In the u.s. legal system, a defendant is presumed innocent
until proven guilty. Consider a null hypothesis, Ho, that
the defendant is innocent, and an alternative hypothesis, HI,
that the defendant is guilty. A jury has two possible decisions:
Convict the defendant (i.e., reject the null hypothesis)
or do not convict the defendant (i.e., do not reject the null
hypothesis). Explain the meaning of the risks of committing
either a Type I or Type
Question 9.10
Suppose the defendant in Problem 9.9 is presumed
guilty until proven innocent, as in some other judicial systems.
How do the null and alternative hypotheses differ from
those in Problem 9. 9? What are the meanings of the risks of
committing either a Type I or Type II error here?
Question 9.11
The U.S. Food and Drug Administration (FDA) is
responsible for approving new drugs. Many consumer
groups feel that the approval process is too easy and, therefore,
too many drugs are approved that are later found to be
unsafe. On the other hand, a number of industry lobbyists
have pushed for a more lenient approval process so that
pharmaceutical companies can get new drugs approved
more easily and quickly (data extracted from R. Sharpe,
“FDA Tries to Find Right Balance on Drug Approvals,” The
Wall Street Journal, April 20, 1999, p. A24). Consider a null
hypothesis that a new, unapproved drug is unsafe and an
alternative hypothesis that a new, unapproved drug is safe.
a. Explain the risks of committing a Type I or Type II
error.
Which type of error are the consumer groups trying to
avoid? Explain.
c. Which type of error are the industry lobbyists trying to
avoid? Explain.
d. How would it be possible to lower the chances of both
Type I and Type II errors
