Learn how confidence intervals appear in many typical instances: reference ranges for results of blood tests, reported margins of error in political polling, MPG comparisons among makes of cars.
- [Instructor] At your last doctor's appointment, your doctor might have ordered some medical tests, such as a complete blood panel. If you took a look at the results of those tests, you probably saw that most of them included something called a confidence interval. On medical lab printouts, they typically user terms such as reference range or standard range instead of confidence interval. You usually see at least two values: a lower limit and an upper limit. Here for example, the lower limit is 3.8, and the upper limit is 11.0. Ninety-five percent of the people, who are given that particular test, get a result between the lower and the upper limits. With that information, you can compare your result to those two limits to see whether your score is particularly low, particularly high, or comfortably in between the two limits. The laboratory that prepared this reports is usually free to choose how wide the range should be. For example, the lab can choose a lower and upper limit that together would capture 99% of the population, 95%, 90%, or even less. As you'll see in this course, the wider that range, or confidence interval, the more confidence you can have that the range spans a given unknown value. Of course, confidence intervals are used in areas well beyond that of lab reports. When you hear the results of a political poll on the nightly news, you also often hear that the margin of error is plus or minus three points, or plus or minus five points, or some other figure. That margin of error is half the width of the confidence interval. So the confidence interval might be from 47 to 53% or 45 to 55%. When a medical researcher reports that the mean high density lipoprotein, or HDL, cholesterol of a treatment group is consistent with that of the general population, that researcher is saying that the treatment group's mean value is between the confidence interval's lower limit and it's upper limit. When an auto manufacturer reports that one of its models gets significantly better gas mileage than it's competition, it usually means that its average miles per gallon is higher than the upper bound of a confidence interval built on the miles per gallon achieved by the competition. The logic of using confidence intervals is often a little different from the logic of a lab report. When you assess your cholesterol level, in light of its relevant range, you evaluate a known quantity, your cholesterol level, in terms of the population distribution. But in, say, political polls, you assess an observed quantity, such as the percent of sampled females in favor, in light of a hypothetical quantity, the percent of females in favor in the population. Next, let's look at the two basic components of a confidence interval: a point estimate and an interval estimate.