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Uplace and the binomial distribution

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Currently there is a debate in Belgium about the construction of Uplace, a huge shopping mall on the outskirts of Brussels. A marketing professor of the Vlerick School, Gino Van Ossel, did a survey which showed that, contrary to popular believe, quite a big group was actually in favor rather than opposing the plans. So far so good, but the professor's methodology was questioned in the media. The arguments used against the survey findings were not very strong, I believe, and I will not discuss them here. However, a part of the reasoning used by Gino Van Ossel looked rather odd to me and made me think about a more general problem that I would like to discuss here. Those of you who understand Dutch can find all the details on www.marketingblog.vlerick.com . In short, he found that in a sample of 654, representing the total Belgium, 33% was in favor, while in the region where the shopping mall would located, with a sample of 182, 46% were in favor. This was against the popular believ...