I have 20-30 repeated measurements each of which produce a single number. My goal is to determine whether the mean of these numbers is statistically significantly greater than the number 1. (significantly less than 1 does not count, in this case)

I know, for example, that if I want to know whether the means of two populations are different, I can use a t-test, but this does not seem to apply when one of my "populations" is just the fixed number 1. Can anyone help suggest the correct test?