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:

Readmissions 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.