Madam Helga claims to be psychic A national TV talk personal

Madam Helga claims to be psychic. A national TV talk personality plans to test her in a live TV broadcast. The process will entail asking Madam Helga a series of 20 independent questions with Yes/No answers. The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge. She will be considered psychic if she correctly answers more than a specified number (called the cut-off) of the questions. The cut-off must be set so that the chance of guessing that number or more is no greater than 25 percent. What should the cut-off value be?

Solution

This is binomial. N = 20, p = .5.

Using a calculator with binomcdf, the probability of getting 11 or less is binomcdf(20, .5, 11) = 0.7483

So the probability of getting 12 or more is 1