1. Explain the difference between Type 1 errors and Type 2 errors. (2 pts.)

2. As the head of security at Honolulu International Airport, you are considering whether to increase screening measures to prevent a possible terrorist attack. In the context of identifying an individual as a possible threat, discuss what it would mean to commit a Type 1 or Type 2 error. Assume the following null hypothesis: This passenger is not a terrorist. Concerning the null hypothesis, which error is more important to avoid? What tradeoffs would be made in trying to avoid one error or the other? (3 pts.)

3. You are testing the effectiveness of echinacea for preventing colds. There are 2000 people each in your control group and your experimental group. In the control group, which was given a placebo, 400 people came down with the cold. In the experimental group, which was given echinacea, 345 people got the cold. Your p-value for the study is 1%.

a) What is the null hypothesis being tested in this experiment? (1 pt.)

b) What outcome would be expected if the null hypothesis were true? (1 pt.)

c) Find the theoretical standard deviation for the control group. Show that the experimental group result is statistically significant at the 1% level. (1 pt.)

d) What is the correct way to state the conclusion of the study in relation to the null hypothesis? (1 pt.)

e) From this significance test alone, should we conclude that echinacea consumption is responsible for the decrease in illnesses within the experimental group? Why or why not? (1 pt.)