\f2. Not all the dust particles in the air around us cause problems with our lungs. Some particles are too big and stick to other places of our body before it can reach our lungs. Others are so small that they can enter and exit our lungs without settling there. Researchers measured exposure at work to dust particles in tunnel construction workers. A part of the study compared 115 workers who drilled holes (tunnels) to 220 concrete workers outside (tunnels). Total dust exposure is measured in milligram years per cubic meter (W/ m3). The researchers measured the respirable dust, Lg dust which is deposited in the lungs when it is breathed in. For piercers, the average exposure respirable dust is 6.3 mgham/ m3 with a standard deviation of 2.8 m/ m3. The corresponding values for concrete workers are 1.4 vagNa/ m3 and 0.7 ragga\" m3. a) The sample consisted of all workers of a certain construction company of tunnels that have passed routine medical examinations. Discuss how far you believe that these results apply to other workers doing similar work (piercers and concrete workers). b) Calculate a 95% confidence interval to describe the difference in exposure. Write a sentence that gives the interval and meaning of the 95% level. c) Test the null hypothesis that the average exposure of these two types of workers is the same. Justify your choice of a onesided or twosided test. Find the test statistic, degrees of freedom and the pvalue. Give a short summary of your conclusion. d) The authors of the article describing these results noted that the distributions were rather asymmetric. Do you believe that this fact renders the analysis invalid? Justify your