1. A clinical trial is run to compare the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and to placebo. Pregnant women are enrolled and randomly assigned to receive the experimental drug, the standard drug or placebo. Women are followed through delivery and classified as delivering preterm (< 37 weeks) or not. The resulting data are shown below.
|
Preterm Delivery
|
Experimental Drug
|
Standard Drug
|
Placebo
|
|
Yes
|
17
|
23
|
35
|
|
No
|
83
|
77
|
65
|
Is there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups? Run the test at a 5% level of significance.
2. Consider the data presented in Problem 1. Previous studies have shown that approximately 32% of women deliver prematurely without treatment. Is the proportion of women delivering prematurely significantly higher in the placebo group? Run the test at a 5% level of significance.
3. A study is run comparing HDL cholesterol levels between men who exercise regularly and those who do not. The data are shown below.
|
Regular Exercise
|
N
|
Mean
|
Std Dev
|
|
Yes
|
35
|
48.5
|
12.5
|
|
No
|
120
|
56.9
|
11.9
|
Generate a 95% confidence interval for the difference in mean HDL levels between men who exercise regularly and those who do not.
4. A clinical trial is run to assess the effects of different forms of regular exercise on HDL levels in persons between the ages of 18 and 29. Participants in the study are randomly assigned to one of three exercise groups - Weight training, Aerobic exercise or Stretching/Yoga - and instructed to follow the program for 8 weeks. Their HDL levels are measured after 8 weeks and are summarized below.
|
Exercise Group
|
N
|
Mean
|
Std Dev
|
|
Weight Training
|
20
|
49.7
|
10.2
|
|
Aerobic Exercise
|
20
|
43.1
|
11.1
|
|
Stretching/Yoga
|
20
|
57.0
|
12.5
|
Is there a significant difference in mean HDL levels among the exercise groups? Run the test at a 5% level of significance. HINT: SSerror = 7286.5.
5. The following data were collected in a clinical trial to compare a new drug to a placebo for its effectiveness in lowering total serum cholesterol.
|
|
New Drug
(n=75)
|
Placebo
(n=75)
|
Total Sample
(n=150)
|
|
Mean (SD) Total Serum Cholesterol
|
185.0 (24.5)
|
204.3 (21.8)
|
194.7 (23.2)
|
|
% Patients with Total Cholesterol < 200
|
78.0%
|
65.0%
|
71.5%
|
You generated a 95% confidence interval for the difference in mean total cholesterol levels between treatments. Now, using this same data,
a) Generate a 95% confidence interval for the proportion of all patients with total cholesterol < 200.
b) How many patients would be required to ensure that a 95% confidence interval has a margin of error not exceeding 5%?