I used http://www.abtestcalculator.com/ and entered 3000 participants -> 28 conversions and 3000 participants -> 39 conversions.I neglected to record how many views each version had, but should be at least 3000 since the conversion ratio is about 0.5 - 1%.

 Resource provided uses a very naive approach to determining the outcome of an AB test. It's not accurate, given the very small numbers.
 Yes, I don't have much data to work with, and was also surprised that the calculator considered this significant. But even without significance, I assume it still makes sense to go with the winner?
 Does the calculator really use the word "significant"? I don't see it. I am not sure how to interpret the language it uses.As for going with the winner: Yes, if the test result (39/28) is the only information you have and there are only two choices (go with winner / go with loser) then it makes sense to go with the winner.
 The statement I see on that page is "There is a 91% chance that Variation A has a higher conversion rate".I am not sure how to interpret that. We would have to dive into the GitHub repo and figure out which test it performs I guess.
 It looks like the difference of two beta distributions based on the visualization.So, assuming a uniform prior and updating with 39/3000 and 28/3000 conversions the difference between the two distributions is greater than zero 91% of the time. It's only guaranteed to be above zero at about the 80% credible interval, and since we started with an uninformed prior that'd be about p=.2?I'm open to correction here.
 You get 91% if you put a uniform prior on the proportion coming from each alternative.
 Looks like I misunderstood the result, I will change the post to reflect this.
 If you have Google Analyics on your site, you can use the Unique Pageviews metric for each of the two page variations and use that as the metric, instead of arbitrarily assigning 3000 views to both.
 If you had 3000 visits, shouldn't that be 1500 -> 28 and 1500 -> 39? (assuming you're doing a uniform split of both groups)

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