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Module 5
1. Recent recommendations suggest 50 minutes of physical activity per day.  A sample of 60 adults in a study of cardiovascular risk factors report exercising a mean of 83 minutes per day with a standard deviation of 6 minutes.  Based on the sample data, is the physical activity significantly less than recommended?  Run the appropriate test at a 5% level of significance.
2. 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 9 participants.  The objective of the study is to assess how systolic blood pressure changes over time untreated.  Systolic blood pressures are measured at baseline and again 6 weeks later.  Is there a statistically significant difference in blood pressures over time?  Run the test at a 5% level of significance.
Baseline 121 146 131 161 153 144 127
4 Weeks 123 144 136 159 155 141 131
3. The mean lifetime for cardiac stents is 9.9 years.  A medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer.  A study of 44 new devices reveals a mean lifetime of 7.7 years with a standard deviation of 4.4 years.  Is there statistical evidence of a prolonged lifetime of the stents?  Run the test at a 5% level of significance.  
4. An investigator hypothesizes that cholesterol levels in children might be affected by educating their parents on proper nutrition and exercise.  A sample of 50 families with a child between the ages of 10-15 who has been diagnosed with high cholesterol agree 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 157 with a standard deviation of 5.5.  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 185.
Module 6 Quiz
1. Some scientists believe that alcoholism is linked to social isolation.  One measure of social isolation is marital status.  A study of 280 adults is conducted and each participant is classified as not alcoholic, diagnosed alcoholic or undiagnosed alcoholic, and categorized by marital status.  Is there significant evidence of an association?  Run the appropriate test at a 5% level of significance. 
Diagnosed
Alcoholic Undiagnosed
Alcoholic Not Alcoholic
Married 21 37 58
Not Married 59 63 42
                            
2. 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 as follows.  
Standard Treatment Placebo New Treatment
124 134 114
111 143 117
133 148 121
125 142 124
128 150 122
115 160 128
Is there a difference in mean SBP among treatments?  Run the appropriate test at =0.05.   
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 reduction of symptoms.  The data are recorded as follows.
Change in Symptoms
Treatment Much Worse Worse No change Better Much Better
Experimental 10 17 35 28 10
Placebo 12 25 42 12 9
Is there a difference in change in symptoms by treatment group?  Run the appropriate test at a 5% level of significance.
4. The following data was collected in a clinical trial evaluating a new medication designed to improve wound healing in trauma patients.  The new compound is compared against a placebo.  After treatment for 10 days with the new compound or placebo the extent of wound healing is measured and the data are shown below.
Percent Wound Healing
Treatment 0-25% 26-50% 51-75% 76-100%
New psoriasis medication (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.  
module 6
1. The following data was collected in a clinical trial evaluating 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.
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.  
5. 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.  
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
Is there a significant difference in mean fetal heart rates by position?  Run the test 
at a 5% level of significance. 
 
9. In this study patients were recruited from 3 different clinical sites.  Use the following data to test if there is a difference in the proportions of hypertensive patients across clinical sites.
Site 1 Site 2 Site 3
Hypertensive 10 14 12
Not Hypertensive 68 56 40
11. Suppose more detail is actually recorded in the primary outcome in the clinical trial described in Problem 10.  The data are recorded as follows.
Change in Symptoms
Treatment Much Worse Worse No change Better Much Better
Experimental 10 17 35 28 10
Placebo 12 25 42 12 9
Is there a difference in change in symptoms by treatment group?  Run the appropriate test at a 5% level of significance.
 
2. 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.
5.    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 plan is to measure alcohol consumption (the number of drinks on a typical drinking day) before the intervention and then again after participants complete the educational intervention program.  How many participants would be required to ensure that a 95% confidence interval for the mean difference in the number of drinks is within 2 drinks of the true mean difference?  Assume that the standard deviation of the difference in the mean number of drinks is 6.7 drinks and that 20% of the participants will drop out over the course of follow up.