Many clinics offer weight$-$reduction programs. To test the effectiveness of one of these programs, ten people were weighed before starting the program and after following the program for one month. Data are presented below. $($By the way, I am not real sure whether the program will lower or raise weight, but, assume that the underlying population is normally distributed.$)$

$\backslash$table$[[,$Weight$],[$Person$,$Before,After$],[1,132,125],[2,231,220],[3,128,109],[4,165,172],[5,133,130],[6,149,140],[7,260,271],[8,141,134],[9,188,180],[10,193,179]]$All t$-$tests have two things in common: a numerator and a denominator. What are these two terms in the t$-$tests?