1. A study is run to estimate the mean total cholesterol level in children 2-6 years of age. A sample of 9 participants is selected and their total cholesterol levels are measured as follows. 185 225 240 196 175 180 194 147 223 Generate a 95% confidence interval for the true mean total cholesterol levels in adults with a history of hypertension.
2. A clinical trial is planned to compare an experimental medication designed to lower blood pressure to a placebo. Before starting the trial, a pilot study is conducted involving 10 participants. The objective of the study is to assess how systolic blood pressure changes over time untreated. Systolic blood pressures are measured at baseline and again 4 weeks later. Compute a 95% confidence interval for the difference in blood pressures over 4 weeks.
3. After the pilot study (described in #2), the main trial is conducted and involves a total of 200 patients. Patients are enrolled and randomized to receive either the experimental medication or the placebo. The data shown below are data collected at the end of the study after 6 weeks on the assigned treatment. Experimental (n=100) Placebo (n=100) % Hypertensive 14% 22% Generate a 95% confidence interval for the difference in proportions of patients with hypertension between groups.
4. The following data were collected as part of a study of coffee consumption among male and female undergraduate students. The following reflect cups per day consumed: Generate a 95% confidence interval for the difference in mean numbers of cups of coffee consumed between men and women.
5. A clinical trial is conducted comparing a new pain reliever for arthritis to a placebo. Participants are randomly assigned to receive the new treatment or a placebo. The outcome is pain relief within 30 minutes. The data are shown below. Pain Relief No Pain Relief New Medication 44 76 Placebo 21 99.
a. Generate a 95% confidence interval for the proportion of patients on the new medication who report pain relief.
b. Generate a 95% confidence interval for the difference in proportions of patients who report pain relief.