c h a p t e r 8 Confidence Intervals Introduction Air pollution is a serious problem in many places. Particulate matter (PM), which consists of tiny particles in the air, is a form of air pollution that is suspected of causing respiratory illness. PM can come from many sources, such as ash from burning, and tiny particles of rubber from automobile and truck tires. The town of Libby, Montana, has experienced high levels of PM, especially in the winter. Many houses in Libby are heated by wood stoves, which produce a lot of particulate pollution. In an attempt to reduce the winter levels of air pollution in Libby, a program was undertaken in which almost every wood stove in the town was replaced with a newer, cleaner-burning model. Most stoves were replaced in 2006 or early 2007. Measurements of several air pollutants, including PM, were taken both before and after the stove replacement. To determine PM levels after stoves were replaced, the level was measured on a sample of 20 days in the winter of 2007–2008. The units are micrograms per cubic meter. Following are the results: 21.7 27.8 24.7 15.3 18.4 14.4 19.0 23.7 22.4 25.6 15.0 17.0 23.2 17.7 11.1 29.8 20.0 21.6 14.8 21.0 Clearly, the amount varies from day to day. The sample mean is 20.21 and the sample standard deviation is 4.86. We would like to use this information to estimate the population mean, which is the mean over all days of the winter of 2007–2008. What is the best way to do this? If we had to pick a single number to estimate the population mean, the best choice would be the sample mean, which is 20.21. The estimate 20.21 is called a point estimate, because it is a single number. The problem with point estimates is that they are almost 347
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