Anna Audler Stats 10: Section 3A UID: 304295761 TA: Luis Sosa Lab #4 TB or Not TB? Question 1: Based on the column proportions in the table below, it is shown that Streptomycin is more effective as a treatment for TB than bed rest. According to the data, 93% of people given medicine recovered, while only 73% of the control group recovered. Also, the control and treatment groups were about the same size. Of the 18 people that died in the study, 14 of them were NOT given any medicine. Question 2: If treatment and outcome were independent, then the results for the treatment group would look the same as the control. Based on the table in the previous question, 27% of patients would be expected to die. Quantitatively, about 15 people from the Streptomycin group would be expected to die. (0.27 x 55 = 14.85 = 15 people) Question 3: The summary table below shows the data after being scrambled 100 times. Based on chance, about 18% of the Streptomycin receivers should have died in this experiment. The fact that only 7% died in the actual experiment shows that Streptomycin is more effective treatment for tuberculosis than bed rest. Thus, we can conclude that treatment and outcome are dependent.Question 4: Hill's study is an example of an experiment. He had both a group which he applied a treatment to, and a control group. This differs from an observational study, where investigators observe subjects without the assignment of a treatment. We can conclude that the antibiotic was the cause for the difference in data between the two groups because that data resulting from the experiment cannot be replicated by chance. This is shown by comparing the tables in questions 1 and 3. After 100 random samples, the two summaries should look similar if Streptomycin and bed rest were independent. Because the experimental data shoes that Streptomycin always has a lower proportion of deaths than the chance models, it can be concluded that it is a valid cure for tuberculosis. Summary Question: Topics covered in this lab include: visualizing variation in numerical data, causality, probability, random experiments, and observational study vs experimental study. Each of these topics was covered in the Chapter 2 and 6 lectures and on Homework 1 and 5. Topics from chapter 6 that weren’t covered include: central limit theorem, factorials, binomial probabilities, and discrete vs continuous
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