Question: Joe performs remarkably well on remote viewing ESP tests, which require the "viewer" to draw a picture, and then determine which of four possible photos was the intended "target." Because the target is randomly selected from among the four choices, the probability of a correct match by chance is 1/4, or .25. Joe participates in three experiments with n = 10, 20, and 50 trials, respectively. In the three experiments, his numbers correct are 4, 8, and 20, respectively, for a total of 32 correct out of 80 trials.
a. For each experiment, what is the expected number correct if Joe is just guessing?
b. Over all 80 trials, what is the expected number correct? Explain how you found your answer.
c. For each experiment separately, find the approximate probability that someone would get as many correct as Joe did, or more, if the person was just guessing.
d. Out of the 80 trials overall, find the approximate probability that someone would get as many correct as Joe did (32), or more, if the person was just guessing.
e. Compare your answers in parts (c) and (d). If Joe were trying to convince someone of his ability, would it be better to show the three experiments separately, or would it be better to show the combined data? Explain.