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HLTH 501 Biostatistics Final Exam Due 12/11/12 at 2000 Hours 1 BMI is measured in a sample of patients, with a mean of 31.7 and a standard deviation

Is the margin of error always greater than or equal to the standard error


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HLTH 501 Biosta±s±cs Final Exam Due 12/11/12 at 2000 Hours 1 BMI is measured in a sample of patients, with a mean of 31.7 and a standard deviation of 5.9. 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? 2 The mean BMI in patients free of diabetes was elsewhere reported as 28.2. The researcher producing the data in question 1 wonders if the BMI 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. 3 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 o 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. 4 Considering again the study in Problem 3, a different investigator conducts a second study to investigate whether there is a difference in mean P 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 bron Group Mean PEF 25 281 68 25 319 74 5 A clinical trial is run to investigate the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and 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. Is there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups? Run the test at a 5% l Preterm Delivery Standard Drug Placebo Yes 17 23 35 No 83 77 65 6 Is the proportion of women delivering prematurely significantly higher in the placebo group? Run the test at a 5% level of significance. 7 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 Their HDL levels are measured after 8 weeks and are summarized below. Is there a significant difference in mean HDL levels among the exercise groups? Run the test at a 5% level of significance. Exercise Group N Mean Std Dev Weight Training 20 49.7 10.2 Aerobic Exercise 20 43.1 11.1 Stretching/Yoga 20 57 12.5 8 and the mean is 5.2 hours with a standard deviation of 2.1 hours. The equation describing the results is a Estimate the HDL level for a person who exercises 7 hours per week. b Estimate the HDL level for a person who does not exercise. 9 The table below summarizes baseline characteristics on patients participating in a clinical trial. Characteristic P 0.7856 % Female 39% 52% 0.0289 24% 22% 0.0986 37% 36% Number of Children Std Dev PEF Chronic Bronchitis No Chronic Bronchitis Experimental Drug Consider the data presented in Problem 5. Previous studies have shown that approximately 32% of women deliver prematurely without treatme Consider again the data in Problem 7. Suppose that in the aerobic exercise group we also measured the number of hours of aerobic exercise pe Y = 54.6 - 2.22x , where Y = HDL levels. Placebo (n=125) Experimental (n=125) Mean (+ SD) Age 54 + 4.5 53 + 4.9 % Less than High School Education % Completing High School
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39% 42% 0.4736 0.8954 17% 15% 0.5741 % with Diabetes 8% 3% 0.0438 a Are there any statistically significant differences in baseline characteristics between treatment groups? Justify your answer. b c d 10 A study is designed to investigate whether there is a difference in response to various treatments in patients with rheumatoid arthritis. The outcome is patient’s self-reported effect of treatment. The data are shown below. Is there a significant difference in effect of treatment? Run the Symptoms No Effect Total Worsened Treatment 1 22 14 14 50 Treatment 2 14 15 21 50 Treatment 3 9 12 29 50 11 Using the data shown in Problem 10, suppose we focus on the proportions of patients who show improvement. Is there a statistically significant difference in the proportions of patients who show improvement between treatments 1 and 2? Run the test at a 5% l 12 Test the null hypothesis that there is no difference in mean time to pain relief between treatment groups. Treatment Sample Size A 5 33.8 17.7 B 5 27 15.5 C 5 50.8 9.7 D 5 39.6 16.8 13 A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritiona 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 1 155 157 2 1.77 2 142 145 3 5.43 3 176 180 4 11.09 4 180 175 -5 32.15 5 210 209 -1 2.79 6 125 126 1 0.11 TOTAL 4 53.34 14 currently available drug and report improvement in pain on a 5-point ordinal scale: 1=Pain is much worse, 2=Pain is slightly worse, 3= No change, 4= Is there a significant difference in self-reported improvement in pain? Use the Mann-Whitney U test with a 5% level of significance. New Drug: 4 5 3 3 4 2 Standard Drug: 2 3 4 1 2 3 15 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 16 A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children. A total of 250 children are randomized to The mean age of children assigned to the new drug is 12.4 with a standard deviation of 3.6 years. The mean age of children assigned to the placebo i % Completing Some College Mean (+ SD) Systolic Blood Pressure 136 + 13.8 134 + 12.4 Mean (+ SD) Total Cholesterol 214 + 24.9 210 + 23.1 % Current Smokers Write the hypotheses and the test statistic used to compare ages between groups. (No calculations – just H 0 , H 1 and form of the test stat Write the hypotheses and the test statistic used to compare % females between groups. (No calculations – just H 0 , H 1 and form of the te Write the hypotheses and the test statistic used to compare educational levels between groups. (No calculations – just H 0 , H 1 and form o Symptoms Improved An   analysis is conducted to compare mean time to pain relief (measured in minutes) under four competing treatment regimens Summary statist Mean Time to Relief Sample Variance Weight after 6 Weeks D (difference) (D-0.67) 2 A small pilot study is run to compare a new drug for chronic pain to one that is currently available. Participants are randomly assigned to receiv If a test is run and p=0.0356, then we can reject H 0 at a =0.01.
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