In this chapter, you will learn to construct and interpret confidence intervals. You will also learn a new distribution, the Student's-t, and how it is used with these intervals. Throughout the chapter, it is important to keep in mind that the confidence interval is a random variable. It is the population parameter that is fixed.
- 8.1: Estimating Population Means
- A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution.
- 8.2: The t-distribution
- We rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation ss as an estimate for σσ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
- 8.3: Estimating Proportions
- The procedure to find the confidence interval, the sample size, the error bound, and the confidence level for a proportion is similar to that for the population mean, but the formulas are different.
- 8.4: Confidence Intervals
- A plausible range of values for the population parameter is called a confidence interval. In this section, we will emphasize the special case where the point estimate is a sample mean and the parameter is the population mean.
Contributors and Attributions
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