Patients were diagnosed as being either condition A or condition B before undergoing a treatment. The treatment was successful for 56 out of 94 patients classified as condition A, and the treatment was successful for 64 out of 153 patients classified as condition B.
(a) Perform a hypothesis test to assess whether there is sufficient evidence to conclude that the chance of success for patients with condition A is better than 50%.
(b) Construct a two-sided 99'v confidence interval for the difference between the success probabilities for patients with condition A and with condition B.
(c) Perform a chi-square goodness of fit test to investigate whether there is sufficient evidence to conclude that the success probabilities are different for patients with condition A and with condition B. What is your conclusion?