Consider the cancer count data for the Bartlett– Green Acres neighborhood. Between 1964 and 1984, the number of persons at risk was 2314 and the mean duration of residence was 11.5 years, yielding 26,611 for the number of person- years of exposure. Assuming that the national cancer incidence rate is 326 cases per 100,000 people in a year, answer the following:
a. Using the binomial model, find the exact probability that at least 67 cancer cases are observed.
b. Since p = 0.00326 < 6 0.02 and np > 5, the Poisson model will provide a good approximation to the binomial model. Using the Poisson model, compute the approximate probability that at least 67 cancer cases are observed. Compare your answer to that from Part A.
c. Do your answers appear consistent with the information provided in Figures 8.1 and 8.4?