Madam Helga claims to be psychic. A national TV talk personality plans to test h

Question

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 at least a specified number of the questions (called the cut-off). The cut-off must be set so that the chance of guessing that number or more is no greater than 5 percent. The cut-off value should be:

Explanation / Answer

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 - 0.7483 = 0.2517(25.17%), which is greater than 5%, which is too high.

So we'll look go a little higher, the probability of getting 12 or less is binomcdf(20, .5, 12) = 0.8684.

So the probability of getting 13 or more is 1-0.8684 = 0.1316, which is still more than 5%.

The probability of getting 13 or less is binomcdf(20, .5, 13) = 0.9423.

So the probability of getting 14 or more is 1-0.9423 = 0.0577, which is still more than 5%.

The probability of getting 14 or less is binomcdf(20, .5, 14) = 0.9793.

So the probability of getting 15 or more is 1-0.9423 = 0.0207, which is less than 5%.

So the cut-off value should be 15.

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