Preliminary results of a study (The journal Environmental News reported in April 1975 that “The continuing analysis of lead levels in the drinking water of several Boston communities has verified elevated lead concentrations in the water supplies of Somerville, Brighton and Beacon Hill.”) found that “20% of the 248 randomly chosen households tested in these communities showed lead levels exceeding the U.S. Public Health Service standard of 50 parts per million.” In contrast, in Cambridge, which adds anticorrosive to its water in an attempt to keep the lead from leaching out of the pipes, “only 5% of the 100 randomly sampled households showed lead levels exceeding the standard.” Find a 95% confidence interval for the difference in the proportions of households in Somerville, Brighton and Beacon Hill on the one hand and Cambridge on the other that had lead levels exceeding the government standard, and carry out a test of the hypothesis of no difference at α = 0.05.