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Answer the above questions: (1): A clinical trial evaluates a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing is measured and the data are shown in Table 7.51. Is there a difference in the extent of wound healing by treatment? Run the appropriate test at a 5% level of significance. (Hint: Are treatment and the percent of wound healing independent?) (2): Use the data in Problem 1 and pool the data across the treatments into one sample of size n = 250. Use the pooled data to test whether the distribution of the percent of wound healing is approximately normal. Specifically, use the following distribution: 30%, 40%, 20%, and 10%, and α = 0.05 to run the appropriate test. Table 7-51 Wound Healing by Treatment Percent Wound Healing Treatment 0-25 26-50 51-75 76- 100 New Compound 15 37 32 41 (n=125) Placebo(n=125) 36 45 34 10 (3): Table 7.52 displays summary statistics on the participants involved in the study described in Problem 1. Are any of the characteristics significantly different between groups? Justify briefly. (Hint: No calculations, just an interpretation.) Table 7-52 Summary Statistics by Treatment New Compound Placebo p Value Mean age(years) 47.2 46.1 0.7564 Men(%) 44% 59% 0.0215 Mean educational level (Years) 13.1 14.2 0.6898 Mean annual income $36,560 $37,470 0.3546 Mean body mass index (BMI),kg/m 24.7 25.1 0.0851 (4): An investigator hypothesizes that cholesterol levels in children might be affected by educating their parents on proper nutrition and exercise. A sample of 40 families with a child between the ages of 10 to 15 years who has been diagnosed with high cholesterol agrees to participate in the study. All parents are provided educational information on nutrition and exercise. After following the prescribed program, their child’s total cholesterol level is measured. The children’s mean cholesterol level is 175 mg/dL with a standard deviation of 19.5 mg/dL. Is there significant evidence of a reduction in total cholesterol in the children? Run the appropriate test at the 5% level of significance and assume that the null value for total cholesterol is 191 mg/dL. (5): An experiment is designed to investigate the impact of different positions of the mother during ultrasound on fetal heart rate. Fetal heart rate is measured by ultrasound in beats per minute. The study includes 20 women who are assigned to one position and have the fetal heart rate measured in that position. Each woman is between 28 and 32 weeks’ gestation. The data are shown in Table 7.53. Is there a significant difference in mean fetal heart rates by position? Run the test at a 5% level of significance. Table 7-53 Fetal Heart Rate by Position Back: Side: Sitting: Standing: 140 141 144 147 144 143 145 145 146 145 147 148 141 144 148 149 139 136 144 145 Mean=142.0 Mean=141.8 Mean =145.6 Mean=146.8 (6): 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 and the outcome is pain relief within 30 minutes. The data are shown in Table 7.54. Is there a significant difference in the proportions of patients reporting pain relief? Run the test at a 5% level of significance. Table 7-54 Pain Relief by Treatment Pain Relief No Pain Relief New medication 44 76 Placebo 21 99 (7): 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 seven participants. The objective of the study is to assess how systolic blood pressures change over time if left untreated. Systolic blood pressures are measured at baseline and again 4 weeks later. Is there a statistically significant difference in blood pressures over time? Run the test at a 5% level of significance. Baseline: 120 145 130 160 152 143 126 4 Weeks: 122 142 135 158 155 140 130 (8): The main trial in Problem 7 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 in Table 7.55 are collected at the end of the study after 6 weeks on the assigned treatment. (a): Test if there is a significant difference in mean systolic blood pressures between groups using α = 0.05. (b): Test if there is a significant difference in the proportions of hypertensive patients between groups using α = 0.05. Table 7-55 Outcomes by Treatment Experimental (n = 100) Placebo (n = 100) 120.2 (15.4) 131.4 (18.9) Mean (SD) systolic blood pressure, mm Hg Hypertensive (%) 14 22 Side effects (%) 6 8

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