This problem set is a series of questions related to the radon example we used in class. For the house in New Brunswick, n = 51 hourly radon measurements were taken in the winter of 2006. The sample average of those measurements is y = 1.68 and the sample variance is s2 = 0.851. For the house in Ithaca, NY, n = 44 hourly radon measurements were taken in the winter of 1999. The sample average of those measurements is y = 4.19 and the sample variance is s2 = 0.3098. 1. Test the null hypothesis that the population mean, 0, of the radon in the New Brunswick house is equal to the EPA cutoff of 4, i.e., H0 : 0 = 4 v.s. H1 : 0 6 = 4. Assume you do not know the population distribution of radon. You will have to rely on the central limit theorem and approximate the null distribution of your t- statistic using the N (0, 1) distribution. Carry out your test at the 5% significance level ( = 0.05). (a) Clearly explain how you compute the t-statistic. (b) Clearly state the rejection rule you are using. (c) How do you obtain your