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I C ESP

Though Martin Gardner wrote very little specifically about statistics, he often touched on it via connections. My example below is taken from his book Mathematics--Magic and Mystery, first published in 1956.

When discussing mind-reading experiments, Martin Gardner mentions a magician's technique known as "psychological forces." This element supposedly increases the "odds for success" in favor of the mind-reader. For example, Martin Gardner claimed:

  • If asked for a number between 1-5, most people tend to pick the number 3.
  • If asked for a number between 1-10, most people tend to pick the number 7.
  • If asked for a number between 1-50 with both digits odd and different (e.g. not 11), most people tend to pick the number 37.
  • If asked for a number between 50-100 with both digits even and different, most people tend to pick the number 68.
Your Task: Devise statistical experiments where you test the validity of Martin Gardner's claims. That is, do "psychological forces" exist?

Source: Martin Gardner, Mathematics, Magic and Mystery, Dover, 1956, pp. 173-174