Math assignment

1. A study is run to estimate the mean total cholesterol level in children 2-6 years of age. A sample of 9 participants is selected and their total cholesterol levels are measured as follows.
185 225 240 196 175 180 194 147 223
Generate a 95% confidence interval for the true mean total cholesterol levels in adults with a history of hypertension.

2. The following data were collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound was compared against a placebo. After treatment for 5 days with the new compound or placebo the extent of wound healing was measured and the data are shown below.
Percent Wound Healing
Treatment 0-25% 26-50% 51-75% 76-100%
New Compound (n=125) 15 37 32 41
Placebo (n=125) 36 45 34 10
Is there a difference in the extent of wound healing by treatment? (Hint: Are treatment and the percent wound healing independent?) Run the appropriate test at a 5% level of significance.

3. 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 wound healing is approximately normal. Specifically, use the following distribution: 30%, 40%, 20% and 10% and =0.05 to run the appropriate test.

4. The following data were collected in an experiment designed to investigate the impact of different positions of the mother on fetal heart rate. Fetal heart rate is measured by ultrasound in beats per minute. The study included 20 women who were assigned to one position and had the fetal heart rate measured in that position. Each woman was between 28-32 weeks gestation. The data are shown below.
Back Side Sitting Standing
20 21 24 26
24 23 25 25
26 25 27 28
21 24 28 29
19 16 24 25

Is there a significant difference in mean fetal heart rates by position? Run the test
at a 5% level of significance.