A/B testing and Pearson's chi-squared test of independence

A good friend of mine asked me recently about how to do A/B testing. As he explained, A/B testing refers to the process in which when someone visits a website, the site sends them to one of two (or possibly more) different 'landing' or home pages, and which one they are sent to is chosen at random. The purpose is to determine which page version generates a superior outcome, e.g. which page generates more advertising revenue, or which which page leads a greater proportion of visitors to continue visiting the site.

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