A simple one question Yes/No survey was sent to about 250 people from a population of 481. 135 responses received showed about 80% “Yes” and 20% “No”. How do I calculate my 95% and 99% confidence level ranges? I ended up with roughly 70% to 90% being the range but have been challenged on its validity. A couple of online calculators gave similar results as mine. The sample was based on those who had provided an email address for general communication, so reasonably random.

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    $\begingroup$ Computing a confidence interval will not address challenges to validity. The issue is whether your results generalize to the population. There are two strong reasons to suspect not: the non-randomness of the sample selection and the high non-response rate. Those are what you need to address. $\endgroup$ – whuber Jan 11 at 21:51
  • $\begingroup$ The 481 members are renowned for their apathy in participation in “club” matters! At least the 250 who provided email addresses had shown a basic level of interest, and had provided them for newsletters etc, not because of the survey. $\endgroup$ – JohnB Jan 11 at 22:01
  • $\begingroup$ I missed the 5 minute Edit window! Rookie. .... As for the non-response, 135 replies out of 250 is spectacular considering only about 15-20 show up for the Annual Meeting, and 5 of them are on the Board so have to! The underying question is really if this 80% sample “Yes” (i.e. Yes, I’m interested) is enough to predict a 70% or better “Yes” In a formal vote - which will probably get a 60% response if we’re lucky. $\endgroup$ – JohnB Jan 11 at 22:13

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