Finding Gifted ESP Participants An ESP test is conducted by randomly selecting one of five video clips and playing it in one building while a participant in another building tries to describe what is playing. Later, the participant is shown the five video clips and is asked to determine which one best matches the description he or she had given. By chance, the participant would get this correct with probability 1/5. Individual participants are each tested eight times, with five new video clips each time. They are identified as “gifted” if they guess correctly at least five times out of the eight tries. Suppose that people actually do have some ESP and can guess correctly with probability .30 (instead of the .20 expected by chance). What is the probability that a participant will be identified as “gifted”?
In Chapter 8, you will learn how to solve this kind of problem, but we can simulate the answer using a random number generator that produces the digits 0, 1, 2, … , 9 with equal likelihood. Many calculators and computers will simulate these digits. Here are the steps needed for one “repetition”:
• Each “guess” is simulated with a digit, equally likely to be 0 to 9.
• For each participant, we simulate eight “guesses” resulting in a string of eight digits.
• If a digit is 7, 8, or 9, we count that guess as “correct,” so P(correct) = 3/10 = .3, as required in the problem. If the digit is 0 to 6, the guess is “incorrect.” (There is nothing special about 7, 8, 9; we could have used any three digits.)
• If there are five or more “correct” guesses (digits 7, 8, 9), we count that as “gifted.”
The entire process is repeated many times, and the proportion of times that the process results in a “gifted” participant provides an estimate of the desired probability. Let’s use Minitab to simulate the experiment for 1000 participants, each making eight guesses.
