If the same hypothesis is tested often enough, it is likely to be rejected at least once, even if it is true. A professor of biology, attempting to demonstrate this fact, ran white mice through a maze to determine if white mice ran the maze faster than the norm established by many previous tests involving various colors of mice.
(a) If the professor conducts this experiment once with several mice (using the 0.05 level of significance), what is the probability that he will come up with a "significant" result even if the color of the mouse does not affect its speed in running the maze?
(b) If the professor repeats the experiment with a new set of white mice, what is the probability that at least one of the experiments will yield a "significant" result even if the color of a mouse does not affect its maze-running speed?
(c) If the professor has 30 of his students independently run the same experiment, each with a different group of white mice, what is the probability that at least one of these experiments will come up "significant" even if mouse color plays no role in their maze-running speed?