In a November 16, 2016, Corvallis Gazette-Times article, it was reported that a new drug given along with a cholesterol-lowering statin medicine has proved able to shrink plaque that is clogging arteries. The study that was performed was a clinical trial where 900 heart disease patients were given a strong statin. Some were assigned to a group where they were also given monthly shots of the drug Repatha. The rest were assigned to a placebo group in which they were also given a monthly shot, but it contained a “dummy solution”. Suppose the percent reduction in plaque in the clogged arteries was recorded for each patient.

1. State the null and alternative hypotheses in notation. Define the parameters used in the hypotheses in the context of the problem.

Suppose the researchers provided a 90% confidence interval for the difference in means (µ(Repatha) - µ(Control)) of (0.6%, 2.2%)

2. If the formula method was used, what is x ̅Repatha- x ̅Control? Report your answer to one decimal place.

3. Again, if the formula method was used, what is the margin of error? Report your answer to one decimal place

4. Interpret this confidence interval in the context of the problem.

5. Based solely on the confidence interval, what decision would be made about the null hypothesis? Why?

6. At what significance level was this decision (from question #5) made?

7. What type of error could the researchers have made in the decision made in question 5?

8. What is the probability of making the error in question #7?

9. Describe the error from question 7 in the context of the problem.

Suppose instead that a 99% confidence interval for the difference in means (µ(Repatha)- µ(Control)) was constructed instead. Suppose it was (-0.2%, 3.0%).

10. What decision would the researchers make?

11. At what significance level was this decision (from question #10) made?

12. What type of error could the researchers have made in the decision made in question 10?

13. Describe the error from question #12 in the context of the problem

14. Which error would you consider more serious? Why?