# Hypothesis testing for one sample proportions

$H_0: p = 0.1$

$H_a: p \neq 0.1$

So here I have a pretty small sample, and I read somewhere that in order to approximate this binomial distribution with the normal distribution, I have to have $n*p > 5$ and $n*(1-p) > 5$. Since $30 * 0.1 = 3 < 5$, does that mean I cannot use the $Z$ statistic here? If so, what can I do to overcome this?

• The Binomial distribution gives you an exact distribution for the number of successes in $n$ trials when these are independent and each trial has success probability $p$. – Christoph Hanck May 28 '15 at 7:38
• @Adrian You don't need the normal approximation. You're doing an exact test and can derive the p-value directly. Use that p-value. Google "Exact test". – SmallChess May 28 '15 at 8:05
• two tailed binomial test – Glen_b May 28 '15 at 13:18