If your survey gives you an answer where over 70% say the same thing, a margin of error of plus or minus 2.5% is more than enough.From the article:
- If you want a smaller margin of error, you must have a larger sample size given the same population.
- The higher the sampling confidence level you want to have, the larger your sample size will need to be.
On a survey that essentially asks very few questions, especially when the answers would be yes or no, the margin of error used should be less than what was used here. Probably no more than 2% and I would argue closer to 1% would be more suitable.
Therefore the sample size would be larger.
Insisting on trying to get it down to 2 or 1% is ludicrous, since we aren't talking about changing the result in any meaningful way.