Parapsychology (psi) is a field of study that deals with clairvoyance or precognition. Psi made its way back into the news when a professional, refereed journal published an article by Cornell psychologist Daryl Bem, in which he claimed to demonstrate that psi is a real phenomenon. In the article Bem stated that certain individuals behave today as if they already know what is going to happen in the future. That is, individuals adjust current behavior in anticipation of events that are going to happen in the future. Here, we will present a simplified version of Bem's research.
(a) Suppose an individual claims to have the ability to predict the color (red or black) of a card
from a standard 52-card deck. Of course, simply by guessing we would expect the individual to
get half the predictions correct, and half incorrect. What is the statement of no change or no
effect in this type of experiment? What statement would we be looking to demonstrate? Based on
this, what would be the null and alternative hypotheses?
(b) Suppose you ask the individual to guess the correct color of a card 40 times, and the alleged
savant (wise person) guesses the correct color 24 times. Would you consider this to be convincing evidence that that individual can guess the color of the card at better than a 50/50
rate? To answer this question, we want to determine the likelihood of getting 24 or more colors
correct even if the individual is simply guessing. To do this, we assume the individual is guessing so that the probability of a successful guess is 0.5. Explain how 40 coins flipped independently with heads representing a successful guess can be used to model the card-guessing experiment.
(c) Now, use a random number generator, or applet such as the Coin-Flip applet in StatCrunch
to flip 40 fair coins, 1000 different times. What proportion of time did you observe 24 or more
heads due to chance alone? What does this tell you? Do you believe the individual has the ability
to guess card color based on the results of the simulation, or could the results simply have
occurred due to chance?
(d)Explain why guessing card color (or flipping coins) 40 times and recording the number of
correct guesses (or heads) is a binomial experiment.
(e)Use the binomial probability function to find the probability of at least 24 correct guesses in
40 trials assuming the probability of success is 0.5.
(f)Look at the graph of the outcomes of the simulation from part (c). Explain why the normal
model might be used to estimate the probability of obtaining at least 24 correct guesses in 40
trials assuming the probability of success is 0.5. Use the model to estimate the P-value.
(g)Based on the probabilities found in parts (c), (e), and (f), what might you conclude about the
alleged savants ability to predict card color?