Question;PU 515;Applied Biostatistics;Final Exam;1. 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. 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 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.;4. Consider the data;presented in problem #4. 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.;5. 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.;6. 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;SSwithin = 21,860.;7. Consider again the data in problem #6. 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) Is there evidence of a significant correlation;between number of hours of exercise per week and;HDL cholesterol;level? Run the test at a 5% level of;significance.;b) 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).;c) Estimate the;HDL level for a person who exercises 7 hours per week.;d) Estimate the;HDL level for a person who does not exercise.;8. 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.;Generate a 95% confidence interval for the;difference in;mean total cholesterol levels between treatments.;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%;9. A small pilot study is conducted to;investigate the effect of a nutritional supplement on total body;weight. Six participants agree to take the;nutritional supplement. To assess its;effect on body;weight, weights;are measured before starting the supplementation and then after 6 weeks. The data;are shown;below. Is there a significant increase;in body weight following supplementation?;Run;the test at a 5%;level of significance.;Subject;Initial Weight;Weight after 6;Weeks;1;155;157;2;142;145;3;176;180;4;180;175;5;210;209;6;125;126;10. Answer True or False to each of the;following;a) The margin of;error is always greater than or equal to the standard error.;b) If a test is;run and p=0.0356, then we can reject H0 at?=0.01.;c) If a 95% CI;for the difference in two independent means is (-4.5 to 2.1), then the point;estimate;is -2.1.;d) If a 95% CI;for the difference in two independent means is (2.1 to 4.5), there is no;significant;difference in;means.
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