Statistics and probability

Question 2: Three surgical procedures currently are used to install pacemakers (a medical device to regulate the beating of the heart). If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center has collected the following numbers of patients from their own records: Procedures A B C Total Clear 27 41 21 89 Return 11 15 9 35 Total 38 56 30 124 A patient is randomly selected from the sample. Find the probabilities of a randomly selected patient: a) Underwent procedure B and is "Clear". b) Is a "Return" patient given we know that the patient underwent either procedure A or B. c) Underwent Procedure A or C given we know that it is a "Return" patient. d) Determine if the type of procedures and the results of operation are independent using a significance level of 0.05. Show your working and steps clearly. e) Find the 95% confidence interval estimate of the proportion of procedures that gives a "Clear". f) A z- statistic can be used to find a confidence interval for the difference in proportion of patients who underwent Procedures B among Clear and Return. State and check the assumptions needed to make this procedure reasonable. g) Calculate a 95% confidence interval for the difference in proportion of patients who underwent Procedures B among Clear and Return Focus 100%