In: Statistics and Probability
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 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.
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 wound healing is approximately normal. Specifically, use the following distribution: 30%, 40%, 20% and 10% and a=0.05 to run the appropriate test.
| 
 Percent Wound Healing  | 
|||||
| 
 Treatment  | 
 0-25%  | 
 26-50%  | 
 51-75%  | 
 76-100%  | 
 Total  | 
| 
 Number of Patients  | 
 51  | 
 82  | 
 66  | 
 51  | 
 250  |