14 Jun The following are body mass index
The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Generate a 95% confidence interval estimate of the true BMI.
25 27 31 33 26 28 38 41 24 32 35 40
2. Consider the data in Problem 1. How many subjects would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 2 units?
3. The mean BMI in patients free of diabetes was reported as 28.2. The investigator conducting the study described in Problem 1 hypothesizes that the BMI in patients free of diabetes is higher. Based on the data in Problem 1 is there evidence that the BMI is significantly higher that 28.2? Use a 5% level of significance.
4. Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator wants to test whether children with chronic bronchitis have restricted PEF. A sample of 40 children with chronic bronchitis are studied and their mean PEF is 279 with a standard deviation of 71. Is there statistical evidence of a lower mean PEF in children with chronic bronchitis? Run the appropriate test at a=0.05.
5. Consider again the study in Problem 4, a different investigator conducts a second study to investigate whether there is a difference in mean PEF in children with chronic bronchitis as compared to those without. Data on PEF are collected and summarized below. Based on the data, is there statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without? Run the appropriate test at a=0.05.
Group
Number of Children
Mean PEF
Std Dev PEF
Chronic Bronchitis
25
281
68
No Chronic Bronchitis
25
319
74
6. Using the data presented in Problem 5,
a) Construct a 95% confidence interval for the mean PEF in children without chronic bronchitis.
b) How many children would be required to ensure that the margin of error in (a) does not exceed 10 units?
7. A clinical trial is run to investigate 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 either the experimental drug, the standard drug or placebo. Women are followed through delivery and classified as delivering preterm (< 37 weeks) or not. The 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. 8. Using the data in Problem 7, generate a 95% confidence interval for the difference in proportions of women delivering preterm in the experimental and standard drug treatment groups. 9. Consider the data presented in Problem 7. 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. 10. 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. 11. 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. 12. Consider again the data in Problem 11. Suppose that in the aerobic exercise group we also measured the number of hours of aerobic exercise per week and the mean is 5.2 hours with a standard deviation of 2.1 hours. The sample correlation is -0.42. a) Estimate the equation of the regression line that best describes the relationship between number of hours of exercise per week and HDL cholesterol level (Assume that the dependent variable is HDL level). b) Estimate the HDL level for a person who exercises 7 hours per week. c) Estimate the HDL level for a person who does not exercise. 13. The table below summarizes baseline characteristics on patients participating in a clinical trial. Characteristic Placebo (n=125) Experimental (n=125) P Mean (+SD) Age 54 + 4.5 53 + 4.9 0.7856 % Female 39% 52% 0.0289 % Less than High School Education 24% 22% 0.0986 % Completing High School 37% 36% % Completing Some College 39% 42% Mean (+SD) Systolic Blood Pressure 136 + 13.8 134 + 12.4 0.4736 Mean (+SD) Total Cholesterol 214 + 24.9 210 + 23.1 0.8954 % Current Smokers 17% 15%
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