The article “Odds Are, It’s Wrong” (Science News, March 27, 2010) poses the following scenario: Suppose that a test for steroid use among baseball players is 95% accurate—that is, it correctly identifies actual steroid users 95% of the time, and misidentifies non-users as users = percent of the time. . . . Now suppose, based on previous testing, that experts have established that about = percent of professional baseball players use steroids. Answer the following questions for this scenario.
a. If 400 professional baseball players are selected at random, how many would you expect to be steroid users and how many would you expect to be non-users?
b. How many of the steroid users would you expect to test positive for steroid use?
c. How many of the players who do not use steroids would you expect to test positive for steroid use (a false positive)?
d. Use your answers to Parts (b) and (c) to estimate the proportion of those who test positive for steroid use who actually do use steroids.
e. Write a few sentences explaining why, in this scenario, the proportion of those who test positive for steroid use who actually use steroids is not .95.