#Problem 3.54
z <- c(2.5,0,3.7,-0.6,1.7,0,5.9,4.6,0,-1.4,5.4,4.6,3.1,-2,6.3) 
z1 <- z[z!=0]
B1 <- sum(z1>0)
B1
n1 <- length(z1)
n1
B2 <- sum(z>0)
B2
n2 <- length(z>0)
n2
#(i)Test with discarding zeros
binom.test(B1, n1, p=0.5, alternative="greater")
#(ii)Test with zeros being negative
binom.test(B2, n2, p=0.5, alternative="greater")
#p-value for (i) is 0.073 and (ii) is 0.3036
#The p-value for the conservative method (ii) is more than
#four times larger and therefore harder to reject than (i).