Question

6) For the following problems, identify the hypotheses, define Type I and Type II errors, and discuss the consequences of each error. (When you set up the hypotheses, consider which is the hypothesis you are ”trying to prove”, and that is your alternative. The null hypothesis is then the status quo.)

a. The FDA judges the safety of new drugs. When faced with a new drug, there are two possible decisions: approve the drug or disapprove the drug.

b. You are faced with two investments. One is very risky, but potential returns are high, while the other one is safe but the potential is quite limited. Pick one.

c. You are an airline pilot. You smell smoke in the cockpit, and the nearest airport is less than 5 minutes away. Should you land the plane immediately?

Answer 1

a. Alternative hypothesis: New drugs are not safe. Type I error will arise if I reject the null hypothesis when the new drugs are actually safe. I will reject the safe new drugs. The type II error is when I do not reject null hypothesis when the new drugs are not actually safe. as a consequence of type II error, I will approve the unsafe new drugs.

b. Alternative hypothesis: Limited investment and Risky investment, both yields are not same. Type I error - I have a chance of 5% in general to reject the claim of the difference in two yields are same when there is actually no significant difference in their mean return. I may end up choosing either one of the two investments as both are same in returns. Type II error- I do not reject the null hypothesis when there is actually significant difference in their mean return. so I will investment in low return and earn lesser money.

c. Alternative hypothesis: Aero plane is not going to get fire accident in 5 minutes. I should not land the plane immediately. Type I error, I will meet with an accident by rejecting the null hypothesis when it is true. It means that the fire accident in that aero plane was sure but i did not land as if thinking that my alternative hypothesis is false. Type II even though there is a higher chance of fire accident, and the null hypothesis is false, but i fail to reject the null hypothesis. I will meet with an accident.