You were presented with the option to finance a home for 15 years or 20 years. Would you expect to have the same interest rate on either mortgage or would one of them have a lower interest rate?

When considering mortgage rates, there is no reason to rely on intuition or expectations when one can easily do research to discover what the actual rates are. Currently, as of June 2018, a fixed rate mortgage with a 15-year term has a lower interest rate than a 20-year mortgage, with 30-year mortgages having even higher rates than both of the shorter-term options. As a consumer, though, one should be aware that the difference in terms of the loans means that over the lifetime of a loan, even if interest rates are equal, one ends up paying considerably less interest on a shorter-term loan, and so, despite the higher monthly payments, shorter-term loans are the best financial choice, assuming one can afford the payments.
The reason for this difference is that lenders carry risk for a longer time in the case of longer-term loans, something that is reflected in the higher interest rates.