+ if ,
0 if ,
- if .
H0: Pr(X > Y) = Pr(X < Y), that is, H0: Pr(+) = Pr(-).
H1: , that is, H1: (why?)
The test is based on the test statistic Z = freq(+). Under H0, Z ~ Binomial(n = n*, 0.5) where n* is the number of observations of + or - signs.
Calculate where Z ~ Binomial(n = 82, p = 0.5).