# Sign Test

A sign test is used to decide whether a binomial distribution has the equal chance of success and failure.

#### Example

A soft drink company has invented a new drink, and would like to find out if it will be as popular as the existing favorite drink. For this purpose, its research department arranges 18 participants for taste testing. Each participant tries both drinks in random order before giving his or her opinion.

#### Problem

It turns out that 5 of the participants like the new drink better, and the rest prefer the old one. At .05 significance level, can we reject the notion that the two drinks are equally popular?

#### Solution

The null hypothesis is that the drinks are equally popular. Here we apply the binom.test function. As the p-value turns out to be 0.096525, and is greater than the .05 significance level, we do not reject the null hypothesis.

> binom.test(5, 18)

Exact binomial test

data:  5 and 18
number of successes = 5, number of trials = 18,
p-value = 0.09625
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
0.09695 0.53480
sample estimates:
probability of success
0.27778