**Problem
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 below. 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. Based on this result, does
the new treatment appear to be any different from the placebo?

**Problem
2: **The following data were collected in an
experiment 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 28-32 weeks
gestation. The data are shown
below. Is there a significant difference
in mean fetal heart rates by position?
Run the test at a 5% level of significance. Based on this result, does
position appear to effect fetal heart rate?

**Problem
3: **A clinical trial is conducted to compare an
experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the
study and randomized to receive either the experimental medication or
placebo. The primary outcome is
self-reported change of symptoms. The
data are shown below. Is there a difference in change in symptoms by treatment
group? Run the appropriate test at a 5%
level of significance. Based on this result, does there appear to be a
difference between the experimental medication and the placebo?

**Problem
4: **Suppose a hypertension trial is mounted and 18
participants are randomly assigned to one of the comparison treatments. Each participant takes the assigned
medication and their systolic blood pressure (SBP) is recorded after 6 months
on the assigned treatment. The data are
given below. Is there a difference in mean SBP among treatments? Run the appropriate test at?= 0.05. Based on this result, does the new medication
appear to be any different from the standard treatment and the placebo?

**Problem
5: **An investigator wants to estimate caffeine
consumption in high school students. How
many students would be required to ensure that a 95% confidence interval
estimate for the mean caffeine intake (measured in mg) is within 15 mg of the
true mean? Assume that the standard
deviation in caffeine intake is 68 mg.

**Problem
6: **Consider the study proposed in problem 5. How many students would be required to
estimate the proportion of students who consume coffee? Suppose we want the estimate to be within 5%
of the true proportion with 95% confidence.

**Problem
7: **A crossover trial is planned to evaluate the
impact of an educational intervention program to reduce alcohol consumption in
patients determined to be at risk for alcohol problems. The parameter of interest is the mean
reduction in number of drinks per day. To get the desired margin of error,
statisticians determine the necessary sample size is n = 150. However,
researchers anticipate that 20% of the participants will drop out over the
course of follow-up. How many participants should be enrolled?

**Problem
8: **The mean body mass index (BMI) for boys age 12
is 23.6. An investigator wants to test
if the BMI is higher in 12-year-old boys living in New York City. How many boys are needed to ensure that a
two-sided test of hypothesis has 80% power to detect a difference in BMI of 2
units? Assume that the standard
deviation in BMI is 5.7.

**Problem
9: **Recently it has been observed that HIV-infected
patients develop peripheral lypoatrophy while on potent antiretroviral
therapy. A clinical trial is planned to
determine if a new chemical will improve this condition. In the trial, participants will be randomized
to receive the new chemical or a placebo and changes from baseline in
subcutaneous adipose cross-sectional area as measured by CT scan will be
calculated after 24 weeks of treatment.
Investigators hope to show that the increases in patients receiving the
chemical are greater than the increases in patients receiving the placebo. They hypothesize that the participants
assigned to the chemical arm will exhibit a mean change of 30% and the
participants assigned to the placebo arm will exhibit a mean change of 0%. Prior literature suggests that the standard
deviation of the changes will be 57% in both arms. How many participants are needed to ensure
80% power? Assume ?=0.05, equal numbers
in each group, and that 20% of the participants will drop out over the course
of follow-up.

**Problem
10: **In the worksheet CI Simulation of the Excel
workbook Chapter 8, change the population parameters and the confidence level
to assorted values. Each time press the F9 key several times to repeat the
simulation. Compare the confidence level to the proportion of confidence
intervals that contain?. In your own words, state what the
confidence level means when constructing a confidence interval estimate of a
population parameter.