Investigation 9: Heart Transplant Mortality (due Thursday, October 14)

You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are preferred to hand-written ones.

In September of 2000, heart transplantation at St. George’s Hospital in London was suspended because of concern that more patients were dying than previously. Newspapers reported that the 80% mortality rate in the last 10 cases at the hospital was of particular concern because it was over five times the national average.

Let the random variable X represent the number of deaths in a random sample of 10 cases. Suppose that the probability of death at this hospital is equal to the national rate of 15%.

(a) Identify the probability distribution of X (both its name and its parameter values).

(b) Report the probabilities for the possible values of X, and provide a line graph of this probability distribution. [Feel free to use Minitab.]

(c) Identify the most likely value of X and its probability.

(d) St. George’s Hospital had seen 8 deaths in the previous 10 heart transplant cases. Determine the p-value for assessing whether a result this extreme is unlikely to have occurred by chance if in fact p=.15.

(e) Determine the smallest number of deaths in these 10 cases that would have resulted in a p-value of less than .05.

(f) When analyzing data on all 371 patients who received a heart transplant at this hospital between 1986 and 2000, researchers found that 79 had died. Determine the p-value based on these data.

(g) Summarize your conclusions from this five-year data, and explain how they follow from your probability analysis.