If I'd do such a study, I'd pick a lower confidence interval, like 0.2. This is not a big scientific break through, or a business critical decision. This is a theorem that we're evaluating to be worthy of deeper investigation.
If there's an 80% (also known as 'a significant') chance that the conversion rate is significantly lower than that of Google hits then I'd say that warrants deeper investigation.
That's why it's important to always begin research with a hypothesis, not just randomly throw a confidence interval of a something in there :)
