Chapter 11
Confidence Intervals and the Student’s t-Distribution
IN THIS CHAPTER
Getting familiar with the t-distribution
Developing techniques for constructing confidence intervals
A confidence interval is a range of numbers that’s likely to contain the true value of an unknown population parameter, such as the population mean. (Parameters are numerical values that describe the properties of a population; they are discussed in Chapter 10.)
Here’s an example. Suppose that you are asked to estimate how long it takes to commute to work each day. You respond by saying, “On average, it takes about 20 minutes to get to work.” This estimate may be useful, but it doesn’t give any indication how much your commuting time may vary from one day to the next.
Suppose that instead you respond by saying “Most days, it takes between 15 and 25 minutes to get to work.” This range of values is more meaningful than the estimated average time of 20 minutes. With this interval, it’s clear that the average commute time is 20 minutes (because this is halfway between 15 and 25 minutes). In addition, the numbers tell you that it’ll be an unusual day if your commuting time is more than 25 minutes or fewer than 15 minutes.
This range of estimated values is known as a confidence interval. The starting point ...