a high paying keyword is going to be sandboxed, so it isn't going to rank well for a period of at least 3 months - and possibly up to a year. To be considered an authority site, you will probably find extreme competition for the keyword (depending on how many searches are done for the keyword).
You will probably be competing against authority sites that can spend in a lot of money on
SEO. Some keywords (like mortgage related sites) can spend over $100,000 a year for a top ranking. I have some sites for sectors where the top position is more than you mentioned and they pay in the $1 to $2 a click. I think there are a lot of adsense publishers who would be happy to average 50 to 75 cents a click. Clicks in the dollar range would be considered on the high side for most keywords in my experience. Without knowing the keyword, it's impossible to say, but a click might pay 50 cents up to several dollars.
To get clicks on competitive keywords that pay in dollars you should be prepared to spend a considerable amount of time to rank well with google. Some keywords are so competitive is can be a near impossible task without a large budget. It can be done, but it's not something that you should expect for some time. I would also check to see what the #10 position would cost to get a better idea of the potential. Also check to see how many people are competing for the word and what the
PR of the top rankings sites are, and how many backlinks google shows for their site.