You solved the game show problem of whether or not to switch your choice of three doors, one of which hides a prize, after the host reveals what is behind a door that is not chosen. (Despite the natural inclination of many to keep one's first choice, the correct answer is that you should switch your choice of doors.) This problem is sometimes called the "Monty Hall Dilemma," named for Monty Hall, the host of the popular TV game show Let's Make a Deal. In Thinking & Reasoning (July, 2007), Wichita State University professors set up an experiment designed to influence subjects to switch their original choice of doors.

Each subject participated in 23 trials. In trial 1, three (boxes) representing doors were presented on a computer screen; only one box hid a prize. In each subsequent trial, an additional box was presented, so that in trial 23, twenty five boxes were presented. In each trial, after a box was selected, all of the remaining boxes except for one either (1) were shown to be empty ( Empty condition), (2) disappeared ( Vanish condition), (3) disappeared, and the chosen box was enlarged ( Steroids condition), or (4) disappeared, and the remaining box not chosen was enlarged ( Steroids2 condition). Twenty-seven subjects were assigned to each condition. The number of subjects who ultimately switched boxes is tallied, by condition, in the following table for both the first trial and the last trial, These data are saved in the

MONTYHALL file.

a. For a selected trial, does the likelihood of switching boxes depend on condition?
b. For a given condition, does the likelihood of switching boxes depend on trial number?
c. On the basis of the results you obtained in parts a and b , what factors influence a subject to switch choices?

First Trial (1) Last Trial (23) Switch Switch Condition Bxes No Switch Boxes No Switch Empty Vanish Steroids Steroids2 10 17 24 23 12 21 19 4 15 19