This report describes a study to assess the feasibility of an epidemiologic investigation of the relationship between residential radon exposure and lung cancer. Field measurements of residential radon levels in the State of Maine are described. Using these radon measurements and BEIR, 1980 risk assessments, it is estimated that at most 10% of lung cancers in Maine can be considered attributable to residential radon exposure. Calculations are made of sample sizes necessary for a case-control study of radon and lung cancer, for several levels of radon and smoking health effects. The effects of misclassification of exposure variables on the probability of detecting a radon health effect are discussed. A comparison is made of three different mathematical models which could be used for sample size estimation. Dollar cost estimates are given for conducting an epidemiologic case-control study of the relationship between residential radon exposure and lung cancer.