Can a percentage be estimated as reliably with a small group? I realise that my question is quite simplistic for this site but I will ask anyway.     I am wondering if percentage results become more unreliable the smaller the group is (I am not referring to a sample of the group rather questioning the whole group). If yes, is there a way to determine that?
For example 5% of the 30 people that received a direct-sales call hang up the phone. Does that mean that 5% of 8 people called would be expected to hang up? Or is the percentage unreliable the smaller the number which is my main question?
I hope that this was clear enough.   Thank you very much 
 A: The sample proportion $\hat{p}$ is an unbiased estimator to the population proportion $p$, regardless of $n$. Therefore, if 5% hanged-up in one sample, and you no other information or prior beliefs, your best bet regarding the proportion of people that will hang-up, both in general and in any other sample is also 5%. 
Your suspicion that the reliability of $\hat{p}$ is reduced for small $p$ is of course correct. Consider the case of a sample of a single person! You can build a Binomial confidence interval around $\hat{p}$ - it's determined only by the number of 'successes' and the number of total events ($n$). This confidence interval will reflect the uncertainty caused by the finite size of the sample - the smaller $n$ is, the larger the interval will become.
If the population proportion $p$ is known (you know that in general, 5% hang-up) and you want to know what is the probability to observe a particular $\hat{p}$ for a sample with a particular size ($n$), you can look at the Binomial distribution defined by $p$ and $n$. This could tell you what is the probability that 1/8 will hang up, 2/8 will hang up, etc. 
