> #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
[1] 9
> n1 <- length(z1)
> n1
[1] 12
> B2 <- sum(z>0)
> B2
[1] 9
> n2 <- length(z>0)
> n2
[1] 15
> #(i)Test with discarding zeros
> binom.test(B1, n1, p=0.5, alternative="greater")

	Exact binomial test

data:  B1 and n1 
number of successes = 9, number of trials = 12, p-value = 0.073
alternative hypothesis: true probability of success is greater than 0.5 
95 percent confidence interval:
 0.4726734 1.0000000 
sample estimates:
probability of success 
                  0.75 

> #(ii)Test with zeros being negative
> binom.test(B2, n2, p=0.5, alternative="greater")

	Exact binomial test

data:  B2 and n2 
number of successes = 9, number of trials = 15, p-value = 0.3036
alternative hypothesis: true probability of success is greater than 0.5 
95 percent confidence interval:
 0.3595652 1.0000000 
sample estimates:
probability of success 
                   0.6 

> #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).