A website always has different problems to solve. E.g. higher bounce rate, lower conversion rate, users dropping out during shopping and checkout process etc. One would carry out A/B tests to solve these problems on juicy sections (Checkout, home page, product page etc.) of the site, which would directly or indirectly impact conversion rates. This blog post gets in to details of how to find hypothesis for A/B test experiments on these juicy sections, which wouldimpact the most on conversion rates.
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a b testing | google website optimizer