4. (4 marks) Consider the diagnostic test from Assignment 2, with the following results on a sample of 1, 000 individuals: Test Result Positive Negative Truth Present 91 Absent 46 856 (a) (Not marked.) Recall the value of the sensitivity you obtained in Question 4 of Assignment 2. Write it down here. (b) If an individual tests positive, what is the probability that they actually have this disease? Calculate this value using a function in R. Then, verify it by calculating by hand. (c) What is the estimated prevalence of this disease? You can calculate this either by hand or in R, whichever you prefer. (d) Now, suppose that the prevalence was much smaller than what it currently is. As an example, divide each count in the first row of the table by 5. (Note: Normally, these would have to be whole numbers. However, for the purpose of this exercise, DON'T round your results.) Display the resulting contingency table, You can do this either by hand or in R, whichever you prefer. (e) For your table in part (d), re-calculate both the sensitivity and the value you obtained in part (b). Which value has changed? Which has not changed? Has it increased or decreased