Is A truly better than B, given that 56% of 131 respondednts said so? I have asked subjects whether procedure A is better than procedure B. Slightly more said yes (56% of a group of 131 subjects). How can I tell if this answer tells me that indeed procedure A is better than B, instead of the students just randomizing their answers?
 A: First, @NuclearWang is correct.  If your survey is as stated, you're learning about what procedure people prefer, not what is better (for some unspecified purpose).  I don't think it's a pedantic point, its important to measure what we intend to measure.
The statistics here is pretty simple.  You want to know if your data indicates that the respondents were not guessing randomly.  The standard approach is to assume that they are guessing randomly (usually called the null hypothesis), then show that your data is very unlikely to have been collected under that hypothesis.
Under the random guessing assumption, your data would be generated from a binomial process:
$$ \text{# of votes for A} \sim \text{Binomial}(n = 131, p = 0.5) $$
You actually observed $72$ votes for A.  We can easily calculate the probability that we would observe greater than or equal to $72$ votes for A if the respondents were guessing randomly.  I'll use python:
In [1]: import scipy.stats as stats

In [2]: 1 - stats.binom(n=131, p=0.5).cdf(71)
Out[2]: 0.14720307826175671

It looks like there's a 15% chance of observing data equal or more extreme than you actually collected when the respondents were guessing randomly.  How you use this probability to affect your beliefs is up to you.
