1) A doctor wants to evaluate the effectiveness of a new medication in reducing cholesterol levels.
The cholesterol levels (in mg/dL) for 12 patients before and after taking the medication for 8
weeks are given below:
Before Medication: 210, 220, 225, 230, 215, 235, 240, 245, 250, 260, 255, 270
After Medication: 205, 215, 220, 225, 210, 230, 235, 240, 245, 250, 248, 265
a) Calculate the differences in cholesterol levels (Before - After) for each patient.
b) Calculate the sample mean and sample standard deviation of the differences.
c) Construct a 90% confidence interval for the mean difference in cholesterol levels.
d) What assumption is necessary for the confidence interval in part (c) to be valid?
e) Calculate the margin of error for the confidence interval in part (c).
f) What is the width of the 95% confidence interval?