HW3 Solutions

45 points total

1. (10 points) We've used the word "random" in two different contexts in class: "random samples" and "randomized designed experiments". Describe what each of these terms means. Why do we collect random samples? Why do we randomize in good designed experiments?
    
   Answer: A random sample is a sample collected in such a way that every member of the population has the same probability of being included in the sample. A randomized designed experiment is an experiment where each subject is randomly assigned to a treatment, which is to say the probability of being in any treatment group is the same for each subject.
    
   We collect random samples to insure that the sample is representative.
    
   We randomize in a designed experiment to insure that there will be no confounding factors in the experiment.
    
   Randomized designed experiments can be, and usually are, conducted on non-random samples.
    
2. (5 points each) A drug company is testing a new drug that is supposed to increase the speed at which broken bones heal. During a one year period the company picked at random 25 females and 25 males that went to a local emergency room with broken femurs (a leg bone). The males got the new drug and the females received a placebo. Subjects who took the test drug healed much faster than those who didn't.
    
   1. What do you think the target population was?
       
      Answer: All people
       
   2. What was the sampled population?
       
      Answer: All people who broke their legs during a certain time frame and went to the local emergency room.
       
   3. Was the sample a random sample of the target population?
       
      Answer: No. Only people who used the local emergency room had any chance to be in the sample.
       
   4. What was the treatment and response variables?
       
      Answer: The treatment was the drug: test drug or placebo. The response was time it took for the bones to heal.
       
   5. Was this a designed or observational study? Why?
       
      Answer: Designed. The treatment was assigned to subjects.
       
   6. Are confounding factors a problem in this study? If not, why not? If yes, name a potential confounding factor and justify why it might be a confounding factor.
       
      Answer: Gender is an obvious confounding factor. It differs between treatment groups and might influence how fast bones heal.
       
   7. Other than increasing the number of subjects in the study, how could this study be improved?
       
      Answer: The study should have been randomized.
       

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