One classical experiment on ESP (extrasensory perception) tests for the ability of an individual to show telepathy. This test uses five cards with different designs, all known to both participants. In...

One classical experiment on ESP (extrasensory perception) tests for the ability of an individual to show telepathy. This test uses five cards with different designs, all known to both participants. In a trial, the “sender" sees a randomly chosen card and concentrates on its design. The “receiver" attempts to guess the identity of the card. Each of the five cards is equally likely to be chosen, and only one card is the correct answer at any point.

1. Out of 10 trials, a receiver got 4 cards correct. Is there reliable evidence that the receiver has telepathic abilities? Carry out the appropriate test.


2. Assume another (extremely hypothetical) individual tried to guess the ESP cards 1000 times and was correct 350 of those times. Carry out the appropriate test for whether the rate is different from the random guess rate. The result should be significant, yet the proportion of her successes is lower than the individual in part (a). Explain this apparent contradiction.