Confidence Intervals

In this first example, let's estimate the proportion of major pipeline disturbances in the United States in which natural gas actually ignites. We already know how to calculate the proportion of ignition incidents within our sample (about 0.81 or 81%), but that only describes the sample rather than the entire population. We shouldn't say that 81% of all disruptions involve fires, because that is overstating what we know. What we want to say is something like this: "Because our sample proportion was 0.81 and because we know a bit about sampling variability, we can comfortably conclude that the population proportion is ...."

We will use a confidence interval to express an inferential estimate. A confidence interval estimates the parameter, while acknowledging the uncertainty that unavoidably comes with sampling. The technique is rooted in the sampling distributions that we studied in the prior chapter. Simply put, rather than estimating the parameter as a single value between 0 and 1, we estimate lower and upper bounds for the parameter, and tag the bounded region with a specific degree of confidence. In most fields of endeavor, we customarily use confidence levels of 90%, 95%, or 99%. There is nothing sacred about these values (although you might think so after reading statistics texts); they are conventional for sensible reasons. Like most statistical software, JMP assumes we'll want to use one of these confidence levels, but it also offers the ability to choose any level.