If the same hypothesis is tested often enough, it is likely to be rejected at least once, even if it is true. A pro-fessor of biology, attempting to demonstrate this fact, ran white mice through a maze to determine if white miceran the maze faster than the norm established by manyprevious tests involving various colors of mice.(a) If the professor conducts this experiment once withseveral mice (using the 0.05 level of significance), what isthe probability that he will come up with a “significant”result even if the color of the mouse does not affect itsspeed in running the maze?(b) If the professor repeats the experiment with a new setof white mice, what is the probability that at least oneof the experiments will yield a “significant” result evenif the color of a mouse does not affect its maze-runningspeed?(c) If the professor has 30 of his students independentlyrun the same experiment, each with a different groupof white mice, what is the probability that at least oneof these experiments will come up “significant” even ifmouse color plays no role in their maze-running speed?
If the same hypothesis is tested often enough, it is
likely to be rejected at least once, even if it is true. A pro-
fessor 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?
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