Z-Statistic and proportion

#1
Hi:) ,

I'm having some difficulty with this question. The question asks

A matched pairs experiment compares the taste of instant versus fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 40 subjects who participate in the study, 12 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers freshly brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)


1. Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic and its P-value.


Our professor provided us with this hint:

H0: p = .5
Ha: p > .5


I justed to know why use would we use .5, is it because the testing majority would be 50% or more ???

Please Help and Thank You:)