E X E R C IS E S
Exercises 11.1-11.5 feature nonstatistical applications of hypothesis testing. For each, identify the
hypotheses, define Type I and Type II errors, and discuss the consequences of each error. In setting
up the hypotheses, you will have to consider where to place the “burden of proof.”
11.1
It is the responsibility of the federal government to judge the safety and effectiveness of
new drugs. There are two possible decisions: approve the drug or disapprove the drug.
H0: The drug is approved
H1: The drug is not approved
Type I: The judge disapproves of the drug. After the drug has been proven safe and
effective.
Type II: The judge approves the drug and it has been proven to not be safe and effective.
11.2
You are contemplating a Ph.D. in business or economics. If you succeed, a life of fame,
fortune, and happiness awaits you. If you fail, you’ve wasted 5 years of your life. Should
you go for it?
H0: You do get your Ph.D. in business
H1: You do not get your Ph.D. business
Type I: You do not get your Ph.D. business and receive your Ph.D. in economics, so you
do not have a life of fame, fortune, and happiness.
Type II: You do receive your Ph.D. in business and do not receive a life of fame, fortune,
and happiness.
11.3
You are the centerfielder of the New York Yankees. It is the bottom of the ninth inning of
the seventh game of the World Series. The Yanks lead by 2 with 2 outs and men on second
and third. The batter is known to hit for high average and runs very well but only has
mediocre power. A single will tie the game, and a hit over your head will likely result in
the Yankees losing. Do you play shallow?
H0: You do play shallow
H1: You do not play shallow
Type I: You do not play shallow and the batter hits the ball shallow.
Type II: You play shallow and the batter hits the ball over your head.
11.4
You are faced with two investments. One is very risky, but the potential returns are high. The
other is safe, but the potential is quite limited. Pick one.
H0: You invest in the safe option
H1: You do not invest in the safe option
Type I: You do not invest in the safe option and end up losing money on the risky option
when you could’ve made money off the safe option.
Type II: You do invest in the safe option. When you could’ve made more money off the risky
option.
11.5
You are the pilot of a jumbo jet. You smell smoke in the cockpit. The nearest airport is less
than 5 minutes away. Should you land the plane immediately?
H0: You do land the plane
H1: You do not land the plane
Type I: You do not land the plane immediately and the plane has issues before you land at your
final destination.
Type II: You do land the plane immediately and you would have been capable of making it to the
final destination.