Exercises below 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."

a)) 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.

When we state the hypotheses, we list the null and alternative hypotheses.

H0:The federal government approves the safety and effectiveness of new drugs.

H1:The federal government disapproves the safety and effectiveness of new drugs.

We define the Type I and Type II errors.

Type I error is made when the federal government approves the safety and effectiveness of new drugs is rejected.

Type II error is made when the federal government disapproves the safety and effectiveness of new drugs is false and it is not rejected.

b) 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?

c) 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 Yanks losing. Do you play shallow?

d) 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.

e) 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?

f) Several years ago in a high-profile case, a defendant was acquitted in a double-murder trial but was subsequently found responsible for the deaths in a civil trial. (Guess the name of the defendantthe answer is in Appendix C.) In a civil trial the plaintiff (the victims' relatives) are required only to show that the preponderance of evidence points to the guilt of the defendant. Aside from the other issues in the cases, discuss why these results are logical.