Carbon monoxide concentrations (in µg/m3 ) are measured on 6different days in city A and on 4 different days in city B. Thefollowing measurements have been obtained in cities A and B,respectively: 3.9, 4.7, 7.1, 6.9, 4.3, 6.3 and 7.3, 6.9, 7.6, 9.1.We assume that these two samples are independent.
(a) Assume that both samples are from normally distributedpopulations. We also assume that the same type of measurementdevice was used in both cities so that the measurement error(variance) is the same for both samples. Construct the 95%confidence interval for ? = µA?µB where µA and µB are meanconcentrations of carbon monoxide in cities A and B, respectively.(b) Do we reject H0 : ? = 0 in favor of H1 : ? 6= 0 at the 5%significance level? Why or why not? Find the p-value of thistest.
(c) Now assume that both samples are from normally distributedpopulations, as before, but two different measurement devices wereused and their measurements errors are known. We assume that thevariances are 2 and 1, respectively, for the two samples. Constructthe 95% confidence interval for ?.
(d) Compare confidence intervals you obtained in (a) and (c).Which one is narrower? Briefly explain why.
(e) Show that (3.9, 7.1) is an approximate 97% confidenceinterval for the median concentration of carbon monoxide in cityA.
