A researcher is investigating the relationship between living near powerlines and prevalence of cancer in a certain city. She takes a random sample of 1000 residents that have lived within 500 feet of a power line for at least 10 years, a random sample of 1000 residents that have lived within 500 feet of a power line for less than 10 years, and a random sample of 5000 residents that have never lived within 500 feet of a power line and assesses the prevalence of caner cases among them. She finds 41 cases in the sample with 10 or more years of power line exposure, 38 in the sample with less than 10 years of power line exposure, and 160 in the unexposed sample.
a) What kind fo test should we use to evaluate whether there are differences in the proportion of people with cancer in the different power line exposure groups? State any assumptions that are required to perform the test and evaluate whether they are met in this sample.
b) Perform the hypothesis test chosen in part a) and present your finding.