Question: A regional cancer treatment center has had success treating localized cancers with a linear accelerator. Whereas admissions for further treatment nationally average 2.1 per patient per year, the center's director thinks that readmissions with the new treatment are Poisson distributed, with a mean of 1.2 patients per year. He has collected the following data on a random sample of 300 patients:

Re-admission Last Year         Patients
          0                             139

          1                              87

          2                              48

          3                              14

          4                                8

          5                                1

          6                                1

          7                                0

          8                                2

                                        300

a. Adjust the data so that you can test the director's claim using a test statistic whose sampling distribution can be approximated by a chi-square distribution.

b. Assume the Type I error rate is to be controlled at 0.05. Do you agree with the director's claim? Why? Conduct a statistical procedure to support your opinion.