Demonstrate that "data snooping," that is, testing hypotheses that are suggested by the data, is generally not a good practice.
(a) Show that, for any random variable Y and constants a and b with a > b and P(Y > b) < 1, P(Y > a | Y > b) > P(Y > a).
(b) Apply the inequality in part (a) to the size of a data-suggested hypothesis test by letting Y be a test statistic and a be a cutoff point.