I have a hypothetical problem were say I have a sample size of about 5000 people. I then will collect data on them say, how man calories of food they eat per day for a month. Now I can't obviously run the sample on all 5000 (we'll just say this is not feasible), how do I determine an appropriate sample size. Is it enough to just say what is the confidence level I want (we'll take 95%) and confidence interval 5%, in which case I will then need about 357 people. Or am I over simplifying the problem, because this isn't a "survey" but rather data collection.
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If you want exactly 5% error margin you need to know the standard diviation of the population. To make the central limit theorem valid you need to ask at least 30 people. I assume that the standard diviation of calories will be pretty high so I would suggest to take as big sample size as possible.