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How would I go about comparing two percentage figures from two different sample sizes? For example:

  • Sample 1 - 10% (220,510 out of 2,205,100) of respondents answered "yes",
  • Sample 2 - 31% (12 out of 38) respondents answered "yes".

I want to compare these two percentages to determine if there is any significant difference. The larger sample is market data and I'm trying to compare sample 2 to the market data(sample 1). I don't have the means or SD so not sure how to go about comparing these two samples?

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    $\begingroup$ You will find a very detailed response in dummies.com/education/math/statistics/… although without any exact calculations it is clear that the difference is significant, $\endgroup$
    – Zahava Kor
    Commented Mar 8, 2017 at 1:42
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    $\begingroup$ I would look into a $\chi^2$ goodness of fit test itl.nist.gov/div898/handbook//eda/section3/eda35f.htm $\endgroup$
    – Tavrock
    Commented Mar 8, 2017 at 5:41
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    $\begingroup$ (I deleted some very misleading comments.) Note that you have enough information to find all relevant means, SDs, SEs, and any moments you choose. Thus you could compare the two samples very simply by quoting their means and standard errors or you could conduct a formal hypothesis test to compare their means. Have you reviewed our posts on tests of proportions? $\endgroup$
    – whuber ♦
    Commented Sep 5, 2017 at 20:29

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