A carpal tunnel syndrome is a common wrist complaint resulting from a compressed nerve. Among various treatments, two are common: apply a splint or perform a surgery. In one randomized trial, 156 patients were identified as having the syndrome and were treated with one of either the splint or surgery. Among 73 patients treated surgically and evaluated one year later, 67 were healed. Among 83 patients treated with splints, after a year 60 claimed to be healed.
a. Perform a two-tailed test comparing the response rates (proportions) at α=0.05.
b. Form a confidence interval for the difference of proportions, without pooling the samples. Does it include zero?