I was watching a lecture earlier by Marcus du Sautoy called: 'Thinking Better with Mathematics.'

Marcus discusses the statistical sample sizes to verify statements about the population. In his own example, he addresses a statement about cat food.

In particular, a cat food brand in the 1970s/80s, argued that "8 out of 10 cats preferred this cat food."

The population size (in the UK) at that time, was 7 million. But to verify this statement, only a relatively small sample of 246 would be required.

I wondered if someone could derive this, given the the limited information? Or if not, provide a link/direction on this type of information.

The video lecture with the information is here at 13:30 to 15:20 mins. https://www.youtube.com/watch?v=4PlmsnyWXMw