In a certain hospital, knee surgeries are performed by either Dr. Almasri or Dr. Casio. Last year’s number of surgeries performed and number that were successful are given in the following tables for three patient age groups.

a) Draw a chart showing the number of successful and unsuccessful knee surgeries performed by Dr. Casio, split among the three age groups given. Give your reason for choice of chart.

b) Use a different type of chart to show the number of successful knee surgeries performed by Dr. Almasri, split among the three age groups given.

c) Construct a table showing, for each age group, the proportions of successful knee surgeries performed by the two doctors so that each column adds to 1. What does this table tell us about elderly patients treated by Dr. Almasri?

d) Construct a table showing, for each doctor, the proportions of knee surgeries performed in each age group so that each row adds to 1. What does this table tell us about elderly patients treated by Dr. Almasri?

e) Construct a table with 12 percentages (corresponding to the 12 numbers in the tables at the start of this exercise) showing the success rates in each of the categories given above. Is this a contingency table in the sense that the rows or columns add to the totals? Are the two tables given at the start of this exercise contingency tables? Are the tables in (c) and (d) contingency tables?

f) Dr. Casio claims that she is the more successful doctor since her success rate is 77/108 = 71%, whereas Dr. Almasri’s success rate is only 101/148 = 68%. If you were Dr. Almasri, what response would you give? How do you reconcile Dr. Casio’s claim with Dr. Almasri’s response?

g) Suppose you are a hospital administrator allocating patients to doctors based on their success rate last year in performing knee surgery. To which doctor would you allocate (i) a young patient, (ii) a middle aged patient, or (iii) an elderly patient? State the reason(s) for your answer.

Transcribed Image Text:

Number of Knee Surgeries Performed Young Middle Aged Elderly 89 21 110 Total Dr. Almasri Dr. Casio Total 35 42 24 148 108 45 69 77 256 Number of Successful Knee Surgeries Young Middle Aged 52 Elderly Dr. Almasri Dr. Casio Total Total 101 77 178 20 35 29 33 55 62 61