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ESP and Statistics

I need some help answering this question without calculus:
In 1973, Charles Tart ran an experiment at UC Davis to test for ESP abilities. Tart used an electronic random number generators called the Aquarius with four "targets". The machine randomly picked one of the fours targets, and the subject guessed which target the machine had picked. Tart select 15 subjects who had "previously shown clairvoyant abilities". Each of these subjects made 500 guesses for a total of 7500 guesses, of these 2006 were correct - a proportion of 0.2675 correct guesses. Even if the subjects had no real ESP, we would expect them to be right in 1 out of 4 guesses:
a. If the subjects have no real ESP abilities, what is the probability that, just by random chance they would guess at least 0.2675 of the answers correctly?
b. Do you think the subjects had ESP? Why or why not?

Solution Summary

This solution determines the probability that a subject with no real ESP can guess 0.2675 of the answers correctly and also if the experiment could determine if the subjects had ESP. All workings and explanations are included as well as a diagram for further understanding.

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