The R Book

A Two-Class Table of Counts

You count 47 animals and find that 29 of them are males and 18 are females. Are these data sufficiently male-biased to reject the null hypothesis of an even sex ratio? With an even sex ratio the expected number of males and females is 47/2 = 23.5. The simplest test is Pearson's chi-squared in which we calculate

Substituting our observed and expected values, we get

This is less than the critical value for chi-squared with 1 degree of freedom (3.841), so we conclude that the sex ratio is not significantly different from 50:50. There is a built-in function for this

observed<-c(29,18)
chisq.test(observed)

    Chi-squared test for given probabilities

data: observed
x-squared = 2.5745, df = 1, p-value = 0.1086

which indicates that a sex ratio of this size or more extreme than this would arise by chance alone about 10% of the time (p = 0.1086). Alternatively, you could carry out a binomial test:

binom.test(observed)

Exact binomial test
data: observed
number of successes = 29, number of trials = 47, p-value = 0.1439
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
0.4637994   0.7549318
sample estimates:
probability of success
             0.6170213

You can see that the 95% confidence interval for the proportion of males ...