8. John Lister (for whom Listerine is named) was a British physician who was pioneer in reducing deaths of surgical patients from infections. He suspected that bacteria were involved in transmitting infection, so he tried using carbolic acid as an operating room disinfectant. In 75 amputations, he used carbolic acid 40 times. He did not use carbolic acid during the other 35 amputations. With the exception of the use of carbolic acid for 40 amputations, all other conditions in the operating room were the same for all 75 amputations.
a. Explain why this study is an experiment.
b. What else would need to be done to make this a randomized experiment? Explain how randomization could be accomplished.
c. What is the null hypothesis that Dr. Lister should have tested? What alternative hypothesis should he have considered?
d. Assume that randomization was carried out as you described in part (b) and 40 patients were randomly assigned to have their amputation done using carbolic acid as a disinfectant and the other 35 had their amputation done with no disinfectant. Dr. Lister recorded that of the 40 amputations performed using carbolic acid, 34 patients lived. Of the 35 amputations done without using carbolic acid, 19 patients lived. What conclusion could Dr. Lister make from these results? Perform the appropriate hypothesis test, check if appropriate conditions are met, report a value of the test statistic, report a p-value, and state your conclusion. Use a .05 level of significance. Is a cause and effect conclusion justified?