"Kids Overdo Headache Meds" reports on a study by Dr. David Rothner, a pediatric neurologist at the Cleveland Clinic: "In a study of 680 headache patients ages 6 to 18, Rothner found that 22% were overusing nonprescription pain relievers. Overuse is defined as taking at least three doses each week for longer than 6 weeks."24
a. Use software to produce a 95% confidence interval for the proportion of all headache patients in that age group who overuse nonprescription pain relievers.
b. Suppose we had sampled from all children ages 6 to 18 (not just headache patients) to set up a confidence interval for the proportion of all children in that age group who overuse nonprescription pain relievers. Would the interval be centered the same as the one you produced in part (a), or centered to the left of it, or centered to the right of it?
c. Suppose overuse was defined as taking at least three doses each week for longer than 6 months, instead of 6 weeks. Would a confidence interval for the proportion of all headache patients ages 6 to 18 who overuse nonprescription pain relievers be centered the same as the one you produced in part (a), or centered to the left of it, or centered to the right of it?