How many answers are needed to consider that a survey represents the opinion of a group? Context
I'm preparing a survey that will be sent to a group of people that have attended an event. I will send the survey to all participants (310 people). I cannot force them to answer the questions, and thus I'm not sure how many answers I will get.
Question
Is there a way to evaluate the minimal number of answers I need to receive in order to be allowed to consider that the survey represents the opinion of the population having attended the event (with an acceptable error margin of 10%) ?
What I tried so far
I found a formula and a calculator to calculate the error margin on surveymonkey website. Documentation states that :
errorMargin = z * (stdDeviation / sqrt(sample))

where z, for a level of confidence of 95% equals 1.96. When playing with the calculator and providing the following three data :


*

*population = 310, 

*confidence = 95%, 

*sample (various values) 


I see that I get my target errorMargin of 10% when the size of the sample is at least "69". My understanding is that having 69 answers seems to be enough.  
However I don't get how this calculator works (or rather how it can calculate a standard deviation out of the values I provided), and thus I do not trust this result. But maybe I'm wrong.
Thank you in advance,
 A: Your calculations are right (except they apply to normally distributed variables and/or very big samples, which may or not be your case, but it's an OK approximation. In case of doubt, be slightly more conservative), except for the fact that that 69-individuals sample should be a simple random sample, where repetitions could occur. The difference is not a big one, though.
Note that the formula is independent of population sample, but here you really need to get answeres/non-answers at random from the population (i.e: your sample must be representative of the entire population) and that may not be the case.
This means that you may get biased results by considering only the part of the population that answered to your question (depending on the topic, individuals with some "opinion" may be more/less likely to respond to your poll) This is a problem that concerns each particular case differently and therefore there is no "gold standard" here.
In a nutshell, your calculations are right, but stay aware of where it applies and where it does not! Your sample will only be representative of your sample and only sometmies it generalizes to the entire population. The variables on which this generalization validity depends are not always mathematical/statistical
