Question 4: (20 marks) A medical researcher in Melbourne is interested to know if there is any association between the age of COVID-19 patients in Melbourne and their survival status. The researcher observed a random selection of 385 COVID-19 patients' information and their data are summarised in the following table. Age of COVID-19 patient Survival status 55 years Total Yes 83 137 140 360 No 5 7 13 25 Total 88 144 153 385 (a) Suppose you randomly select a patient from these 385 COVID-19 patients. i. What is the probability that the selected patient has survived? [1 mark] ii. What is the probability that the selected patient has survived or is in age less than 30 years? [2 marks] iii. Given that the selected patient is older than 55 years, what is the probability that the patient has survived. [3 marks] (b) Under the assumption of no association between the age of COVID-19 patients in Melbourne and their survival status, some of the expected numbers have been calculated and are provided in the following table. Age of COVID-19 patient Survival status 55 years Yes 134.65 No 5.71 ifi. 9.94 Calculate the three missing expected numbers [ to M.] in the table above. Compare your findings with the actual counts. [3 marks] (c) Perform a hypothesis test at the 5% level to determine whether the age of COVID-19 patients in Melbourne and their survival status are independent. You may use the output below. Clearly identify the test you use (e.g. test statistic and distribution); state clearly the null and alternative hypotheses, decision rule, test result and conclusion in terms of the original problem. [6 marks] Pearson's Chi-squared test data: .Table X-squared = 1.7386, df = 2, p-value = 0. 4192 (d) State the assumptions required for the hypothesis test in part (c) to be valid and demonstrate that they are satisfied. [5 marks]