1. Suppose that 100 people are given lipid lowering drugs and that the drug appears to be effective in about 20 of them. Effective is defined as lowering their cholesterol values by 10 points in one month.
a. What is the most appropriate point estimate of the probability of p of the drug being effective?
b. What if you knew that 10% of people who are given a placebo form of the lipid lowering drugs will also show a 10 point drop in one month? How could we be sure we are not just seeing a placebo effect? What procedure could we carry out to check this? And what are the assumptions of this procedure?
Now assume that we decide that this “effectiveness” measure isn’t as good as looking at the average decrease in points. Suppose that the sample mean of the average decrease is 5.3 with a sample variance of 144?
c. What is the standard error of the mean decrease?
d. What is the 95% confidence interval for the population mean decrease?
e. Interpret the 95% confidence interval.
f. What can we now say about the effectiveness of the drug?