Exam 11: Asking and Answering Questions About the Difference Between Two Proportions

Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample.

An article describes the results of an experiment. Patients suffering from chronic somatic diseases were randomly assigned to the two groups. One group was a control group of patients who received treatment A. Of the 58 patients in this group, 9 reported improvements at the end of the study period. Patients in the second group received treatment B. Of the 33 patients in this group, 4 reported improvements at the end of the study period. ​ Do these data provide evidence that the proportion of success for patients who received treatment A differs from the proportion of success for patients who received treatment B? Use a randomization test to select the appropriate output for one set of 1000 simulated proportions and carry out a hypothesis test for a difference in proportions. Use a significance level of 0.05. ​